id sid tid token lemma pos en-wikipedia-org-2350 1 1 Coulomb Coulomb NNP en-wikipedia-org-2350 1 2 's 's POS en-wikipedia-org-2350 1 3 law law NN en-wikipedia-org-2350 1 4 - - HYPH en-wikipedia-org-2350 1 5 Wikipedia Wikipedia NNP en-wikipedia-org-2350 1 6 Coulomb Coulomb NNP en-wikipedia-org-2350 1 7 's 's POS en-wikipedia-org-2350 1 8 law law NN en-wikipedia-org-2350 1 9 From from IN en-wikipedia-org-2350 1 10 Wikipedia Wikipedia NNP en-wikipedia-org-2350 1 11 , , , en-wikipedia-org-2350 1 12 the the DT en-wikipedia-org-2350 1 13 free free JJ en-wikipedia-org-2350 1 14 encyclopedia encyclopedia NN en-wikipedia-org-2350 1 15 Jump Jump NNP en-wikipedia-org-2350 1 16 to to IN en-wikipedia-org-2350 1 17 navigation navigation NN en-wikipedia-org-2350 1 18 Jump Jump NNP en-wikipedia-org-2350 1 19 to to TO en-wikipedia-org-2350 1 20 search search VB en-wikipedia-org-2350 1 21 This this DT en-wikipedia-org-2350 1 22 article article NN en-wikipedia-org-2350 1 23 may may MD en-wikipedia-org-2350 1 24 require require VB en-wikipedia-org-2350 1 25 cleanup cleanup NN en-wikipedia-org-2350 1 26 to to TO en-wikipedia-org-2350 1 27 meet meet VB en-wikipedia-org-2350 1 28 Wikipedia Wikipedia NNP en-wikipedia-org-2350 1 29 's 's POS en-wikipedia-org-2350 1 30 quality quality NN en-wikipedia-org-2350 1 31 standards standard NNS en-wikipedia-org-2350 1 32 . . . en-wikipedia-org-2350 2 1 The the DT en-wikipedia-org-2350 2 2 specific specific JJ en-wikipedia-org-2350 2 3 problem problem NN en-wikipedia-org-2350 2 4 is be VBZ en-wikipedia-org-2350 2 5 : : : en-wikipedia-org-2350 2 6 this this DT en-wikipedia-org-2350 2 7 article article NN en-wikipedia-org-2350 2 8 's 's POS en-wikipedia-org-2350 2 9 source source NN en-wikipedia-org-2350 2 10 code code NN en-wikipedia-org-2350 2 11 may may MD en-wikipedia-org-2350 2 12 still still RB en-wikipedia-org-2350 2 13 contain contain VB en-wikipedia-org-2350 2 14 inconsistent inconsistent JJ en-wikipedia-org-2350 2 15 formatting formatting NN en-wikipedia-org-2350 2 16 , , , en-wikipedia-org-2350 2 17 necessitating necessitate VBG en-wikipedia-org-2350 2 18 further further JJ en-wikipedia-org-2350 2 19 inspection inspection NN en-wikipedia-org-2350 2 20 . . . en-wikipedia-org-2350 3 1 Please please UH en-wikipedia-org-2350 3 2 help help VB en-wikipedia-org-2350 3 3 improve improve VB en-wikipedia-org-2350 3 4 this this DT en-wikipedia-org-2350 3 5 article article NN en-wikipedia-org-2350 3 6 if if IN en-wikipedia-org-2350 3 7 you -PRON- PRP en-wikipedia-org-2350 3 8 can can MD en-wikipedia-org-2350 3 9 . . . en-wikipedia-org-2350 4 1 ( ( -LRB- en-wikipedia-org-2350 4 2 March March NNP en-wikipedia-org-2350 4 3 2020 2020 CD en-wikipedia-org-2350 4 4 ) ) -RRB- en-wikipedia-org-2350 4 5 ( ( -LRB- en-wikipedia-org-2350 4 6 Learn learn VB en-wikipedia-org-2350 4 7 how how WRB en-wikipedia-org-2350 4 8 and and CC en-wikipedia-org-2350 4 9 when when WRB en-wikipedia-org-2350 4 10 to to TO en-wikipedia-org-2350 4 11 remove remove VB en-wikipedia-org-2350 4 12 this this DT en-wikipedia-org-2350 4 13 template template NN en-wikipedia-org-2350 4 14 message message NN en-wikipedia-org-2350 4 15 ) ) -RRB- en-wikipedia-org-2350 4 16 Fundamental fundamental JJ en-wikipedia-org-2350 4 17 physical physical JJ en-wikipedia-org-2350 4 18 law law NN en-wikipedia-org-2350 4 19 of of IN en-wikipedia-org-2350 4 20 electromagnetism electromagnetism NN en-wikipedia-org-2350 4 21 The the DT en-wikipedia-org-2350 4 22 magnitude magnitude NN en-wikipedia-org-2350 4 23 of of IN en-wikipedia-org-2350 4 24 the the DT en-wikipedia-org-2350 4 25 electrostatic electrostatic JJ en-wikipedia-org-2350 4 26 force force NN en-wikipedia-org-2350 4 27 F F NNP en-wikipedia-org-2350 4 28 between between IN en-wikipedia-org-2350 4 29 two two CD en-wikipedia-org-2350 4 30 point point NN en-wikipedia-org-2350 4 31 charges charge NNS en-wikipedia-org-2350 4 32 q1 q1 NNP en-wikipedia-org-2350 4 33 and and CC en-wikipedia-org-2350 4 34 q2 q2 NNP en-wikipedia-org-2350 4 35 is be VBZ en-wikipedia-org-2350 4 36 directly directly RB en-wikipedia-org-2350 4 37 proportional proportional JJ en-wikipedia-org-2350 4 38 to to IN en-wikipedia-org-2350 4 39 the the DT en-wikipedia-org-2350 4 40 product product NN en-wikipedia-org-2350 4 41 of of IN en-wikipedia-org-2350 4 42 the the DT en-wikipedia-org-2350 4 43 magnitudes magnitude NNS en-wikipedia-org-2350 4 44 of of IN en-wikipedia-org-2350 4 45 charges charge NNS en-wikipedia-org-2350 4 46 and and CC en-wikipedia-org-2350 4 47 inversely inversely RB en-wikipedia-org-2350 4 48 proportional proportional JJ en-wikipedia-org-2350 4 49 to to IN en-wikipedia-org-2350 4 50 the the DT en-wikipedia-org-2350 4 51 square square NN en-wikipedia-org-2350 4 52 of of IN en-wikipedia-org-2350 4 53 the the DT en-wikipedia-org-2350 4 54 distance distance NN en-wikipedia-org-2350 4 55 between between IN en-wikipedia-org-2350 4 56 them -PRON- PRP en-wikipedia-org-2350 4 57 . . . en-wikipedia-org-2350 5 1 Like like IN en-wikipedia-org-2350 5 2 charges charge NNS en-wikipedia-org-2350 5 3 repel repel VBP en-wikipedia-org-2350 5 4 each each DT en-wikipedia-org-2350 5 5 other other JJ en-wikipedia-org-2350 5 6 , , , en-wikipedia-org-2350 5 7 and and CC en-wikipedia-org-2350 5 8 opposite opposite JJ en-wikipedia-org-2350 5 9 charges charge NNS en-wikipedia-org-2350 5 10 mutually mutually RB en-wikipedia-org-2350 5 11 attract attract VBP en-wikipedia-org-2350 5 12 . . . en-wikipedia-org-2350 6 1 Coulomb Coulomb NNP en-wikipedia-org-2350 6 2 's 's POS en-wikipedia-org-2350 6 3 law law NN en-wikipedia-org-2350 6 4 , , , en-wikipedia-org-2350 6 5 or or CC en-wikipedia-org-2350 6 6 Coulomb Coulomb NNP en-wikipedia-org-2350 6 7 's 's POS en-wikipedia-org-2350 6 8 inverse inverse NN en-wikipedia-org-2350 6 9 - - HYPH en-wikipedia-org-2350 6 10 square square JJ en-wikipedia-org-2350 6 11 law law NN en-wikipedia-org-2350 6 12 , , , en-wikipedia-org-2350 6 13 is be VBZ en-wikipedia-org-2350 6 14 an an DT en-wikipedia-org-2350 6 15 experimental experimental JJ en-wikipedia-org-2350 6 16 law[1 law[1 -LRB- en-wikipedia-org-2350 6 17 ] ] -RRB- en-wikipedia-org-2350 6 18 of of IN en-wikipedia-org-2350 6 19 physics physics NN en-wikipedia-org-2350 6 20 that that WDT en-wikipedia-org-2350 6 21 quantifies quantify VBZ en-wikipedia-org-2350 6 22 the the DT en-wikipedia-org-2350 6 23 amount amount NN en-wikipedia-org-2350 6 24 of of IN en-wikipedia-org-2350 6 25 force force NN en-wikipedia-org-2350 6 26 between between IN en-wikipedia-org-2350 6 27 two two CD en-wikipedia-org-2350 6 28 stationary stationary JJ en-wikipedia-org-2350 6 29 , , , en-wikipedia-org-2350 6 30 electrically electrically RB en-wikipedia-org-2350 6 31 charged charge VBN en-wikipedia-org-2350 6 32 particles particle NNS en-wikipedia-org-2350 6 33 . . . en-wikipedia-org-2350 7 1 The the DT en-wikipedia-org-2350 7 2 electric electric JJ en-wikipedia-org-2350 7 3 force force NN en-wikipedia-org-2350 7 4 between between IN en-wikipedia-org-2350 7 5 charged charged JJ en-wikipedia-org-2350 7 6 bodies body NNS en-wikipedia-org-2350 7 7 at at IN en-wikipedia-org-2350 7 8 rest rest NN en-wikipedia-org-2350 7 9 is be VBZ en-wikipedia-org-2350 7 10 conventionally conventionally RB en-wikipedia-org-2350 7 11 called call VBN en-wikipedia-org-2350 7 12 electrostatic electrostatic JJ en-wikipedia-org-2350 7 13 force force NN en-wikipedia-org-2350 7 14 or or CC en-wikipedia-org-2350 7 15 Coulomb Coulomb NNP en-wikipedia-org-2350 7 16 force force NN en-wikipedia-org-2350 7 17 . . . en-wikipedia-org-2350 8 1 [ [ -LRB- en-wikipedia-org-2350 8 2 2 2 LS en-wikipedia-org-2350 8 3 ] ] -RRB- en-wikipedia-org-2350 8 4 The the DT en-wikipedia-org-2350 8 5 law law NN en-wikipedia-org-2350 8 6 was be VBD en-wikipedia-org-2350 8 7 first first RB en-wikipedia-org-2350 8 8 discovered discover VBN en-wikipedia-org-2350 8 9 in in IN en-wikipedia-org-2350 8 10 1785 1785 CD en-wikipedia-org-2350 8 11 by by IN en-wikipedia-org-2350 8 12 French french JJ en-wikipedia-org-2350 8 13 physicist physicist NN en-wikipedia-org-2350 8 14 Charles Charles NNP en-wikipedia-org-2350 8 15 - - HYPH en-wikipedia-org-2350 8 16 Augustin Augustin NNP en-wikipedia-org-2350 8 17 de de NNP en-wikipedia-org-2350 8 18 Coulomb Coulomb NNP en-wikipedia-org-2350 8 19 , , , en-wikipedia-org-2350 8 20 hence hence RB en-wikipedia-org-2350 8 21 the the DT en-wikipedia-org-2350 8 22 name name NN en-wikipedia-org-2350 8 23 . . . en-wikipedia-org-2350 9 1 Coulomb Coulomb NNP en-wikipedia-org-2350 9 2 's 's POS en-wikipedia-org-2350 9 3 law law NN en-wikipedia-org-2350 9 4 was be VBD en-wikipedia-org-2350 9 5 essential essential JJ en-wikipedia-org-2350 9 6 to to IN en-wikipedia-org-2350 9 7 the the DT en-wikipedia-org-2350 9 8 development development NN en-wikipedia-org-2350 9 9 of of IN en-wikipedia-org-2350 9 10 the the DT en-wikipedia-org-2350 9 11 theory theory NN en-wikipedia-org-2350 9 12 of of IN en-wikipedia-org-2350 9 13 electromagnetism electromagnetism NN en-wikipedia-org-2350 9 14 , , , en-wikipedia-org-2350 9 15 maybe maybe RB en-wikipedia-org-2350 9 16 even even RB en-wikipedia-org-2350 9 17 its -PRON- PRP$ en-wikipedia-org-2350 9 18 starting start VBG en-wikipedia-org-2350 9 19 point,[1 point,[1 NN en-wikipedia-org-2350 9 20 ] ] -RRB- en-wikipedia-org-2350 9 21 as as IN en-wikipedia-org-2350 9 22 it -PRON- PRP en-wikipedia-org-2350 9 23 made make VBD en-wikipedia-org-2350 9 24 it -PRON- PRP en-wikipedia-org-2350 9 25 possible possible JJ en-wikipedia-org-2350 9 26 to to TO en-wikipedia-org-2350 9 27 discuss discuss VB en-wikipedia-org-2350 9 28 the the DT en-wikipedia-org-2350 9 29 quantity quantity NN en-wikipedia-org-2350 9 30 of of IN en-wikipedia-org-2350 9 31 electric electric JJ en-wikipedia-org-2350 9 32 charge charge NN en-wikipedia-org-2350 9 33 in in IN en-wikipedia-org-2350 9 34 a a DT en-wikipedia-org-2350 9 35 meaningful meaningful JJ en-wikipedia-org-2350 9 36 way way NN en-wikipedia-org-2350 9 37 . . . en-wikipedia-org-2350 10 1 [ [ -LRB- en-wikipedia-org-2350 10 2 3 3 LS en-wikipedia-org-2350 10 3 ] ] -RRB- en-wikipedia-org-2350 10 4 The the DT en-wikipedia-org-2350 10 5 law law NN en-wikipedia-org-2350 10 6 states state VBZ en-wikipedia-org-2350 10 7 that that IN en-wikipedia-org-2350 10 8 the the DT en-wikipedia-org-2350 10 9 magnitude magnitude NN en-wikipedia-org-2350 10 10 of of IN en-wikipedia-org-2350 10 11 the the DT en-wikipedia-org-2350 10 12 electrostatic electrostatic JJ en-wikipedia-org-2350 10 13 force force NN en-wikipedia-org-2350 10 14 of of IN en-wikipedia-org-2350 10 15 attraction attraction NN en-wikipedia-org-2350 10 16 or or CC en-wikipedia-org-2350 10 17 repulsion repulsion NN en-wikipedia-org-2350 10 18 between between IN en-wikipedia-org-2350 10 19 two two CD en-wikipedia-org-2350 10 20 point point NN en-wikipedia-org-2350 10 21 charges charge NNS en-wikipedia-org-2350 10 22 is be VBZ en-wikipedia-org-2350 10 23 directly directly RB en-wikipedia-org-2350 10 24 proportional proportional JJ en-wikipedia-org-2350 10 25 to to IN en-wikipedia-org-2350 10 26 the the DT en-wikipedia-org-2350 10 27 product product NN en-wikipedia-org-2350 10 28 of of IN en-wikipedia-org-2350 10 29 the the DT en-wikipedia-org-2350 10 30 magnitudes magnitude NNS en-wikipedia-org-2350 10 31 of of IN en-wikipedia-org-2350 10 32 charges charge NNS en-wikipedia-org-2350 10 33 and and CC en-wikipedia-org-2350 10 34 inversely inversely RB en-wikipedia-org-2350 10 35 proportional proportional JJ en-wikipedia-org-2350 10 36 to to IN en-wikipedia-org-2350 10 37 the the DT en-wikipedia-org-2350 10 38 square square NN en-wikipedia-org-2350 10 39 of of IN en-wikipedia-org-2350 10 40 the the DT en-wikipedia-org-2350 10 41 distance distance NN en-wikipedia-org-2350 10 42 between between IN en-wikipedia-org-2350 10 43 them,[4 them,[4 NN en-wikipedia-org-2350 10 44 ] ] -RRB- en-wikipedia-org-2350 10 45 | | NNP en-wikipedia-org-2350 10 46 F F NNP en-wikipedia-org-2350 10 47 | | NNP en-wikipedia-org-2350 10 48 = = SYM en-wikipedia-org-2350 10 49 k k NNP en-wikipedia-org-2350 10 50 e e NNP en-wikipedia-org-2350 10 51 | | NNP en-wikipedia-org-2350 10 52 q q NNP en-wikipedia-org-2350 10 53 1 1 CD en-wikipedia-org-2350 10 54 q q NNP en-wikipedia-org-2350 10 55 2 2 CD en-wikipedia-org-2350 10 56 | | CD en-wikipedia-org-2350 10 57 r r NN en-wikipedia-org-2350 10 58 2 2 CD en-wikipedia-org-2350 10 59 { { -LRB- en-wikipedia-org-2350 10 60 \displaystyle \displaystyle CD en-wikipedia-org-2350 10 61 |F|=k_{\text{e}}{\frac |f|=k_{\text{e}}{\frac CD en-wikipedia-org-2350 10 62 { { -LRB- en-wikipedia-org-2350 10 63 |q_{1}q_{2}|}{r^{2 |q_{1}q_{2}|}{r^{2 NN en-wikipedia-org-2350 10 64 } } -RRB- en-wikipedia-org-2350 10 65 } } -RRB- en-wikipedia-org-2350 10 66 } } -RRB- en-wikipedia-org-2350 10 67 } } -RRB- en-wikipedia-org-2350 10 68 Here here RB en-wikipedia-org-2350 10 69 , , , en-wikipedia-org-2350 10 70 ke ke NNP en-wikipedia-org-2350 10 71 is be VBZ en-wikipedia-org-2350 10 72 Coulomb Coulomb NNP en-wikipedia-org-2350 10 73 's 's POS en-wikipedia-org-2350 10 74 constant constant NN en-wikipedia-org-2350 10 75 ( ( -LRB- en-wikipedia-org-2350 10 76 ke ke NNP en-wikipedia-org-2350 10 77 ≈ ≈ NNP en-wikipedia-org-2350 10 78 8.988×109 8.988×109 NNP en-wikipedia-org-2350 10 79   _SP en-wikipedia-org-2350 10 80 N⋅m2⋅C−2),[1 N⋅m2⋅C−2),[1 NNP en-wikipedia-org-2350 10 81 ] ] -RRB- en-wikipedia-org-2350 10 82 q1 q1 NNP en-wikipedia-org-2350 10 83 and and CC en-wikipedia-org-2350 10 84 q2 q2 NNP en-wikipedia-org-2350 10 85 are be VBP en-wikipedia-org-2350 10 86 the the DT en-wikipedia-org-2350 10 87 signed sign VBN en-wikipedia-org-2350 10 88 magnitudes magnitude NNS en-wikipedia-org-2350 10 89 of of IN en-wikipedia-org-2350 10 90 the the DT en-wikipedia-org-2350 10 91 charges charge NNS en-wikipedia-org-2350 10 92 , , , en-wikipedia-org-2350 10 93 and and CC en-wikipedia-org-2350 10 94 the the DT en-wikipedia-org-2350 10 95 scalar scalar JJ en-wikipedia-org-2350 10 96 r r NNP en-wikipedia-org-2350 10 97 is be VBZ en-wikipedia-org-2350 10 98 the the DT en-wikipedia-org-2350 10 99 distance distance NN en-wikipedia-org-2350 10 100 between between IN en-wikipedia-org-2350 10 101 the the DT en-wikipedia-org-2350 10 102 charges charge NNS en-wikipedia-org-2350 10 103 . . . en-wikipedia-org-2350 11 1 The the DT en-wikipedia-org-2350 11 2 force force NN en-wikipedia-org-2350 11 3 is be VBZ en-wikipedia-org-2350 11 4 along along IN en-wikipedia-org-2350 11 5 the the DT en-wikipedia-org-2350 11 6 straight straight JJ en-wikipedia-org-2350 11 7 line line NN en-wikipedia-org-2350 11 8 joining join VBG en-wikipedia-org-2350 11 9 the the DT en-wikipedia-org-2350 11 10 two two CD en-wikipedia-org-2350 11 11 charges charge NNS en-wikipedia-org-2350 11 12 . . . en-wikipedia-org-2350 12 1 If if IN en-wikipedia-org-2350 12 2 the the DT en-wikipedia-org-2350 12 3 charges charge NNS en-wikipedia-org-2350 12 4 have have VBP en-wikipedia-org-2350 12 5 the the DT en-wikipedia-org-2350 12 6 same same JJ en-wikipedia-org-2350 12 7 sign sign NN en-wikipedia-org-2350 12 8 , , , en-wikipedia-org-2350 12 9 the the DT en-wikipedia-org-2350 12 10 electrostatic electrostatic JJ en-wikipedia-org-2350 12 11 force force NN en-wikipedia-org-2350 12 12 between between IN en-wikipedia-org-2350 12 13 them -PRON- PRP en-wikipedia-org-2350 12 14 is be VBZ en-wikipedia-org-2350 12 15 repulsive repulsive JJ en-wikipedia-org-2350 12 16 ; ; : en-wikipedia-org-2350 12 17 if if IN en-wikipedia-org-2350 12 18 they -PRON- PRP en-wikipedia-org-2350 12 19 have have VBP en-wikipedia-org-2350 12 20 different different JJ en-wikipedia-org-2350 12 21 signs sign NNS en-wikipedia-org-2350 12 22 , , , en-wikipedia-org-2350 12 23 the the DT en-wikipedia-org-2350 12 24 force force NN en-wikipedia-org-2350 12 25 between between IN en-wikipedia-org-2350 12 26 them -PRON- PRP en-wikipedia-org-2350 12 27 is be VBZ en-wikipedia-org-2350 12 28 attractive attractive JJ en-wikipedia-org-2350 12 29 . . . en-wikipedia-org-2350 13 1 Being be VBG en-wikipedia-org-2350 13 2 an an DT en-wikipedia-org-2350 13 3 inverse inverse NN en-wikipedia-org-2350 13 4 - - HYPH en-wikipedia-org-2350 13 5 square square JJ en-wikipedia-org-2350 13 6 law law NN en-wikipedia-org-2350 13 7 , , , en-wikipedia-org-2350 13 8 the the DT en-wikipedia-org-2350 13 9 law law NN en-wikipedia-org-2350 13 10 is be VBZ en-wikipedia-org-2350 13 11 analogous analogous JJ en-wikipedia-org-2350 13 12 to to IN en-wikipedia-org-2350 13 13 Isaac Isaac NNP en-wikipedia-org-2350 13 14 Newton Newton NNP en-wikipedia-org-2350 13 15 's 's POS en-wikipedia-org-2350 13 16 inverse inverse NN en-wikipedia-org-2350 13 17 - - HYPH en-wikipedia-org-2350 13 18 square square JJ en-wikipedia-org-2350 13 19 law law NN en-wikipedia-org-2350 13 20 of of IN en-wikipedia-org-2350 13 21 universal universal NNP en-wikipedia-org-2350 13 22 gravitation gravitation NNP en-wikipedia-org-2350 13 23 , , , en-wikipedia-org-2350 13 24 but but CC en-wikipedia-org-2350 13 25 gravitational gravitational JJ en-wikipedia-org-2350 13 26 forces force NNS en-wikipedia-org-2350 13 27 are be VBP en-wikipedia-org-2350 13 28 always always RB en-wikipedia-org-2350 13 29 attractive attractive JJ en-wikipedia-org-2350 13 30 , , , en-wikipedia-org-2350 13 31 while while IN en-wikipedia-org-2350 13 32 electrostatic electrostatic JJ en-wikipedia-org-2350 13 33 forces force NNS en-wikipedia-org-2350 13 34 can can MD en-wikipedia-org-2350 13 35 be be VB en-wikipedia-org-2350 13 36 attractive attractive JJ en-wikipedia-org-2350 13 37 or or CC en-wikipedia-org-2350 13 38 repulsive repulsive JJ en-wikipedia-org-2350 13 39 . . . en-wikipedia-org-2350 14 1 [ [ -LRB- en-wikipedia-org-2350 14 2 2 2 LS en-wikipedia-org-2350 14 3 ] ] -RRB- en-wikipedia-org-2350 14 4 Coulomb Coulomb NNP en-wikipedia-org-2350 14 5 's 's POS en-wikipedia-org-2350 14 6 law law NN en-wikipedia-org-2350 14 7 can can MD en-wikipedia-org-2350 14 8 be be VB en-wikipedia-org-2350 14 9 used use VBN en-wikipedia-org-2350 14 10 to to TO en-wikipedia-org-2350 14 11 derive derive VB en-wikipedia-org-2350 14 12 Gauss Gauss NNP en-wikipedia-org-2350 14 13 's 's POS en-wikipedia-org-2350 14 14 law law NN en-wikipedia-org-2350 14 15 , , , en-wikipedia-org-2350 14 16 and and CC en-wikipedia-org-2350 14 17 vice vice NN en-wikipedia-org-2350 14 18 versa versa RB en-wikipedia-org-2350 14 19 . . . en-wikipedia-org-2350 15 1 In in IN en-wikipedia-org-2350 15 2 the the DT en-wikipedia-org-2350 15 3 case case NN en-wikipedia-org-2350 15 4 of of IN en-wikipedia-org-2350 15 5 a a DT en-wikipedia-org-2350 15 6 single single JJ en-wikipedia-org-2350 15 7 stationary stationary JJ en-wikipedia-org-2350 15 8 point point NN en-wikipedia-org-2350 15 9 charge charge NN en-wikipedia-org-2350 15 10 , , , en-wikipedia-org-2350 15 11 the the DT en-wikipedia-org-2350 15 12 two two CD en-wikipedia-org-2350 15 13 laws law NNS en-wikipedia-org-2350 15 14 are be VBP en-wikipedia-org-2350 15 15 equivalent equivalent JJ en-wikipedia-org-2350 15 16 , , , en-wikipedia-org-2350 15 17 expressing express VBG en-wikipedia-org-2350 15 18 the the DT en-wikipedia-org-2350 15 19 same same JJ en-wikipedia-org-2350 15 20 physical physical JJ en-wikipedia-org-2350 15 21 law law NN en-wikipedia-org-2350 15 22 in in IN en-wikipedia-org-2350 15 23 different different JJ en-wikipedia-org-2350 15 24 ways way NNS en-wikipedia-org-2350 15 25 . . . en-wikipedia-org-2350 16 1 [ [ -LRB- en-wikipedia-org-2350 16 2 5 5 LS en-wikipedia-org-2350 16 3 ] ] -RRB- en-wikipedia-org-2350 16 4 The the DT en-wikipedia-org-2350 16 5 law law NN en-wikipedia-org-2350 16 6 has have VBZ en-wikipedia-org-2350 16 7 been be VBN en-wikipedia-org-2350 16 8 tested test VBN en-wikipedia-org-2350 16 9 extensively extensively RB en-wikipedia-org-2350 16 10 , , , en-wikipedia-org-2350 16 11 and and CC en-wikipedia-org-2350 16 12 observations observation NNS en-wikipedia-org-2350 16 13 have have VBP en-wikipedia-org-2350 16 14 upheld uphold VBN en-wikipedia-org-2350 16 15 the the DT en-wikipedia-org-2350 16 16 law law NN en-wikipedia-org-2350 16 17 on on IN en-wikipedia-org-2350 16 18 the the DT en-wikipedia-org-2350 16 19 scale scale NN en-wikipedia-org-2350 16 20 from from IN en-wikipedia-org-2350 16 21 10−16 10−16 CD en-wikipedia-org-2350 16 22 m m NN en-wikipedia-org-2350 16 23 to to IN en-wikipedia-org-2350 16 24 108 108 CD en-wikipedia-org-2350 16 25 m.[5 m.[5 NNP en-wikipedia-org-2350 16 26 ] ] -RRB- en-wikipedia-org-2350 16 27 Contents content NNS en-wikipedia-org-2350 16 28 1 1 CD en-wikipedia-org-2350 16 29 History history NN en-wikipedia-org-2350 16 30 2 2 CD en-wikipedia-org-2350 16 31 Scalar scalar JJ en-wikipedia-org-2350 16 32 form form NN en-wikipedia-org-2350 16 33 of of IN en-wikipedia-org-2350 16 34 the the DT en-wikipedia-org-2350 16 35 law law NN en-wikipedia-org-2350 16 36 3 3 CD en-wikipedia-org-2350 16 37 Vector vector NN en-wikipedia-org-2350 16 38 form form NN en-wikipedia-org-2350 16 39 of of IN en-wikipedia-org-2350 16 40 the the DT en-wikipedia-org-2350 16 41 law law NN en-wikipedia-org-2350 16 42 3.1 3.1 CD en-wikipedia-org-2350 16 43 System System NNP en-wikipedia-org-2350 16 44 of of IN en-wikipedia-org-2350 16 45 discrete discrete JJ en-wikipedia-org-2350 16 46 charges charge NNS en-wikipedia-org-2350 16 47 3.2 3.2 CD en-wikipedia-org-2350 16 48 Continuous continuous JJ en-wikipedia-org-2350 16 49 charge charge NN en-wikipedia-org-2350 16 50 distribution distribution NN en-wikipedia-org-2350 16 51 4 4 CD en-wikipedia-org-2350 16 52 Coulomb Coulomb NNP en-wikipedia-org-2350 16 53 's 's POS en-wikipedia-org-2350 16 54 constant constant JJ en-wikipedia-org-2350 16 55 5 5 CD en-wikipedia-org-2350 16 56 Limitations Limitations NNPS en-wikipedia-org-2350 16 57 6 6 CD en-wikipedia-org-2350 16 58 Electric electric JJ en-wikipedia-org-2350 16 59 field field NN en-wikipedia-org-2350 16 60 7 7 CD en-wikipedia-org-2350 16 61 Atomic atomic JJ en-wikipedia-org-2350 16 62 forces force NNS en-wikipedia-org-2350 16 63 8 8 CD en-wikipedia-org-2350 16 64 Relation relation NN en-wikipedia-org-2350 16 65 to to IN en-wikipedia-org-2350 16 66 Gauss Gauss NNP en-wikipedia-org-2350 16 67 's 's POS en-wikipedia-org-2350 16 68 law law NN en-wikipedia-org-2350 16 69 8.1 8.1 CD en-wikipedia-org-2350 16 70 Deriving Deriving NNP en-wikipedia-org-2350 16 71 Gauss Gauss NNP en-wikipedia-org-2350 16 72 's 's POS en-wikipedia-org-2350 16 73 law law NN en-wikipedia-org-2350 16 74 from from IN en-wikipedia-org-2350 16 75 Coulomb Coulomb NNP en-wikipedia-org-2350 16 76 's 's POS en-wikipedia-org-2350 16 77 law law NN en-wikipedia-org-2350 16 78 8.2 8.2 CD en-wikipedia-org-2350 16 79 Deriving Deriving NNP en-wikipedia-org-2350 16 80 Coulomb Coulomb NNP en-wikipedia-org-2350 16 81 's 's POS en-wikipedia-org-2350 16 82 law law NN en-wikipedia-org-2350 16 83 from from IN en-wikipedia-org-2350 16 84 Gauss Gauss NNP en-wikipedia-org-2350 16 85 's 's POS en-wikipedia-org-2350 16 86 law law NN en-wikipedia-org-2350 16 87 9 9 CD en-wikipedia-org-2350 16 88 Coulomb Coulomb NNP en-wikipedia-org-2350 16 89 potential potential JJ en-wikipedia-org-2350 16 90 9.1 9.1 CD en-wikipedia-org-2350 16 91 Quantum Quantum NNP en-wikipedia-org-2350 16 92 field field NN en-wikipedia-org-2350 16 93 theory theory NN en-wikipedia-org-2350 16 94 10 10 CD en-wikipedia-org-2350 16 95 Simple simple JJ en-wikipedia-org-2350 16 96 experiment experiment NN en-wikipedia-org-2350 16 97 to to TO en-wikipedia-org-2350 16 98 verify verify VB en-wikipedia-org-2350 16 99 Coulomb Coulomb NNP en-wikipedia-org-2350 16 100 's 's POS en-wikipedia-org-2350 16 101 law law NN en-wikipedia-org-2350 16 102 11 11 CD en-wikipedia-org-2350 16 103 See see VB en-wikipedia-org-2350 16 104 also also RB en-wikipedia-org-2350 16 105 12 12 CD en-wikipedia-org-2350 16 106 References reference NNS en-wikipedia-org-2350 16 107 13 13 CD en-wikipedia-org-2350 16 108 Related related JJ en-wikipedia-org-2350 16 109 reading read VBG en-wikipedia-org-2350 16 110 14 14 CD en-wikipedia-org-2350 16 111 External external JJ en-wikipedia-org-2350 16 112 links link NNS en-wikipedia-org-2350 16 113 History[edit history[edit NN en-wikipedia-org-2350 16 114 ] ] -RRB- en-wikipedia-org-2350 16 115 Charles Charles NNP en-wikipedia-org-2350 16 116 - - HYPH en-wikipedia-org-2350 16 117 Augustin Augustin NNP en-wikipedia-org-2350 16 118 de de IN en-wikipedia-org-2350 16 119 Coulomb Coulomb NNP en-wikipedia-org-2350 16 120 Ancient Ancient NNP en-wikipedia-org-2350 16 121 cultures culture NNS en-wikipedia-org-2350 16 122 around around IN en-wikipedia-org-2350 16 123 the the DT en-wikipedia-org-2350 16 124 Mediterranean Mediterranean NNP en-wikipedia-org-2350 16 125 knew know VBD en-wikipedia-org-2350 16 126 that that IN en-wikipedia-org-2350 16 127 certain certain JJ en-wikipedia-org-2350 16 128 objects object NNS en-wikipedia-org-2350 16 129 , , , en-wikipedia-org-2350 16 130 such such JJ en-wikipedia-org-2350 16 131 as as IN en-wikipedia-org-2350 16 132 rods rod NNS en-wikipedia-org-2350 16 133 of of IN en-wikipedia-org-2350 16 134 amber amber NN en-wikipedia-org-2350 16 135 , , , en-wikipedia-org-2350 16 136 could could MD en-wikipedia-org-2350 16 137 be be VB en-wikipedia-org-2350 16 138 rubbed rub VBN en-wikipedia-org-2350 16 139 with with IN en-wikipedia-org-2350 16 140 cat cat NN en-wikipedia-org-2350 16 141 's 's POS en-wikipedia-org-2350 16 142 fur fur NN en-wikipedia-org-2350 16 143 to to TO en-wikipedia-org-2350 16 144 attract attract VB en-wikipedia-org-2350 16 145 light light JJ en-wikipedia-org-2350 16 146 objects object NNS en-wikipedia-org-2350 16 147 like like IN en-wikipedia-org-2350 16 148 feathers feather NNS en-wikipedia-org-2350 16 149 and and CC en-wikipedia-org-2350 16 150 papers paper NNS en-wikipedia-org-2350 16 151 . . . en-wikipedia-org-2350 17 1 Thales thale NNS en-wikipedia-org-2350 17 2 of of IN en-wikipedia-org-2350 17 3 Miletus Miletus NNP en-wikipedia-org-2350 17 4 made make VBD en-wikipedia-org-2350 17 5 the the DT en-wikipedia-org-2350 17 6 first first JJ en-wikipedia-org-2350 17 7 recorded record VBN en-wikipedia-org-2350 17 8 description description NN en-wikipedia-org-2350 17 9 of of IN en-wikipedia-org-2350 17 10 static static JJ en-wikipedia-org-2350 17 11 electricity electricity NN en-wikipedia-org-2350 17 12 around around IN en-wikipedia-org-2350 17 13 600 600 CD en-wikipedia-org-2350 17 14 BC,[6 BC,[6 NNS en-wikipedia-org-2350 17 15 ] ] -RRB- en-wikipedia-org-2350 17 16 when when WRB en-wikipedia-org-2350 17 17 he -PRON- PRP en-wikipedia-org-2350 17 18 noticed notice VBD en-wikipedia-org-2350 17 19 that that IN en-wikipedia-org-2350 17 20 friction friction NN en-wikipedia-org-2350 17 21 could could MD en-wikipedia-org-2350 17 22 render render VB en-wikipedia-org-2350 17 23 a a DT en-wikipedia-org-2350 17 24 piece piece NN en-wikipedia-org-2350 17 25 of of IN en-wikipedia-org-2350 17 26 amber amber NNP en-wikipedia-org-2350 17 27 magnetic magnetic NNP en-wikipedia-org-2350 17 28 . . . en-wikipedia-org-2350 18 1 [ [ -LRB- en-wikipedia-org-2350 18 2 7][8 7][8 NNP en-wikipedia-org-2350 18 3 ] ] -RRB- en-wikipedia-org-2350 18 4 In in IN en-wikipedia-org-2350 18 5 1600 1600 CD en-wikipedia-org-2350 18 6 , , , en-wikipedia-org-2350 18 7 English english JJ en-wikipedia-org-2350 18 8 scientist scientist NN en-wikipedia-org-2350 18 9 William William NNP en-wikipedia-org-2350 18 10 Gilbert Gilbert NNP en-wikipedia-org-2350 18 11 made make VBD en-wikipedia-org-2350 18 12 a a DT en-wikipedia-org-2350 18 13 careful careful JJ en-wikipedia-org-2350 18 14 study study NN en-wikipedia-org-2350 18 15 of of IN en-wikipedia-org-2350 18 16 electricity electricity NN en-wikipedia-org-2350 18 17 and and CC en-wikipedia-org-2350 18 18 magnetism magnetism NN en-wikipedia-org-2350 18 19 , , , en-wikipedia-org-2350 18 20 distinguishing distinguish VBG en-wikipedia-org-2350 18 21 the the DT en-wikipedia-org-2350 18 22 lodestone lodestone CD en-wikipedia-org-2350 18 23 effect effect NN en-wikipedia-org-2350 18 24 from from IN en-wikipedia-org-2350 18 25 static static JJ en-wikipedia-org-2350 18 26 electricity electricity NN en-wikipedia-org-2350 18 27 produced produce VBN en-wikipedia-org-2350 18 28 by by IN en-wikipedia-org-2350 18 29 rubbing rub VBG en-wikipedia-org-2350 18 30 amber amber NN en-wikipedia-org-2350 18 31 . . . en-wikipedia-org-2350 19 1 [ [ -LRB- en-wikipedia-org-2350 19 2 7 7 CD en-wikipedia-org-2350 19 3 ] ] -RRB- en-wikipedia-org-2350 19 4 He -PRON- PRP en-wikipedia-org-2350 19 5 coined coin VBD en-wikipedia-org-2350 19 6 the the DT en-wikipedia-org-2350 19 7 New New NNP en-wikipedia-org-2350 19 8 Latin Latin NNP en-wikipedia-org-2350 19 9 word word NN en-wikipedia-org-2350 19 10 electricus electricus NN en-wikipedia-org-2350 19 11 ( ( -LRB- en-wikipedia-org-2350 19 12 " " `` en-wikipedia-org-2350 19 13 of of IN en-wikipedia-org-2350 19 14 amber amber NN en-wikipedia-org-2350 19 15 " " '' en-wikipedia-org-2350 19 16 or or CC en-wikipedia-org-2350 19 17 " " `` en-wikipedia-org-2350 19 18 like like IN en-wikipedia-org-2350 19 19 amber amber NN en-wikipedia-org-2350 19 20 " " '' en-wikipedia-org-2350 19 21 , , , en-wikipedia-org-2350 19 22 from from IN en-wikipedia-org-2350 19 23 ἤλεκτρον ἤλεκτρον NNP en-wikipedia-org-2350 19 24 [ [ -LRB- en-wikipedia-org-2350 19 25 elektron elektron NNP en-wikipedia-org-2350 19 26 ] ] -RRB- en-wikipedia-org-2350 19 27 , , , en-wikipedia-org-2350 19 28 the the DT en-wikipedia-org-2350 19 29 Greek greek JJ en-wikipedia-org-2350 19 30 word word NN en-wikipedia-org-2350 19 31 for for IN en-wikipedia-org-2350 19 32 " " `` en-wikipedia-org-2350 19 33 amber amber NNP en-wikipedia-org-2350 19 34 " " '' en-wikipedia-org-2350 19 35 ) ) -RRB- en-wikipedia-org-2350 19 36 to to TO en-wikipedia-org-2350 19 37 refer refer VB en-wikipedia-org-2350 19 38 to to IN en-wikipedia-org-2350 19 39 the the DT en-wikipedia-org-2350 19 40 property property NN en-wikipedia-org-2350 19 41 of of IN en-wikipedia-org-2350 19 42 attracting attract VBG en-wikipedia-org-2350 19 43 small small JJ en-wikipedia-org-2350 19 44 objects object NNS en-wikipedia-org-2350 19 45 after after IN en-wikipedia-org-2350 19 46 being be VBG en-wikipedia-org-2350 19 47 rubbed rub VBN en-wikipedia-org-2350 19 48 . . . en-wikipedia-org-2350 20 1 [ [ -LRB- en-wikipedia-org-2350 20 2 9 9 CD en-wikipedia-org-2350 20 3 ] ] -RRB- en-wikipedia-org-2350 20 4 This this DT en-wikipedia-org-2350 20 5 association association NN en-wikipedia-org-2350 20 6 gave give VBD en-wikipedia-org-2350 20 7 rise rise NN en-wikipedia-org-2350 20 8 to to IN en-wikipedia-org-2350 20 9 the the DT en-wikipedia-org-2350 20 10 English english JJ en-wikipedia-org-2350 20 11 words word NNS en-wikipedia-org-2350 20 12 " " `` en-wikipedia-org-2350 20 13 electric electric JJ en-wikipedia-org-2350 20 14 " " '' en-wikipedia-org-2350 20 15 and and CC en-wikipedia-org-2350 20 16 " " `` en-wikipedia-org-2350 20 17 electricity electricity NN en-wikipedia-org-2350 20 18 " " '' en-wikipedia-org-2350 20 19 , , , en-wikipedia-org-2350 20 20 which which WDT en-wikipedia-org-2350 20 21 made make VBD en-wikipedia-org-2350 20 22 their -PRON- PRP$ en-wikipedia-org-2350 20 23 first first JJ en-wikipedia-org-2350 20 24 appearance appearance NN en-wikipedia-org-2350 20 25 in in IN en-wikipedia-org-2350 20 26 print print NN en-wikipedia-org-2350 20 27 in in IN en-wikipedia-org-2350 20 28 Thomas Thomas NNP en-wikipedia-org-2350 20 29 Browne Browne NNP en-wikipedia-org-2350 20 30 's 's POS en-wikipedia-org-2350 20 31 Pseudodoxia Pseudodoxia NNP en-wikipedia-org-2350 20 32 Epidemica Epidemica NNP en-wikipedia-org-2350 20 33 of of IN en-wikipedia-org-2350 20 34 1646 1646 CD en-wikipedia-org-2350 20 35 . . . en-wikipedia-org-2350 21 1 [ [ -LRB- en-wikipedia-org-2350 21 2 10 10 CD en-wikipedia-org-2350 21 3 ] ] -RRB- en-wikipedia-org-2350 21 4 Early early JJ en-wikipedia-org-2350 21 5 investigators investigator NNS en-wikipedia-org-2350 21 6 of of IN en-wikipedia-org-2350 21 7 the the DT en-wikipedia-org-2350 21 8 18th 18th JJ en-wikipedia-org-2350 21 9 century century NN en-wikipedia-org-2350 21 10 who who WP en-wikipedia-org-2350 21 11 suspected suspect VBD en-wikipedia-org-2350 21 12 that that IN en-wikipedia-org-2350 21 13 the the DT en-wikipedia-org-2350 21 14 electrical electrical JJ en-wikipedia-org-2350 21 15 force force NN en-wikipedia-org-2350 21 16 diminished diminish VBN en-wikipedia-org-2350 21 17 with with IN en-wikipedia-org-2350 21 18 distance distance NN en-wikipedia-org-2350 21 19 as as IN en-wikipedia-org-2350 21 20 the the DT en-wikipedia-org-2350 21 21 force force NN en-wikipedia-org-2350 21 22 of of IN en-wikipedia-org-2350 21 23 gravity gravity NNP en-wikipedia-org-2350 21 24 did do VBD en-wikipedia-org-2350 21 25 ( ( -LRB- en-wikipedia-org-2350 21 26 i.e. i.e. FW en-wikipedia-org-2350 21 27 , , , en-wikipedia-org-2350 21 28 as as IN en-wikipedia-org-2350 21 29 the the DT en-wikipedia-org-2350 21 30 inverse inverse NN en-wikipedia-org-2350 21 31 square square NN en-wikipedia-org-2350 21 32 of of IN en-wikipedia-org-2350 21 33 the the DT en-wikipedia-org-2350 21 34 distance distance NN en-wikipedia-org-2350 21 35 ) ) -RRB- en-wikipedia-org-2350 21 36 included include VBD en-wikipedia-org-2350 21 37 Daniel Daniel NNP en-wikipedia-org-2350 21 38 Bernoulli[11 bernoulli[11 ADD en-wikipedia-org-2350 21 39 ] ] -RRB- en-wikipedia-org-2350 21 40 and and CC en-wikipedia-org-2350 21 41 Alessandro Alessandro NNP en-wikipedia-org-2350 21 42 Volta Volta NNP en-wikipedia-org-2350 21 43 , , , en-wikipedia-org-2350 21 44 both both DT en-wikipedia-org-2350 21 45 of of IN en-wikipedia-org-2350 21 46 whom whom WP en-wikipedia-org-2350 21 47 measured measure VBD en-wikipedia-org-2350 21 48 the the DT en-wikipedia-org-2350 21 49 force force NN en-wikipedia-org-2350 21 50 between between IN en-wikipedia-org-2350 21 51 plates plate NNS en-wikipedia-org-2350 21 52 of of IN en-wikipedia-org-2350 21 53 a a DT en-wikipedia-org-2350 21 54 capacitor capacitor NN en-wikipedia-org-2350 21 55 , , , en-wikipedia-org-2350 21 56 and and CC en-wikipedia-org-2350 21 57 Franz Franz NNP en-wikipedia-org-2350 21 58 Aepinus Aepinus NNP en-wikipedia-org-2350 21 59 who who WP en-wikipedia-org-2350 21 60 supposed suppose VBD en-wikipedia-org-2350 21 61 the the DT en-wikipedia-org-2350 21 62 inverse inverse NN en-wikipedia-org-2350 21 63 - - HYPH en-wikipedia-org-2350 21 64 square square JJ en-wikipedia-org-2350 21 65 law law NN en-wikipedia-org-2350 21 66 in in IN en-wikipedia-org-2350 21 67 1758 1758 CD en-wikipedia-org-2350 21 68 . . . en-wikipedia-org-2350 22 1 [ [ -LRB- en-wikipedia-org-2350 22 2 12 12 CD en-wikipedia-org-2350 22 3 ] ] -RRB- en-wikipedia-org-2350 22 4 Based base VBN en-wikipedia-org-2350 22 5 on on IN en-wikipedia-org-2350 22 6 experiments experiment NNS en-wikipedia-org-2350 22 7 with with IN en-wikipedia-org-2350 22 8 electrically electrically RB en-wikipedia-org-2350 22 9 charged charge VBN en-wikipedia-org-2350 22 10 spheres sphere NNS en-wikipedia-org-2350 22 11 , , , en-wikipedia-org-2350 22 12 Joseph Joseph NNP en-wikipedia-org-2350 22 13 Priestley Priestley NNP en-wikipedia-org-2350 22 14 of of IN en-wikipedia-org-2350 22 15 England England NNP en-wikipedia-org-2350 22 16 was be VBD en-wikipedia-org-2350 22 17 among among IN en-wikipedia-org-2350 22 18 the the DT en-wikipedia-org-2350 22 19 first first JJ en-wikipedia-org-2350 22 20 to to TO en-wikipedia-org-2350 22 21 propose propose VB en-wikipedia-org-2350 22 22 that that IN en-wikipedia-org-2350 22 23 electrical electrical JJ en-wikipedia-org-2350 22 24 force force NN en-wikipedia-org-2350 22 25 followed follow VBD en-wikipedia-org-2350 22 26 an an DT en-wikipedia-org-2350 22 27 inverse inverse NN en-wikipedia-org-2350 22 28 - - HYPH en-wikipedia-org-2350 22 29 square square JJ en-wikipedia-org-2350 22 30 law law NN en-wikipedia-org-2350 22 31 , , , en-wikipedia-org-2350 22 32 similar similar JJ en-wikipedia-org-2350 22 33 to to IN en-wikipedia-org-2350 22 34 Newton Newton NNP en-wikipedia-org-2350 22 35 's 's POS en-wikipedia-org-2350 22 36 law law NN en-wikipedia-org-2350 22 37 of of IN en-wikipedia-org-2350 22 38 universal universal NNP en-wikipedia-org-2350 22 39 gravitation gravitation NNP en-wikipedia-org-2350 22 40 . . . en-wikipedia-org-2350 23 1 However however RB en-wikipedia-org-2350 23 2 , , , en-wikipedia-org-2350 23 3 he -PRON- PRP en-wikipedia-org-2350 23 4 did do VBD en-wikipedia-org-2350 23 5 not not RB en-wikipedia-org-2350 23 6 generalize generalize VB en-wikipedia-org-2350 23 7 or or CC en-wikipedia-org-2350 23 8 elaborate elaborate VB en-wikipedia-org-2350 23 9 on on IN en-wikipedia-org-2350 23 10 this this DT en-wikipedia-org-2350 23 11 . . . en-wikipedia-org-2350 24 1 [ [ -LRB- en-wikipedia-org-2350 24 2 13 13 CD en-wikipedia-org-2350 24 3 ] ] -RRB- en-wikipedia-org-2350 24 4 In in IN en-wikipedia-org-2350 24 5 1767 1767 CD en-wikipedia-org-2350 24 6 , , , en-wikipedia-org-2350 24 7 he -PRON- PRP en-wikipedia-org-2350 24 8 conjectured conjecture VBD en-wikipedia-org-2350 24 9 that that IN en-wikipedia-org-2350 24 10 the the DT en-wikipedia-org-2350 24 11 force force NN en-wikipedia-org-2350 24 12 between between IN en-wikipedia-org-2350 24 13 charges charge NNS en-wikipedia-org-2350 24 14 varied varied JJ en-wikipedia-org-2350 24 15 as as IN en-wikipedia-org-2350 24 16 the the DT en-wikipedia-org-2350 24 17 inverse inverse NN en-wikipedia-org-2350 24 18 square square NN en-wikipedia-org-2350 24 19 of of IN en-wikipedia-org-2350 24 20 the the DT en-wikipedia-org-2350 24 21 distance distance NN en-wikipedia-org-2350 24 22 . . . en-wikipedia-org-2350 25 1 [ [ -LRB- en-wikipedia-org-2350 25 2 14][15 14][15 CD en-wikipedia-org-2350 25 3 ] ] -RRB- en-wikipedia-org-2350 25 4 Coulomb Coulomb NNP en-wikipedia-org-2350 25 5 's 's POS en-wikipedia-org-2350 25 6 torsion torsion NN en-wikipedia-org-2350 25 7 balance balance NN en-wikipedia-org-2350 25 8 In in IN en-wikipedia-org-2350 25 9 1769 1769 CD en-wikipedia-org-2350 25 10 , , , en-wikipedia-org-2350 25 11 Scottish scottish JJ en-wikipedia-org-2350 25 12 physicist physicist NN en-wikipedia-org-2350 25 13 John John NNP en-wikipedia-org-2350 25 14 Robison Robison NNP en-wikipedia-org-2350 25 15 announced announce VBD en-wikipedia-org-2350 25 16 that that IN en-wikipedia-org-2350 25 17 , , , en-wikipedia-org-2350 25 18 according accord VBG en-wikipedia-org-2350 25 19 to to IN en-wikipedia-org-2350 25 20 his -PRON- PRP$ en-wikipedia-org-2350 25 21 measurements measurement NNS en-wikipedia-org-2350 25 22 , , , en-wikipedia-org-2350 25 23 the the DT en-wikipedia-org-2350 25 24 force force NN en-wikipedia-org-2350 25 25 of of IN en-wikipedia-org-2350 25 26 repulsion repulsion NN en-wikipedia-org-2350 25 27 between between IN en-wikipedia-org-2350 25 28 two two CD en-wikipedia-org-2350 25 29 spheres sphere NNS en-wikipedia-org-2350 25 30 with with IN en-wikipedia-org-2350 25 31 charges charge NNS en-wikipedia-org-2350 25 32 of of IN en-wikipedia-org-2350 25 33 the the DT en-wikipedia-org-2350 25 34 same same JJ en-wikipedia-org-2350 25 35 sign sign NN en-wikipedia-org-2350 25 36 varied vary VBD en-wikipedia-org-2350 25 37 as as IN en-wikipedia-org-2350 25 38 x−2.06 x−2.06 NNP en-wikipedia-org-2350 25 39 . . . en-wikipedia-org-2350 26 1 [ [ -LRB- en-wikipedia-org-2350 26 2 16 16 CD en-wikipedia-org-2350 26 3 ] ] -RRB- en-wikipedia-org-2350 26 4 In in IN en-wikipedia-org-2350 26 5 the the DT en-wikipedia-org-2350 26 6 early early JJ en-wikipedia-org-2350 26 7 1770s 1770s CD en-wikipedia-org-2350 26 8 , , , en-wikipedia-org-2350 26 9 the the DT en-wikipedia-org-2350 26 10 dependence dependence NN en-wikipedia-org-2350 26 11 of of IN en-wikipedia-org-2350 26 12 the the DT en-wikipedia-org-2350 26 13 force force NN en-wikipedia-org-2350 26 14 between between IN en-wikipedia-org-2350 26 15 charged charged JJ en-wikipedia-org-2350 26 16 bodies body NNS en-wikipedia-org-2350 26 17 upon upon IN en-wikipedia-org-2350 26 18 both both DT en-wikipedia-org-2350 26 19 distance distance NN en-wikipedia-org-2350 26 20 and and CC en-wikipedia-org-2350 26 21 charge charge NN en-wikipedia-org-2350 26 22 had have VBD en-wikipedia-org-2350 26 23 already already RB en-wikipedia-org-2350 26 24 been be VBN en-wikipedia-org-2350 26 25 discovered discover VBN en-wikipedia-org-2350 26 26 , , , en-wikipedia-org-2350 26 27 but but CC en-wikipedia-org-2350 26 28 not not RB en-wikipedia-org-2350 26 29 published publish VBN en-wikipedia-org-2350 26 30 , , , en-wikipedia-org-2350 26 31 by by IN en-wikipedia-org-2350 26 32 Henry Henry NNP en-wikipedia-org-2350 26 33 Cavendish Cavendish NNP en-wikipedia-org-2350 26 34 of of IN en-wikipedia-org-2350 26 35 England England NNP en-wikipedia-org-2350 26 36 . . . en-wikipedia-org-2350 27 1 [ [ -LRB- en-wikipedia-org-2350 27 2 17 17 CD en-wikipedia-org-2350 27 3 ] ] -RRB- en-wikipedia-org-2350 27 4 Finally finally RB en-wikipedia-org-2350 27 5 , , , en-wikipedia-org-2350 27 6 in in IN en-wikipedia-org-2350 27 7 1785 1785 CD en-wikipedia-org-2350 27 8 , , , en-wikipedia-org-2350 27 9 the the DT en-wikipedia-org-2350 27 10 French french JJ en-wikipedia-org-2350 27 11 physicist physicist NN en-wikipedia-org-2350 27 12 Charles Charles NNP en-wikipedia-org-2350 27 13 - - HYPH en-wikipedia-org-2350 27 14 Augustin Augustin NNP en-wikipedia-org-2350 27 15 de de NNP en-wikipedia-org-2350 27 16 Coulomb Coulomb NNP en-wikipedia-org-2350 27 17 published publish VBD en-wikipedia-org-2350 27 18 his -PRON- PRP$ en-wikipedia-org-2350 27 19 first first JJ en-wikipedia-org-2350 27 20 three three CD en-wikipedia-org-2350 27 21 reports report NNS en-wikipedia-org-2350 27 22 of of IN en-wikipedia-org-2350 27 23 electricity electricity NN en-wikipedia-org-2350 27 24 and and CC en-wikipedia-org-2350 27 25 magnetism magnetism NN en-wikipedia-org-2350 27 26 where where WRB en-wikipedia-org-2350 27 27 he -PRON- PRP en-wikipedia-org-2350 27 28 stated state VBD en-wikipedia-org-2350 27 29 his -PRON- PRP$ en-wikipedia-org-2350 27 30 law law NN en-wikipedia-org-2350 27 31 . . . en-wikipedia-org-2350 28 1 This this DT en-wikipedia-org-2350 28 2 publication publication NN en-wikipedia-org-2350 28 3 was be VBD en-wikipedia-org-2350 28 4 essential essential JJ en-wikipedia-org-2350 28 5 to to IN en-wikipedia-org-2350 28 6 the the DT en-wikipedia-org-2350 28 7 development development NN en-wikipedia-org-2350 28 8 of of IN en-wikipedia-org-2350 28 9 the the DT en-wikipedia-org-2350 28 10 theory theory NN en-wikipedia-org-2350 28 11 of of IN en-wikipedia-org-2350 28 12 electromagnetism electromagnetism NN en-wikipedia-org-2350 28 13 . . . en-wikipedia-org-2350 29 1 [ [ -LRB- en-wikipedia-org-2350 29 2 4 4 CD en-wikipedia-org-2350 29 3 ] ] -RRB- en-wikipedia-org-2350 29 4 He -PRON- PRP en-wikipedia-org-2350 29 5 used use VBD en-wikipedia-org-2350 29 6 a a DT en-wikipedia-org-2350 29 7 torsion torsion NN en-wikipedia-org-2350 29 8 balance balance NN en-wikipedia-org-2350 29 9 to to TO en-wikipedia-org-2350 29 10 study study VB en-wikipedia-org-2350 29 11 the the DT en-wikipedia-org-2350 29 12 repulsion repulsion NN en-wikipedia-org-2350 29 13 and and CC en-wikipedia-org-2350 29 14 attraction attraction NN en-wikipedia-org-2350 29 15 forces force NNS en-wikipedia-org-2350 29 16 of of IN en-wikipedia-org-2350 29 17 charged charge VBN en-wikipedia-org-2350 29 18 particles particle NNS en-wikipedia-org-2350 29 19 , , , en-wikipedia-org-2350 29 20 and and CC en-wikipedia-org-2350 29 21 determined determine VBD en-wikipedia-org-2350 29 22 that that IN en-wikipedia-org-2350 29 23 the the DT en-wikipedia-org-2350 29 24 magnitude magnitude NN en-wikipedia-org-2350 29 25 of of IN en-wikipedia-org-2350 29 26 the the DT en-wikipedia-org-2350 29 27 electric electric JJ en-wikipedia-org-2350 29 28 force force NN en-wikipedia-org-2350 29 29 between between IN en-wikipedia-org-2350 29 30 two two CD en-wikipedia-org-2350 29 31 point point NN en-wikipedia-org-2350 29 32 charges charge NNS en-wikipedia-org-2350 29 33 is be VBZ en-wikipedia-org-2350 29 34 directly directly RB en-wikipedia-org-2350 29 35 proportional proportional JJ en-wikipedia-org-2350 29 36 to to IN en-wikipedia-org-2350 29 37 the the DT en-wikipedia-org-2350 29 38 product product NN en-wikipedia-org-2350 29 39 of of IN en-wikipedia-org-2350 29 40 the the DT en-wikipedia-org-2350 29 41 charges charge NNS en-wikipedia-org-2350 29 42 and and CC en-wikipedia-org-2350 29 43 inversely inversely RB en-wikipedia-org-2350 29 44 proportional proportional JJ en-wikipedia-org-2350 29 45 to to IN en-wikipedia-org-2350 29 46 the the DT en-wikipedia-org-2350 29 47 square square NN en-wikipedia-org-2350 29 48 of of IN en-wikipedia-org-2350 29 49 the the DT en-wikipedia-org-2350 29 50 distance distance NN en-wikipedia-org-2350 29 51 between between IN en-wikipedia-org-2350 29 52 them -PRON- PRP en-wikipedia-org-2350 29 53 . . . en-wikipedia-org-2350 30 1 The the DT en-wikipedia-org-2350 30 2 torsion torsion NN en-wikipedia-org-2350 30 3 balance balance NN en-wikipedia-org-2350 30 4 consists consist VBZ en-wikipedia-org-2350 30 5 of of IN en-wikipedia-org-2350 30 6 a a DT en-wikipedia-org-2350 30 7 bar bar NN en-wikipedia-org-2350 30 8 suspended suspend VBN en-wikipedia-org-2350 30 9 from from IN en-wikipedia-org-2350 30 10 its -PRON- PRP$ en-wikipedia-org-2350 30 11 middle middle NN en-wikipedia-org-2350 30 12 by by IN en-wikipedia-org-2350 30 13 a a DT en-wikipedia-org-2350 30 14 thin thin JJ en-wikipedia-org-2350 30 15 fiber fiber NN en-wikipedia-org-2350 30 16 . . . en-wikipedia-org-2350 31 1 The the DT en-wikipedia-org-2350 31 2 fiber fiber NN en-wikipedia-org-2350 31 3 acts act VBZ en-wikipedia-org-2350 31 4 as as IN en-wikipedia-org-2350 31 5 a a DT en-wikipedia-org-2350 31 6 very very RB en-wikipedia-org-2350 31 7 weak weak JJ en-wikipedia-org-2350 31 8 torsion torsion NN en-wikipedia-org-2350 31 9 spring spring NN en-wikipedia-org-2350 31 10 . . . en-wikipedia-org-2350 32 1 In in IN en-wikipedia-org-2350 32 2 Coulomb Coulomb NNP en-wikipedia-org-2350 32 3 's 's POS en-wikipedia-org-2350 32 4 experiment experiment NN en-wikipedia-org-2350 32 5 , , , en-wikipedia-org-2350 32 6 the the DT en-wikipedia-org-2350 32 7 torsion torsion NN en-wikipedia-org-2350 32 8 balance balance NN en-wikipedia-org-2350 32 9 was be VBD en-wikipedia-org-2350 32 10 an an DT en-wikipedia-org-2350 32 11 insulating insulating JJ en-wikipedia-org-2350 32 12 rod rod NN en-wikipedia-org-2350 32 13 with with IN en-wikipedia-org-2350 32 14 a a DT en-wikipedia-org-2350 32 15 metal metal NN en-wikipedia-org-2350 32 16 - - HYPH en-wikipedia-org-2350 32 17 coated coat VBN en-wikipedia-org-2350 32 18 ball ball NN en-wikipedia-org-2350 32 19 attached attach VBN en-wikipedia-org-2350 32 20 to to IN en-wikipedia-org-2350 32 21 one one CD en-wikipedia-org-2350 32 22 end end NN en-wikipedia-org-2350 32 23 , , , en-wikipedia-org-2350 32 24 suspended suspend VBN en-wikipedia-org-2350 32 25 by by IN en-wikipedia-org-2350 32 26 a a DT en-wikipedia-org-2350 32 27 silk silk NN en-wikipedia-org-2350 32 28 thread thread NN en-wikipedia-org-2350 32 29 . . . en-wikipedia-org-2350 33 1 The the DT en-wikipedia-org-2350 33 2 ball ball NN en-wikipedia-org-2350 33 3 was be VBD en-wikipedia-org-2350 33 4 charged charge VBN en-wikipedia-org-2350 33 5 with with IN en-wikipedia-org-2350 33 6 a a DT en-wikipedia-org-2350 33 7 known know VBN en-wikipedia-org-2350 33 8 charge charge NN en-wikipedia-org-2350 33 9 of of IN en-wikipedia-org-2350 33 10 static static JJ en-wikipedia-org-2350 33 11 electricity electricity NN en-wikipedia-org-2350 33 12 , , , en-wikipedia-org-2350 33 13 and and CC en-wikipedia-org-2350 33 14 a a DT en-wikipedia-org-2350 33 15 second second JJ en-wikipedia-org-2350 33 16 charged charge VBN en-wikipedia-org-2350 33 17 ball ball NN en-wikipedia-org-2350 33 18 of of IN en-wikipedia-org-2350 33 19 the the DT en-wikipedia-org-2350 33 20 same same JJ en-wikipedia-org-2350 33 21 polarity polarity NN en-wikipedia-org-2350 33 22 was be VBD en-wikipedia-org-2350 33 23 brought bring VBN en-wikipedia-org-2350 33 24 near near IN en-wikipedia-org-2350 33 25 it -PRON- PRP en-wikipedia-org-2350 33 26 . . . en-wikipedia-org-2350 34 1 The the DT en-wikipedia-org-2350 34 2 two two CD en-wikipedia-org-2350 34 3 charged charge VBN en-wikipedia-org-2350 34 4 balls ball NNS en-wikipedia-org-2350 34 5 repelled repel VBD en-wikipedia-org-2350 34 6 one one CD en-wikipedia-org-2350 34 7 another another DT en-wikipedia-org-2350 34 8 , , , en-wikipedia-org-2350 34 9 twisting twist VBG en-wikipedia-org-2350 34 10 the the DT en-wikipedia-org-2350 34 11 fiber fiber NN en-wikipedia-org-2350 34 12 through through IN en-wikipedia-org-2350 34 13 a a DT en-wikipedia-org-2350 34 14 certain certain JJ en-wikipedia-org-2350 34 15 angle angle NN en-wikipedia-org-2350 34 16 , , , en-wikipedia-org-2350 34 17 which which WDT en-wikipedia-org-2350 34 18 could could MD en-wikipedia-org-2350 34 19 be be VB en-wikipedia-org-2350 34 20 read read VBN en-wikipedia-org-2350 34 21 from from IN en-wikipedia-org-2350 34 22 a a DT en-wikipedia-org-2350 34 23 scale scale NN en-wikipedia-org-2350 34 24 on on IN en-wikipedia-org-2350 34 25 the the DT en-wikipedia-org-2350 34 26 instrument instrument NN en-wikipedia-org-2350 34 27 . . . en-wikipedia-org-2350 35 1 By by IN en-wikipedia-org-2350 35 2 knowing know VBG en-wikipedia-org-2350 35 3 how how WRB en-wikipedia-org-2350 35 4 much much JJ en-wikipedia-org-2350 35 5 force force NN en-wikipedia-org-2350 35 6 it -PRON- PRP en-wikipedia-org-2350 35 7 took take VBD en-wikipedia-org-2350 35 8 to to TO en-wikipedia-org-2350 35 9 twist twist VB en-wikipedia-org-2350 35 10 the the DT en-wikipedia-org-2350 35 11 fiber fiber NN en-wikipedia-org-2350 35 12 through through IN en-wikipedia-org-2350 35 13 a a DT en-wikipedia-org-2350 35 14 given give VBN en-wikipedia-org-2350 35 15 angle angle NN en-wikipedia-org-2350 35 16 , , , en-wikipedia-org-2350 35 17 Coulomb Coulomb NNP en-wikipedia-org-2350 35 18 was be VBD en-wikipedia-org-2350 35 19 able able JJ en-wikipedia-org-2350 35 20 to to TO en-wikipedia-org-2350 35 21 calculate calculate VB en-wikipedia-org-2350 35 22 the the DT en-wikipedia-org-2350 35 23 force force NN en-wikipedia-org-2350 35 24 between between IN en-wikipedia-org-2350 35 25 the the DT en-wikipedia-org-2350 35 26 balls ball NNS en-wikipedia-org-2350 35 27 and and CC en-wikipedia-org-2350 35 28 derive derive VB en-wikipedia-org-2350 35 29 his -PRON- PRP$ en-wikipedia-org-2350 35 30 inverse inverse NN en-wikipedia-org-2350 35 31 - - HYPH en-wikipedia-org-2350 35 32 square square JJ en-wikipedia-org-2350 35 33 proportionality proportionality NN en-wikipedia-org-2350 35 34 law law NN en-wikipedia-org-2350 35 35 . . . en-wikipedia-org-2350 36 1 Scalar scalar JJ en-wikipedia-org-2350 36 2 form form NN en-wikipedia-org-2350 36 3 of of IN en-wikipedia-org-2350 36 4 the the DT en-wikipedia-org-2350 36 5 law[edit law[edit NN en-wikipedia-org-2350 36 6 ] ] -RRB- en-wikipedia-org-2350 36 7 Coulomb Coulomb NNP en-wikipedia-org-2350 36 8 's 's POS en-wikipedia-org-2350 36 9 law law NN en-wikipedia-org-2350 36 10 can can MD en-wikipedia-org-2350 36 11 be be VB en-wikipedia-org-2350 36 12 stated state VBN en-wikipedia-org-2350 36 13 as as IN en-wikipedia-org-2350 36 14 a a DT en-wikipedia-org-2350 36 15 simple simple JJ en-wikipedia-org-2350 36 16 mathematical mathematical JJ en-wikipedia-org-2350 36 17 expression expression NN en-wikipedia-org-2350 36 18 . . . en-wikipedia-org-2350 37 1 The the DT en-wikipedia-org-2350 37 2 scalar scalar JJ en-wikipedia-org-2350 37 3 form form NN en-wikipedia-org-2350 37 4 gives give VBZ en-wikipedia-org-2350 37 5 the the DT en-wikipedia-org-2350 37 6 magnitude magnitude NN en-wikipedia-org-2350 37 7 of of IN en-wikipedia-org-2350 37 8 the the DT en-wikipedia-org-2350 37 9 vector vector NN en-wikipedia-org-2350 37 10 of of IN en-wikipedia-org-2350 37 11 the the DT en-wikipedia-org-2350 37 12 electrostatic electrostatic JJ en-wikipedia-org-2350 37 13 force force NN en-wikipedia-org-2350 37 14 F F NNP en-wikipedia-org-2350 37 15 between between IN en-wikipedia-org-2350 37 16 two two CD en-wikipedia-org-2350 37 17 point point NN en-wikipedia-org-2350 37 18 charges charge NNS en-wikipedia-org-2350 37 19 q1 q1 NNP en-wikipedia-org-2350 37 20 and and CC en-wikipedia-org-2350 37 21 q2 q2 NNP en-wikipedia-org-2350 37 22 , , , en-wikipedia-org-2350 37 23 but but CC en-wikipedia-org-2350 37 24 not not RB en-wikipedia-org-2350 37 25 its -PRON- PRP$ en-wikipedia-org-2350 37 26 direction direction NN en-wikipedia-org-2350 37 27 . . . en-wikipedia-org-2350 38 1 If if IN en-wikipedia-org-2350 38 2 r r NN en-wikipedia-org-2350 38 3 is be VBZ en-wikipedia-org-2350 38 4 the the DT en-wikipedia-org-2350 38 5 distance distance NN en-wikipedia-org-2350 38 6 between between IN en-wikipedia-org-2350 38 7 the the DT en-wikipedia-org-2350 38 8 charges charge NNS en-wikipedia-org-2350 38 9 , , , en-wikipedia-org-2350 38 10 the the DT en-wikipedia-org-2350 38 11 magnitude magnitude NN en-wikipedia-org-2350 38 12 of of IN en-wikipedia-org-2350 38 13 the the DT en-wikipedia-org-2350 38 14 force force NN en-wikipedia-org-2350 38 15 is be VBZ en-wikipedia-org-2350 38 16 | | NNP en-wikipedia-org-2350 38 17 F F NNP en-wikipedia-org-2350 38 18 | | NNP en-wikipedia-org-2350 38 19 = = SYM en-wikipedia-org-2350 38 20 k k NNP en-wikipedia-org-2350 38 21 e e NNP en-wikipedia-org-2350 38 22 | | NNP en-wikipedia-org-2350 38 23 q q NNP en-wikipedia-org-2350 38 24 1 1 CD en-wikipedia-org-2350 38 25 q q NNP en-wikipedia-org-2350 38 26 2 2 CD en-wikipedia-org-2350 38 27 | | CD en-wikipedia-org-2350 38 28 r r NN en-wikipedia-org-2350 38 29 2 2 CD en-wikipedia-org-2350 38 30 { { -LRB- en-wikipedia-org-2350 38 31 \displaystyle \displaystyle CD en-wikipedia-org-2350 38 32 |\mathbf |\mathbf NNP en-wikipedia-org-2350 38 33 { { -LRB- en-wikipedia-org-2350 38 34 F F NNP en-wikipedia-org-2350 38 35 } } -RRB- en-wikipedia-org-2350 38 36 |=k_{\text{e}}{\frac |=k_{\text{e}}{\frac NNP en-wikipedia-org-2350 38 37 { { -LRB- en-wikipedia-org-2350 38 38 |q_{1}q_{2}|}{r^{2 |q_{1}q_{2}|}{r^{2 NN en-wikipedia-org-2350 38 39 } } -RRB- en-wikipedia-org-2350 38 40 } } -RRB- en-wikipedia-org-2350 38 41 } } -RRB- en-wikipedia-org-2350 38 42 } } -RRB- en-wikipedia-org-2350 38 43 The the DT en-wikipedia-org-2350 38 44 constant constant JJ en-wikipedia-org-2350 38 45 ke ke NN en-wikipedia-org-2350 38 46 is be VBZ en-wikipedia-org-2350 38 47 called call VBN en-wikipedia-org-2350 38 48 Coulomb Coulomb NNP en-wikipedia-org-2350 38 49 's 's POS en-wikipedia-org-2350 38 50 constant constant JJ en-wikipedia-org-2350 38 51 and and CC en-wikipedia-org-2350 38 52 is be VBZ en-wikipedia-org-2350 38 53 equal equal JJ en-wikipedia-org-2350 38 54 to to IN en-wikipedia-org-2350 38 55 1/4πε0 1/4πε0 CD en-wikipedia-org-2350 38 56 , , , en-wikipedia-org-2350 38 57 where where WRB en-wikipedia-org-2350 38 58 ε0 ε0 NN en-wikipedia-org-2350 38 59 is be VBZ en-wikipedia-org-2350 38 60 the the DT en-wikipedia-org-2350 38 61 electric electric JJ en-wikipedia-org-2350 38 62 constant constant NN en-wikipedia-org-2350 38 63 ; ; : en-wikipedia-org-2350 38 64 ke ke NNP en-wikipedia-org-2350 38 65 = = SYM en-wikipedia-org-2350 38 66 8.988×109 8.988×109 NNP en-wikipedia-org-2350 38 67   _SP en-wikipedia-org-2350 38 68 N⋅m2⋅C−2 N⋅m2⋅C−2 NNP en-wikipedia-org-2350 38 69 . . . en-wikipedia-org-2350 39 1 If if IN en-wikipedia-org-2350 39 2 the the DT en-wikipedia-org-2350 39 3 product product NN en-wikipedia-org-2350 39 4 q1q2 q1q2 : en-wikipedia-org-2350 39 5 is be VBZ en-wikipedia-org-2350 39 6 positive positive JJ en-wikipedia-org-2350 39 7 , , , en-wikipedia-org-2350 39 8 the the DT en-wikipedia-org-2350 39 9 force force NN en-wikipedia-org-2350 39 10 between between IN en-wikipedia-org-2350 39 11 the the DT en-wikipedia-org-2350 39 12 two two CD en-wikipedia-org-2350 39 13 charges charge NNS en-wikipedia-org-2350 39 14 is be VBZ en-wikipedia-org-2350 39 15 repulsive repulsive JJ en-wikipedia-org-2350 39 16 ; ; : en-wikipedia-org-2350 39 17 if if IN en-wikipedia-org-2350 39 18 the the DT en-wikipedia-org-2350 39 19 product product NN en-wikipedia-org-2350 39 20 is be VBZ en-wikipedia-org-2350 39 21 negative negative JJ en-wikipedia-org-2350 39 22 , , , en-wikipedia-org-2350 39 23 the the DT en-wikipedia-org-2350 39 24 force force NN en-wikipedia-org-2350 39 25 between between IN en-wikipedia-org-2350 39 26 them -PRON- PRP en-wikipedia-org-2350 39 27 is be VBZ en-wikipedia-org-2350 39 28 attractive attractive JJ en-wikipedia-org-2350 39 29 . . . en-wikipedia-org-2350 40 1 [ [ -LRB- en-wikipedia-org-2350 40 2 18 18 CD en-wikipedia-org-2350 40 3 ] ] -RRB- en-wikipedia-org-2350 40 4 Vector vector NN en-wikipedia-org-2350 40 5 form form NN en-wikipedia-org-2350 40 6 of of IN en-wikipedia-org-2350 40 7 the the DT en-wikipedia-org-2350 40 8 law[edit law[edit NN en-wikipedia-org-2350 40 9 ] ] -RRB- en-wikipedia-org-2350 40 10 In in IN en-wikipedia-org-2350 40 11 the the DT en-wikipedia-org-2350 40 12 image image NN en-wikipedia-org-2350 40 13 , , , en-wikipedia-org-2350 40 14 the the DT en-wikipedia-org-2350 40 15 vector vector NN en-wikipedia-org-2350 40 16 F1 F1 NNP en-wikipedia-org-2350 40 17 is be VBZ en-wikipedia-org-2350 40 18 the the DT en-wikipedia-org-2350 40 19 force force NN en-wikipedia-org-2350 40 20 experienced experience VBN en-wikipedia-org-2350 40 21 by by IN en-wikipedia-org-2350 40 22 q1 q1 NNP en-wikipedia-org-2350 40 23 , , , en-wikipedia-org-2350 40 24 and and CC en-wikipedia-org-2350 40 25 the the DT en-wikipedia-org-2350 40 26 vector vector NN en-wikipedia-org-2350 40 27 F2 F2 NNP en-wikipedia-org-2350 40 28 is be VBZ en-wikipedia-org-2350 40 29 the the DT en-wikipedia-org-2350 40 30 force force NN en-wikipedia-org-2350 40 31 experienced experience VBN en-wikipedia-org-2350 40 32 by by IN en-wikipedia-org-2350 40 33 q2 q2 NNP en-wikipedia-org-2350 40 34 . . . en-wikipedia-org-2350 41 1 When when WRB en-wikipedia-org-2350 41 2 q1q2 q1q2 NNP en-wikipedia-org-2350 41 3 > > XX en-wikipedia-org-2350 41 4 0 0 NFP en-wikipedia-org-2350 41 5 the the DT en-wikipedia-org-2350 41 6 forces force NNS en-wikipedia-org-2350 41 7 are be VBP en-wikipedia-org-2350 41 8 repulsive repulsive JJ en-wikipedia-org-2350 41 9 ( ( -LRB- en-wikipedia-org-2350 41 10 as as IN en-wikipedia-org-2350 41 11 in in IN en-wikipedia-org-2350 41 12 the the DT en-wikipedia-org-2350 41 13 image image NN en-wikipedia-org-2350 41 14 ) ) -RRB- en-wikipedia-org-2350 41 15 and and CC en-wikipedia-org-2350 41 16 when when WRB en-wikipedia-org-2350 41 17 q1q2 q1q2 NNP en-wikipedia-org-2350 41 18 < < XX en-wikipedia-org-2350 41 19 0 0 NFP en-wikipedia-org-2350 41 20 the the DT en-wikipedia-org-2350 41 21 forces force NNS en-wikipedia-org-2350 41 22 are be VBP en-wikipedia-org-2350 41 23 attractive attractive JJ en-wikipedia-org-2350 41 24 ( ( -LRB- en-wikipedia-org-2350 41 25 opposite opposite JJ en-wikipedia-org-2350 41 26 to to IN en-wikipedia-org-2350 41 27 the the DT en-wikipedia-org-2350 41 28 image image NN en-wikipedia-org-2350 41 29 ) ) -RRB- en-wikipedia-org-2350 41 30 . . . en-wikipedia-org-2350 42 1 The the DT en-wikipedia-org-2350 42 2 magnitude magnitude NN en-wikipedia-org-2350 42 3 of of IN en-wikipedia-org-2350 42 4 the the DT en-wikipedia-org-2350 42 5 forces force NNS en-wikipedia-org-2350 42 6 will will MD en-wikipedia-org-2350 42 7 always always RB en-wikipedia-org-2350 42 8 be be VB en-wikipedia-org-2350 42 9 equal equal JJ en-wikipedia-org-2350 42 10 . . . en-wikipedia-org-2350 43 1 Coulomb Coulomb NNP en-wikipedia-org-2350 43 2 's 's POS en-wikipedia-org-2350 43 3 law law NN en-wikipedia-org-2350 43 4 in in IN en-wikipedia-org-2350 43 5 states state NNS en-wikipedia-org-2350 43 6 that that IN en-wikipedia-org-2350 43 7 the the DT en-wikipedia-org-2350 43 8 electrostatic electrostatic JJ en-wikipedia-org-2350 43 9 force force NN en-wikipedia-org-2350 43 10 F F NNP en-wikipedia-org-2350 43 11 1 1 CD en-wikipedia-org-2350 43 12 { { -LRB- en-wikipedia-org-2350 43 13 \textstyle \textstyle CD en-wikipedia-org-2350 43 14 { { -LRB- en-wikipedia-org-2350 43 15 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 43 16 { { -LRB- en-wikipedia-org-2350 43 17 F}}_{1 F}}_{1 NNS en-wikipedia-org-2350 43 18 } } -RRB- en-wikipedia-org-2350 43 19 } } -RRB- en-wikipedia-org-2350 43 20 experienced experience VBN en-wikipedia-org-2350 43 21 by by IN en-wikipedia-org-2350 43 22 a a DT en-wikipedia-org-2350 43 23 charge charge NN en-wikipedia-org-2350 43 24 , , , en-wikipedia-org-2350 43 25 q q NNP en-wikipedia-org-2350 43 26 1 1 CD en-wikipedia-org-2350 43 27 { { -LRB- en-wikipedia-org-2350 43 28 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 29 q_{1 q_{1 NN en-wikipedia-org-2350 43 30 } } -RRB- en-wikipedia-org-2350 43 31 } } -RRB- en-wikipedia-org-2350 43 32 at at IN en-wikipedia-org-2350 43 33 position position NN en-wikipedia-org-2350 43 34 r r NNP en-wikipedia-org-2350 43 35 1 1 CD en-wikipedia-org-2350 43 36 { { -LRB- en-wikipedia-org-2350 43 37 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 38 { { -LRB- en-wikipedia-org-2350 43 39 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 43 40 { { -LRB- en-wikipedia-org-2350 43 41 r}}_{1 r}}_{1 NNP en-wikipedia-org-2350 43 42 } } -RRB- en-wikipedia-org-2350 43 43 } } -RRB- en-wikipedia-org-2350 43 44 , , , en-wikipedia-org-2350 43 45 in in IN en-wikipedia-org-2350 43 46 the the DT en-wikipedia-org-2350 43 47 vicinity vicinity NN en-wikipedia-org-2350 43 48 of of IN en-wikipedia-org-2350 43 49 another another DT en-wikipedia-org-2350 43 50 charge charge NN en-wikipedia-org-2350 43 51 , , , en-wikipedia-org-2350 43 52 q q NNP en-wikipedia-org-2350 43 53 2 2 CD en-wikipedia-org-2350 43 54 { { -LRB- en-wikipedia-org-2350 43 55 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 56 q_{2 q_{2 NN en-wikipedia-org-2350 43 57 } } -RRB- en-wikipedia-org-2350 43 58 } } -RRB- en-wikipedia-org-2350 43 59 at at IN en-wikipedia-org-2350 43 60 position position NN en-wikipedia-org-2350 43 61 r r NNP en-wikipedia-org-2350 43 62 2 2 CD en-wikipedia-org-2350 43 63 { { -LRB- en-wikipedia-org-2350 43 64 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 65 { { -LRB- en-wikipedia-org-2350 43 66 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 43 67 { { -LRB- en-wikipedia-org-2350 43 68 r}}_{2 r}}_{2 NNP en-wikipedia-org-2350 43 69 } } -RRB- en-wikipedia-org-2350 43 70 } } -RRB- en-wikipedia-org-2350 43 71 , , , en-wikipedia-org-2350 43 72 in in IN en-wikipedia-org-2350 43 73 a a DT en-wikipedia-org-2350 43 74 vacuum vacuum NN en-wikipedia-org-2350 43 75 is be VBZ en-wikipedia-org-2350 43 76 equal equal JJ en-wikipedia-org-2350 43 77 to[19 to[19 NNP en-wikipedia-org-2350 43 78 ] ] -RRB- en-wikipedia-org-2350 43 79 F F NNP en-wikipedia-org-2350 43 80 1 1 CD en-wikipedia-org-2350 43 81 = = SYM en-wikipedia-org-2350 43 82 q q NNP en-wikipedia-org-2350 43 83 1 1 CD en-wikipedia-org-2350 43 84 q q NNP en-wikipedia-org-2350 43 85 2 2 CD en-wikipedia-org-2350 43 86 4 4 CD en-wikipedia-org-2350 43 87 π π NN en-wikipedia-org-2350 43 88 ε ε NN en-wikipedia-org-2350 43 89 0 0 CD en-wikipedia-org-2350 43 90 r r NN en-wikipedia-org-2350 43 91 1 1 CD en-wikipedia-org-2350 43 92 − − NNP en-wikipedia-org-2350 43 93 r r NNP en-wikipedia-org-2350 43 94 2 2 CD en-wikipedia-org-2350 43 95 | | CD en-wikipedia-org-2350 43 96 r r NN en-wikipedia-org-2350 43 97 1 1 CD en-wikipedia-org-2350 43 98 − − NNP en-wikipedia-org-2350 43 99 r r NN en-wikipedia-org-2350 43 100 2 2 CD en-wikipedia-org-2350 43 101 | | CD en-wikipedia-org-2350 43 102 3 3 CD en-wikipedia-org-2350 43 103 = = SYM en-wikipedia-org-2350 43 104 q q NNP en-wikipedia-org-2350 43 105 1 1 CD en-wikipedia-org-2350 43 106 q q NNP en-wikipedia-org-2350 43 107 2 2 CD en-wikipedia-org-2350 43 108 4 4 CD en-wikipedia-org-2350 43 109 π π NN en-wikipedia-org-2350 43 110 ε ε NN en-wikipedia-org-2350 43 111 0 0 CD en-wikipedia-org-2350 43 112 r r NN en-wikipedia-org-2350 43 113 ^ ^ NN en-wikipedia-org-2350 43 114 12 12 CD en-wikipedia-org-2350 43 115 | | CD en-wikipedia-org-2350 43 116 r r NNP en-wikipedia-org-2350 43 117 12 12 CD en-wikipedia-org-2350 43 118 | | CD en-wikipedia-org-2350 43 119 2 2 CD en-wikipedia-org-2350 43 120 { { -LRB- en-wikipedia-org-2350 43 121 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 122 { { -LRB- en-wikipedia-org-2350 43 123 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 43 124 { { -LRB- en-wikipedia-org-2350 43 125 F}}_{1}={q_{1}q_{2 F}}_{1}={q_{1}q_{2 NNP en-wikipedia-org-2350 43 126 } } -RRB- en-wikipedia-org-2350 43 127 \over \over CD en-wikipedia-org-2350 43 128 4\pi 4\pi CD en-wikipedia-org-2350 43 129 \varepsilon \varepsilon CD en-wikipedia-org-2350 43 130 _ _ NNP en-wikipedia-org-2350 43 131 { { -LRB- en-wikipedia-org-2350 43 132 0}}{{\boldsymbol 0}}{{\boldsymbol NNP en-wikipedia-org-2350 43 133 { { -LRB- en-wikipedia-org-2350 43 134 r}}_{1}-{\boldsymbol r}}_{1}-{\boldsymbol NNP en-wikipedia-org-2350 43 135 { { -LRB- en-wikipedia-org-2350 43 136 r}}_{2 r}}_{2 NNP en-wikipedia-org-2350 43 137 } } -RRB- en-wikipedia-org-2350 43 138 \over \over CD en-wikipedia-org-2350 43 139 |{\boldsymbol |{\boldsymbol NN en-wikipedia-org-2350 43 140 { { -LRB- en-wikipedia-org-2350 43 141 r}}_{1}-{\boldsymbol r}}_{1}-{\boldsymbol NNP en-wikipedia-org-2350 43 142 { { -LRB- en-wikipedia-org-2350 43 143 r}}_{2}|^{3}}={q_{1}q_{2 r}}_{2}|^{3}}={q_{1}q_{2 NNP en-wikipedia-org-2350 43 144 } } -RRB- en-wikipedia-org-2350 43 145 \over \over CD en-wikipedia-org-2350 43 146 4\pi 4\pi CD en-wikipedia-org-2350 43 147 \varepsilon \varepsilon CD en-wikipedia-org-2350 43 148 _ _ NNP en-wikipedia-org-2350 43 149 { { -LRB- en-wikipedia-org-2350 43 150 0}}{{\boldsymbol 0}}{{\boldsymbol NNP en-wikipedia-org-2350 43 151 { { -LRB- en-wikipedia-org-2350 43 152 \hat \hat CD en-wikipedia-org-2350 43 153 { { -LRB- en-wikipedia-org-2350 43 154 r}}}_{12 r}}}_{12 NN en-wikipedia-org-2350 43 155 } } -RRB- en-wikipedia-org-2350 43 156 \over \over CD en-wikipedia-org-2350 43 157 |{\boldsymbol |{\boldsymbol NN en-wikipedia-org-2350 43 158 { { -LRB- en-wikipedia-org-2350 43 159 r}}_{12}|^{2 r}}_{12}|^{2 NNP en-wikipedia-org-2350 43 160 } } -RRB- en-wikipedia-org-2350 43 161 } } -RRB- en-wikipedia-org-2350 43 162 } } -RRB- en-wikipedia-org-2350 43 163 where where WRB en-wikipedia-org-2350 43 164 r r NNP en-wikipedia-org-2350 43 165 12 12 CD en-wikipedia-org-2350 43 166 = = SYM en-wikipedia-org-2350 43 167 r r NN en-wikipedia-org-2350 43 168 1 1 CD en-wikipedia-org-2350 43 169 − − NNP en-wikipedia-org-2350 43 170 r r NN en-wikipedia-org-2350 43 171 2 2 CD en-wikipedia-org-2350 43 172 { { -LRB- en-wikipedia-org-2350 43 173 \textstyle \textstyle CD en-wikipedia-org-2350 43 174 { { -LRB- en-wikipedia-org-2350 43 175 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 43 176 { { -LRB- en-wikipedia-org-2350 43 177 r}}_{12}={\boldsymbol r}}_{12}={\boldsymbol NNP en-wikipedia-org-2350 43 178 { { -LRB- en-wikipedia-org-2350 43 179 r}}_{1}-{\boldsymbol r}}_{1}-{\boldsymbol NNP en-wikipedia-org-2350 43 180 { { -LRB- en-wikipedia-org-2350 43 181 r}}_{2 r}}_{2 NNP en-wikipedia-org-2350 43 182 } } -RRB- en-wikipedia-org-2350 43 183 } } -RRB- en-wikipedia-org-2350 43 184 is be VBZ en-wikipedia-org-2350 43 185 the the DT en-wikipedia-org-2350 43 186 vectorial vectorial JJ en-wikipedia-org-2350 43 187 distance distance NN en-wikipedia-org-2350 43 188 between between IN en-wikipedia-org-2350 43 189 the the DT en-wikipedia-org-2350 43 190 charges charge NNS en-wikipedia-org-2350 43 191 , , , en-wikipedia-org-2350 43 192 r r NN en-wikipedia-org-2350 43 193 ^ ^ NN en-wikipedia-org-2350 43 194 12 12 CD en-wikipedia-org-2350 43 195 = = SYM en-wikipedia-org-2350 43 196 r r NNP en-wikipedia-org-2350 43 197 12 12 CD en-wikipedia-org-2350 43 198 | | CD en-wikipedia-org-2350 43 199 r r CD en-wikipedia-org-2350 43 200 12 12 CD en-wikipedia-org-2350 43 201 | | CD en-wikipedia-org-2350 43 202 { { -LRB- en-wikipedia-org-2350 43 203 \textstyle \textstyle CD en-wikipedia-org-2350 43 204 { { -LRB- en-wikipedia-org-2350 43 205 \widehat \widehat CD en-wikipedia-org-2350 43 206 { { -LRB- en-wikipedia-org-2350 43 207 \mathbf \mathbf CD en-wikipedia-org-2350 43 208 { { -LRB- en-wikipedia-org-2350 43 209 r r NN en-wikipedia-org-2350 43 210 } } -RRB- en-wikipedia-org-2350 43 211 } } -RRB- en-wikipedia-org-2350 43 212 } } -RRB- en-wikipedia-org-2350 43 213 _ _ NNP en-wikipedia-org-2350 43 214 { { -LRB- en-wikipedia-org-2350 43 215 12}={\frac 12}={\frac NNP en-wikipedia-org-2350 43 216 { { -LRB- en-wikipedia-org-2350 43 217 \mathbf \mathbf CD en-wikipedia-org-2350 43 218 { { -LRB- en-wikipedia-org-2350 43 219 r r NN en-wikipedia-org-2350 43 220 } } -RRB- en-wikipedia-org-2350 43 221 _ _ NNP en-wikipedia-org-2350 43 222 { { -LRB- en-wikipedia-org-2350 43 223 12}}{|\mathbf 12}}{|\mathbf NNP en-wikipedia-org-2350 43 224 { { -LRB- en-wikipedia-org-2350 43 225 r r NN en-wikipedia-org-2350 43 226 } } -RRB- en-wikipedia-org-2350 43 227 _ _ NNP en-wikipedia-org-2350 43 228 { { -LRB- en-wikipedia-org-2350 43 229 12}| 12}| NNP en-wikipedia-org-2350 43 230 } } -RRB- en-wikipedia-org-2350 43 231 } } -RRB- en-wikipedia-org-2350 43 232 } } -RRB- en-wikipedia-org-2350 43 233 a a DT en-wikipedia-org-2350 43 234 unit unit NN en-wikipedia-org-2350 43 235 vector vector NN en-wikipedia-org-2350 43 236 pointing point VBG en-wikipedia-org-2350 43 237 from from IN en-wikipedia-org-2350 43 238 q q NNP en-wikipedia-org-2350 43 239 2 2 CD en-wikipedia-org-2350 43 240 { { -LRB- en-wikipedia-org-2350 43 241 \textstyle \textstyle CD en-wikipedia-org-2350 43 242 q_{2 q_{2 NNP en-wikipedia-org-2350 43 243 } } -RRB- en-wikipedia-org-2350 43 244 } } -RRB- en-wikipedia-org-2350 43 245 to to IN en-wikipedia-org-2350 43 246 q q NNP en-wikipedia-org-2350 43 247 1 1 CD en-wikipedia-org-2350 43 248 { { -LRB- en-wikipedia-org-2350 43 249 \textstyle \textstyle CD en-wikipedia-org-2350 43 250 q_{1 q_{1 NN en-wikipedia-org-2350 43 251 } } -RRB- en-wikipedia-org-2350 43 252 } } -RRB- en-wikipedia-org-2350 43 253 , , , en-wikipedia-org-2350 43 254 and and CC en-wikipedia-org-2350 43 255 ε ε DT en-wikipedia-org-2350 43 256 0 0 CD en-wikipedia-org-2350 43 257 { { -LRB- en-wikipedia-org-2350 43 258 \displaystyle \displaystyle CD en-wikipedia-org-2350 43 259 \varepsilon \varepsilon CD en-wikipedia-org-2350 43 260 _ _ NNP en-wikipedia-org-2350 43 261 { { -LRB- en-wikipedia-org-2350 43 262 0 0 CD en-wikipedia-org-2350 43 263 } } -RRB- en-wikipedia-org-2350 43 264 } } -RRB- en-wikipedia-org-2350 43 265 the the DT en-wikipedia-org-2350 43 266 electric electric JJ en-wikipedia-org-2350 43 267 constant constant NN en-wikipedia-org-2350 43 268 . . . en-wikipedia-org-2350 44 1 The the DT en-wikipedia-org-2350 44 2 vector vector NN en-wikipedia-org-2350 44 3 form form NN en-wikipedia-org-2350 44 4 of of IN en-wikipedia-org-2350 44 5 Coulomb Coulomb NNP en-wikipedia-org-2350 44 6 's 's POS en-wikipedia-org-2350 44 7 law law NN en-wikipedia-org-2350 44 8 is be VBZ en-wikipedia-org-2350 44 9 simply simply RB en-wikipedia-org-2350 44 10 the the DT en-wikipedia-org-2350 44 11 scalar scalar JJ en-wikipedia-org-2350 44 12 definition definition NN en-wikipedia-org-2350 44 13 of of IN en-wikipedia-org-2350 44 14 the the DT en-wikipedia-org-2350 44 15 law law NN en-wikipedia-org-2350 44 16 with with IN en-wikipedia-org-2350 44 17 the the DT en-wikipedia-org-2350 44 18 direction direction NN en-wikipedia-org-2350 44 19 given give VBN en-wikipedia-org-2350 44 20 by by IN en-wikipedia-org-2350 44 21 the the DT en-wikipedia-org-2350 44 22 unit unit NN en-wikipedia-org-2350 44 23 vector vector NN en-wikipedia-org-2350 44 24 , , , en-wikipedia-org-2350 44 25 r r NNP en-wikipedia-org-2350 44 26 ^ ^ NN en-wikipedia-org-2350 44 27 12 12 CD en-wikipedia-org-2350 44 28 { { -LRB- en-wikipedia-org-2350 44 29 \textstyle \textstyle CD en-wikipedia-org-2350 44 30 { { -LRB- en-wikipedia-org-2350 44 31 \widehat \widehat CD en-wikipedia-org-2350 44 32 { { -LRB- en-wikipedia-org-2350 44 33 \mathbf \mathbf CD en-wikipedia-org-2350 44 34 { { -LRB- en-wikipedia-org-2350 44 35 r r NN en-wikipedia-org-2350 44 36 } } -RRB- en-wikipedia-org-2350 44 37 } } -RRB- en-wikipedia-org-2350 44 38 } } -RRB- en-wikipedia-org-2350 44 39 _ _ NNP en-wikipedia-org-2350 44 40 { { -LRB- en-wikipedia-org-2350 44 41 12 12 CD en-wikipedia-org-2350 44 42 } } -RRB- en-wikipedia-org-2350 44 43 } } -RRB- en-wikipedia-org-2350 44 44 , , , en-wikipedia-org-2350 44 45 parallel parallel JJ en-wikipedia-org-2350 44 46 with with IN en-wikipedia-org-2350 44 47 the the DT en-wikipedia-org-2350 44 48 line line NN en-wikipedia-org-2350 44 49 from from IN en-wikipedia-org-2350 44 50 charge charge NN en-wikipedia-org-2350 44 51 q q NNP en-wikipedia-org-2350 44 52 2 2 CD en-wikipedia-org-2350 44 53 { { -LRB- en-wikipedia-org-2350 44 54 \displaystyle \displaystyle CD en-wikipedia-org-2350 44 55 q_{2 q_{2 NN en-wikipedia-org-2350 44 56 } } -RRB- en-wikipedia-org-2350 44 57 } } -RRB- en-wikipedia-org-2350 44 58 to to TO en-wikipedia-org-2350 44 59 charge charge VB en-wikipedia-org-2350 44 60 q q NNP en-wikipedia-org-2350 44 61 1 1 CD en-wikipedia-org-2350 44 62 { { -LRB- en-wikipedia-org-2350 44 63 \displaystyle \displaystyle CD en-wikipedia-org-2350 44 64 q_{1 q_{1 NN en-wikipedia-org-2350 44 65 } } -RRB- en-wikipedia-org-2350 44 66 } } -RRB- en-wikipedia-org-2350 44 67 . . . en-wikipedia-org-2350 45 1 [ [ -LRB- en-wikipedia-org-2350 45 2 20 20 CD en-wikipedia-org-2350 45 3 ] ] -RRB- en-wikipedia-org-2350 45 4 If if IN en-wikipedia-org-2350 45 5 both both DT en-wikipedia-org-2350 45 6 charges charge NNS en-wikipedia-org-2350 45 7 have have VBP en-wikipedia-org-2350 45 8 the the DT en-wikipedia-org-2350 45 9 same same JJ en-wikipedia-org-2350 45 10 sign sign NN en-wikipedia-org-2350 45 11 ( ( -LRB- en-wikipedia-org-2350 45 12 like like IN en-wikipedia-org-2350 45 13 charges charge NNS en-wikipedia-org-2350 45 14 ) ) -RRB- en-wikipedia-org-2350 45 15 then then RB en-wikipedia-org-2350 45 16 the the DT en-wikipedia-org-2350 45 17 product product NN en-wikipedia-org-2350 45 18 q q NN en-wikipedia-org-2350 45 19 1 1 CD en-wikipedia-org-2350 45 20 q q NN en-wikipedia-org-2350 45 21 2 2 CD en-wikipedia-org-2350 45 22 { { -LRB- en-wikipedia-org-2350 45 23 \displaystyle \displaystyle CD en-wikipedia-org-2350 45 24 q_{1}q_{2 q_{1}q_{2 NNP en-wikipedia-org-2350 45 25 } } -RRB- en-wikipedia-org-2350 45 26 } } -RRB- en-wikipedia-org-2350 45 27 is be VBZ en-wikipedia-org-2350 45 28 positive positive JJ en-wikipedia-org-2350 45 29 and and CC en-wikipedia-org-2350 45 30 the the DT en-wikipedia-org-2350 45 31 direction direction NN en-wikipedia-org-2350 45 32 of of IN en-wikipedia-org-2350 45 33 the the DT en-wikipedia-org-2350 45 34 force force NN en-wikipedia-org-2350 45 35 on on IN en-wikipedia-org-2350 45 36 q q NNP en-wikipedia-org-2350 45 37 1 1 CD en-wikipedia-org-2350 45 38 { { -LRB- en-wikipedia-org-2350 45 39 \displaystyle \displaystyle CD en-wikipedia-org-2350 45 40 q_{1 q_{1 NN en-wikipedia-org-2350 45 41 } } -RRB- en-wikipedia-org-2350 45 42 } } -RRB- en-wikipedia-org-2350 45 43 is be VBZ en-wikipedia-org-2350 45 44 given give VBN en-wikipedia-org-2350 45 45 by by IN en-wikipedia-org-2350 45 46 r r NN en-wikipedia-org-2350 45 47 ^ ^ NNP en-wikipedia-org-2350 45 48 12 12 CD en-wikipedia-org-2350 45 49 { { -LRB- en-wikipedia-org-2350 45 50 \textstyle \textstyle CD en-wikipedia-org-2350 45 51 { { -LRB- en-wikipedia-org-2350 45 52 \widehat \widehat CD en-wikipedia-org-2350 45 53 { { -LRB- en-wikipedia-org-2350 45 54 \mathbf \mathbf CD en-wikipedia-org-2350 45 55 { { -LRB- en-wikipedia-org-2350 45 56 r r NN en-wikipedia-org-2350 45 57 } } -RRB- en-wikipedia-org-2350 45 58 } } -RRB- en-wikipedia-org-2350 45 59 } } -RRB- en-wikipedia-org-2350 45 60 _ _ NNP en-wikipedia-org-2350 45 61 { { -LRB- en-wikipedia-org-2350 45 62 12 12 CD en-wikipedia-org-2350 45 63 } } -RRB- en-wikipedia-org-2350 45 64 } } -RRB- en-wikipedia-org-2350 45 65 ; ; : en-wikipedia-org-2350 45 66 the the DT en-wikipedia-org-2350 45 67 charges charge NNS en-wikipedia-org-2350 45 68 repel repel VBP en-wikipedia-org-2350 45 69 each each DT en-wikipedia-org-2350 45 70 other other JJ en-wikipedia-org-2350 45 71 . . . en-wikipedia-org-2350 46 1 If if IN en-wikipedia-org-2350 46 2 the the DT en-wikipedia-org-2350 46 3 charges charge NNS en-wikipedia-org-2350 46 4 have have VBP en-wikipedia-org-2350 46 5 opposite opposite JJ en-wikipedia-org-2350 46 6 signs sign NNS en-wikipedia-org-2350 46 7 then then RB en-wikipedia-org-2350 46 8 the the DT en-wikipedia-org-2350 46 9 product product NN en-wikipedia-org-2350 46 10 q q NN en-wikipedia-org-2350 46 11 1 1 CD en-wikipedia-org-2350 46 12 q q NN en-wikipedia-org-2350 46 13 2 2 CD en-wikipedia-org-2350 46 14 { { -LRB- en-wikipedia-org-2350 46 15 \displaystyle \displaystyle CD en-wikipedia-org-2350 46 16 q_{1}q_{2 q_{1}q_{2 NNP en-wikipedia-org-2350 46 17 } } -RRB- en-wikipedia-org-2350 46 18 } } -RRB- en-wikipedia-org-2350 46 19 is be VBZ en-wikipedia-org-2350 46 20 negative negative JJ en-wikipedia-org-2350 46 21 and and CC en-wikipedia-org-2350 46 22 the the DT en-wikipedia-org-2350 46 23 direction direction NN en-wikipedia-org-2350 46 24 of of IN en-wikipedia-org-2350 46 25 the the DT en-wikipedia-org-2350 46 26 force force NN en-wikipedia-org-2350 46 27 on on IN en-wikipedia-org-2350 46 28 q q NNP en-wikipedia-org-2350 46 29 1 1 CD en-wikipedia-org-2350 46 30 { { -LRB- en-wikipedia-org-2350 46 31 \displaystyle \displaystyle CD en-wikipedia-org-2350 46 32 q_{1 q_{1 NN en-wikipedia-org-2350 46 33 } } -RRB- en-wikipedia-org-2350 46 34 } } -RRB- en-wikipedia-org-2350 46 35 is be VBZ en-wikipedia-org-2350 46 36 − − NNP en-wikipedia-org-2350 46 37 r r NN en-wikipedia-org-2350 46 38 ^ ^ NN en-wikipedia-org-2350 46 39 12 12 CD en-wikipedia-org-2350 46 40 { { -LRB- en-wikipedia-org-2350 46 41 \textstyle \textstyle CD en-wikipedia-org-2350 46 42 -{\hat -{\hat CD en-wikipedia-org-2350 46 43 { { -LRB- en-wikipedia-org-2350 46 44 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 46 45 { { -LRB- en-wikipedia-org-2350 46 46 r}}}_{12 r}}}_{12 NN en-wikipedia-org-2350 46 47 } } -RRB- en-wikipedia-org-2350 46 48 } } -RRB- en-wikipedia-org-2350 46 49 ; ; : en-wikipedia-org-2350 46 50 the the DT en-wikipedia-org-2350 46 51 charges charge NNS en-wikipedia-org-2350 46 52 attract attract VBP en-wikipedia-org-2350 46 53 each each DT en-wikipedia-org-2350 46 54 other other JJ en-wikipedia-org-2350 46 55 . . . en-wikipedia-org-2350 47 1 The the DT en-wikipedia-org-2350 47 2 electrostatic electrostatic JJ en-wikipedia-org-2350 47 3 force force NN en-wikipedia-org-2350 47 4 F f NN en-wikipedia-org-2350 47 5 2 2 CD en-wikipedia-org-2350 47 6 { { -LRB- en-wikipedia-org-2350 47 7 \textstyle \textstyle CD en-wikipedia-org-2350 47 8 { { -LRB- en-wikipedia-org-2350 47 9 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 47 10 { { -LRB- en-wikipedia-org-2350 47 11 F}}_{2 f}}_{2 NN en-wikipedia-org-2350 47 12 } } -RRB- en-wikipedia-org-2350 47 13 } } -RRB- en-wikipedia-org-2350 47 14 experienced experience VBN en-wikipedia-org-2350 47 15 by by IN en-wikipedia-org-2350 47 16 q q NNP en-wikipedia-org-2350 47 17 2 2 CD en-wikipedia-org-2350 47 18 { { -LRB- en-wikipedia-org-2350 47 19 \displaystyle \displaystyle CD en-wikipedia-org-2350 47 20 q_{2 q_{2 NN en-wikipedia-org-2350 47 21 } } -RRB- en-wikipedia-org-2350 47 22 } } -RRB- en-wikipedia-org-2350 47 23 , , , en-wikipedia-org-2350 47 24 according accord VBG en-wikipedia-org-2350 47 25 to to IN en-wikipedia-org-2350 47 26 Newton Newton NNP en-wikipedia-org-2350 47 27 's 's POS en-wikipedia-org-2350 47 28 third third JJ en-wikipedia-org-2350 47 29 law law NN en-wikipedia-org-2350 47 30 , , , en-wikipedia-org-2350 47 31 is be VBZ en-wikipedia-org-2350 47 32 F f NN en-wikipedia-org-2350 47 33 2 2 CD en-wikipedia-org-2350 47 34 = = SYM en-wikipedia-org-2350 47 35 − − NNP en-wikipedia-org-2350 47 36 F F NNP en-wikipedia-org-2350 47 37 1 1 CD en-wikipedia-org-2350 47 38 { { -LRB- en-wikipedia-org-2350 47 39 \textstyle \textstyle CD en-wikipedia-org-2350 47 40 { { -LRB- en-wikipedia-org-2350 47 41 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 47 42 { { -LRB- en-wikipedia-org-2350 47 43 F}}_{2}=-{\boldsymbol f}}_{2}=-{\boldsymbol IN en-wikipedia-org-2350 47 44 { { -LRB- en-wikipedia-org-2350 47 45 F}}_{1 F}}_{1 NNS en-wikipedia-org-2350 47 46 } } -RRB- en-wikipedia-org-2350 47 47 } } -RRB- en-wikipedia-org-2350 47 48 . . . en-wikipedia-org-2350 48 1 System system NN en-wikipedia-org-2350 48 2 of of IN en-wikipedia-org-2350 48 3 discrete discrete JJ en-wikipedia-org-2350 48 4 charges[edit charges[edit LS en-wikipedia-org-2350 48 5 ] ] -RRB- en-wikipedia-org-2350 48 6 The the DT en-wikipedia-org-2350 48 7 law law NN en-wikipedia-org-2350 48 8 of of IN en-wikipedia-org-2350 48 9 superposition superposition NN en-wikipedia-org-2350 48 10 allows allow VBZ en-wikipedia-org-2350 48 11 Coulomb Coulomb NNP en-wikipedia-org-2350 48 12 's 's POS en-wikipedia-org-2350 48 13 law law NN en-wikipedia-org-2350 48 14 to to TO en-wikipedia-org-2350 48 15 be be VB en-wikipedia-org-2350 48 16 extended extend VBN en-wikipedia-org-2350 48 17 to to TO en-wikipedia-org-2350 48 18 include include VB en-wikipedia-org-2350 48 19 any any DT en-wikipedia-org-2350 48 20 number number NN en-wikipedia-org-2350 48 21 of of IN en-wikipedia-org-2350 48 22 point point NN en-wikipedia-org-2350 48 23 charges charge NNS en-wikipedia-org-2350 48 24 . . . en-wikipedia-org-2350 49 1 The the DT en-wikipedia-org-2350 49 2 force force NN en-wikipedia-org-2350 49 3 acting act VBG en-wikipedia-org-2350 49 4 on on IN en-wikipedia-org-2350 49 5 a a DT en-wikipedia-org-2350 49 6 point point NN en-wikipedia-org-2350 49 7 charge charge NN en-wikipedia-org-2350 49 8 due due IN en-wikipedia-org-2350 49 9 to to IN en-wikipedia-org-2350 49 10 a a DT en-wikipedia-org-2350 49 11 system system NN en-wikipedia-org-2350 49 12 of of IN en-wikipedia-org-2350 49 13 point point NN en-wikipedia-org-2350 49 14 charges charge NNS en-wikipedia-org-2350 49 15 is be VBZ en-wikipedia-org-2350 49 16 simply simply RB en-wikipedia-org-2350 49 17 the the DT en-wikipedia-org-2350 49 18 vector vector NN en-wikipedia-org-2350 49 19 addition addition NN en-wikipedia-org-2350 49 20 of of IN en-wikipedia-org-2350 49 21 the the DT en-wikipedia-org-2350 49 22 individual individual JJ en-wikipedia-org-2350 49 23 forces force NNS en-wikipedia-org-2350 49 24 acting act VBG en-wikipedia-org-2350 49 25 alone alone RB en-wikipedia-org-2350 49 26 on on IN en-wikipedia-org-2350 49 27 that that DT en-wikipedia-org-2350 49 28 point point NN en-wikipedia-org-2350 49 29 charge charge NN en-wikipedia-org-2350 49 30 due due IN en-wikipedia-org-2350 49 31 to to IN en-wikipedia-org-2350 49 32 each each DT en-wikipedia-org-2350 49 33 one one CD en-wikipedia-org-2350 49 34 of of IN en-wikipedia-org-2350 49 35 the the DT en-wikipedia-org-2350 49 36 charges charge NNS en-wikipedia-org-2350 49 37 . . . en-wikipedia-org-2350 50 1 The the DT en-wikipedia-org-2350 50 2 resulting result VBG en-wikipedia-org-2350 50 3 force force NN en-wikipedia-org-2350 50 4 vector vector NN en-wikipedia-org-2350 50 5 is be VBZ en-wikipedia-org-2350 50 6 parallel parallel JJ en-wikipedia-org-2350 50 7 to to IN en-wikipedia-org-2350 50 8 the the DT en-wikipedia-org-2350 50 9 electric electric JJ en-wikipedia-org-2350 50 10 field field NN en-wikipedia-org-2350 50 11 vector vector NN en-wikipedia-org-2350 50 12 at at IN en-wikipedia-org-2350 50 13 that that DT en-wikipedia-org-2350 50 14 point point NN en-wikipedia-org-2350 50 15 , , , en-wikipedia-org-2350 50 16 with with IN en-wikipedia-org-2350 50 17 that that DT en-wikipedia-org-2350 50 18 point point NN en-wikipedia-org-2350 50 19 charge charge NN en-wikipedia-org-2350 50 20 removed remove VBN en-wikipedia-org-2350 50 21 . . . en-wikipedia-org-2350 51 1 The the DT en-wikipedia-org-2350 51 2 force force NN en-wikipedia-org-2350 51 3 F f NN en-wikipedia-org-2350 51 4 { { -LRB- en-wikipedia-org-2350 51 5 \textstyle \textstyle CD en-wikipedia-org-2350 51 6 { { -LRB- en-wikipedia-org-2350 51 7 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 8 { { -LRB- en-wikipedia-org-2350 51 9 F f NN en-wikipedia-org-2350 51 10 } } -RRB- en-wikipedia-org-2350 51 11 } } -RRB- en-wikipedia-org-2350 51 12 } } -RRB- en-wikipedia-org-2350 51 13 on on IN en-wikipedia-org-2350 51 14 a a DT en-wikipedia-org-2350 51 15 small small JJ en-wikipedia-org-2350 51 16 charge charge NN en-wikipedia-org-2350 51 17 q q NN en-wikipedia-org-2350 51 18 { { -LRB- en-wikipedia-org-2350 51 19 \displaystyle \displaystyle CD en-wikipedia-org-2350 51 20 q q NN en-wikipedia-org-2350 51 21 } } -RRB- en-wikipedia-org-2350 51 22 at at IN en-wikipedia-org-2350 51 23 position position NN en-wikipedia-org-2350 51 24 r r NN en-wikipedia-org-2350 51 25 { { -LRB- en-wikipedia-org-2350 51 26 \textstyle \textstyle CD en-wikipedia-org-2350 51 27 { { -LRB- en-wikipedia-org-2350 51 28 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 29 { { -LRB- en-wikipedia-org-2350 51 30 r r NN en-wikipedia-org-2350 51 31 } } -RRB- en-wikipedia-org-2350 51 32 } } -RRB- en-wikipedia-org-2350 51 33 } } -RRB- en-wikipedia-org-2350 51 34 , , , en-wikipedia-org-2350 51 35 due due IN en-wikipedia-org-2350 51 36 to to IN en-wikipedia-org-2350 51 37 a a DT en-wikipedia-org-2350 51 38 system system NN en-wikipedia-org-2350 51 39 of of IN en-wikipedia-org-2350 51 40 N n NN en-wikipedia-org-2350 51 41 { { -LRB- en-wikipedia-org-2350 51 42 \textstyle \textstyle CD en-wikipedia-org-2350 51 43 N n NN en-wikipedia-org-2350 51 44 } } -RRB- en-wikipedia-org-2350 51 45 discrete discrete JJ en-wikipedia-org-2350 51 46 charges charge NNS en-wikipedia-org-2350 51 47 in in IN en-wikipedia-org-2350 51 48 vacuum vacuum NN en-wikipedia-org-2350 51 49 is[19 is[19 NNP en-wikipedia-org-2350 51 50 ] ] -RRB- en-wikipedia-org-2350 51 51 F F NNP en-wikipedia-org-2350 51 52 ( ( -LRB- en-wikipedia-org-2350 51 53 r r NNP en-wikipedia-org-2350 51 54 ) ) -RRB- en-wikipedia-org-2350 51 55 = = SYM en-wikipedia-org-2350 51 56 q q NNP en-wikipedia-org-2350 51 57 4 4 CD en-wikipedia-org-2350 51 58 π π NN en-wikipedia-org-2350 51 59 ε ε NN en-wikipedia-org-2350 51 60 0 0 CD en-wikipedia-org-2350 51 61 ∑ ∑ . en-wikipedia-org-2350 51 62 i i NN en-wikipedia-org-2350 51 63 = = SYM en-wikipedia-org-2350 51 64 1 1 CD en-wikipedia-org-2350 51 65 N n CD en-wikipedia-org-2350 51 66 q q NNP en-wikipedia-org-2350 51 67 i i NN en-wikipedia-org-2350 51 68 r r NN en-wikipedia-org-2350 51 69 − − NNP en-wikipedia-org-2350 51 70 r r NNP en-wikipedia-org-2350 51 71 i i NN en-wikipedia-org-2350 51 72 | | NNP en-wikipedia-org-2350 51 73 r r NNP en-wikipedia-org-2350 51 74 − − NNP en-wikipedia-org-2350 51 75 r r NNP en-wikipedia-org-2350 51 76 i i NN en-wikipedia-org-2350 51 77 | | CD en-wikipedia-org-2350 51 78 3 3 CD en-wikipedia-org-2350 51 79 = = SYM en-wikipedia-org-2350 51 80 q q NNP en-wikipedia-org-2350 51 81 4 4 CD en-wikipedia-org-2350 51 82 π π NN en-wikipedia-org-2350 51 83 ε ε NN en-wikipedia-org-2350 51 84 0 0 CD en-wikipedia-org-2350 51 85 ∑ ∑ . en-wikipedia-org-2350 51 86 i i NN en-wikipedia-org-2350 51 87 = = SYM en-wikipedia-org-2350 51 88 1 1 CD en-wikipedia-org-2350 51 89 N n CD en-wikipedia-org-2350 51 90 q q NN en-wikipedia-org-2350 51 91 i i NN en-wikipedia-org-2350 51 92 R r NN en-wikipedia-org-2350 51 93 i i PRP en-wikipedia-org-2350 51 94 ^ ^ VBP en-wikipedia-org-2350 51 95 | | NNP en-wikipedia-org-2350 51 96 R r NN en-wikipedia-org-2350 51 97 i i NN en-wikipedia-org-2350 51 98 | | CD en-wikipedia-org-2350 51 99 2 2 CD en-wikipedia-org-2350 51 100 { { -LRB- en-wikipedia-org-2350 51 101 \displaystyle \displaystyle CD en-wikipedia-org-2350 51 102 { { -LRB- en-wikipedia-org-2350 51 103 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 104 { { -LRB- en-wikipedia-org-2350 51 105 F}}({\boldsymbol F}}({\boldsymbol NNP en-wikipedia-org-2350 51 106 { { -LRB- en-wikipedia-org-2350 51 107 r}})={q r}})={q NNP en-wikipedia-org-2350 51 108 \over \over NNP en-wikipedia-org-2350 51 109 4\pi 4\pi CD en-wikipedia-org-2350 51 110 \varepsilon \varepsilon CD en-wikipedia-org-2350 51 111 _ _ NNP en-wikipedia-org-2350 51 112 { { -LRB- en-wikipedia-org-2350 51 113 0}}\sum 0}}\sum CD en-wikipedia-org-2350 51 114 _ _ NNP en-wikipedia-org-2350 51 115 { { -LRB- en-wikipedia-org-2350 51 116 i=1}^{N}q_{i}{\frac i=1}^{n}q_{i}{\frac RB en-wikipedia-org-2350 51 117 { { -LRB- en-wikipedia-org-2350 51 118 { { -LRB- en-wikipedia-org-2350 51 119 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 120 { { -LRB- en-wikipedia-org-2350 51 121 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 51 122 { { -LRB- en-wikipedia-org-2350 51 123 r}}_{i}}{|{\boldsymbol r}}_{i}}{|{\boldsymbol NNP en-wikipedia-org-2350 51 124 { { -LRB- en-wikipedia-org-2350 51 125 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 51 126 { { -LRB- en-wikipedia-org-2350 51 127 r}}_{i}|^{3}}}={q r}}_{i}|^{3}}}={q NNP en-wikipedia-org-2350 51 128 \over \over CD en-wikipedia-org-2350 51 129 4\pi 4\pi CD en-wikipedia-org-2350 51 130 \varepsilon \varepsilon CD en-wikipedia-org-2350 51 131 _ _ NNP en-wikipedia-org-2350 51 132 { { -LRB- en-wikipedia-org-2350 51 133 0}}\sum 0}}\sum CD en-wikipedia-org-2350 51 134 _ _ NNP en-wikipedia-org-2350 51 135 { { -LRB- en-wikipedia-org-2350 51 136 i=1}^{N}q_{i}{{\hat i=1}^{n}q_{i}{{\hat DT en-wikipedia-org-2350 51 137 { { -LRB- en-wikipedia-org-2350 51 138 { { -LRB- en-wikipedia-org-2350 51 139 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 140 { { -LRB- en-wikipedia-org-2350 51 141 R}}_{i r}}_{i NN en-wikipedia-org-2350 51 142 } } -RRB- en-wikipedia-org-2350 51 143 } } -RRB- en-wikipedia-org-2350 51 144 } } -RRB- en-wikipedia-org-2350 51 145 \over \over CD en-wikipedia-org-2350 51 146 |{\boldsymbol |{\boldsymbol NN en-wikipedia-org-2350 51 147 { { -LRB- en-wikipedia-org-2350 51 148 R}}_{i}|^{2 r}}_{i}|^{2 NN en-wikipedia-org-2350 51 149 } } -RRB- en-wikipedia-org-2350 51 150 } } -RRB- en-wikipedia-org-2350 51 151 } } -RRB- en-wikipedia-org-2350 51 152 , , , en-wikipedia-org-2350 51 153 where where WRB en-wikipedia-org-2350 51 154 q q NNP en-wikipedia-org-2350 51 155 i i PRP en-wikipedia-org-2350 51 156 { { -LRB- en-wikipedia-org-2350 51 157 \displaystyle \displaystyle CD en-wikipedia-org-2350 51 158 q_{i q_{i NN en-wikipedia-org-2350 51 159 } } -RRB- en-wikipedia-org-2350 51 160 } } -RRB- en-wikipedia-org-2350 51 161 and and CC en-wikipedia-org-2350 51 162 r r NN en-wikipedia-org-2350 51 163 i i NN en-wikipedia-org-2350 51 164 { { -LRB- en-wikipedia-org-2350 51 165 \textstyle \textstyle CD en-wikipedia-org-2350 51 166 { { -LRB- en-wikipedia-org-2350 51 167 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 168 { { -LRB- en-wikipedia-org-2350 51 169 r}}_{i r}}_{i NNP en-wikipedia-org-2350 51 170 } } -RRB- en-wikipedia-org-2350 51 171 } } -RRB- en-wikipedia-org-2350 51 172 are be VBP en-wikipedia-org-2350 51 173 the the DT en-wikipedia-org-2350 51 174 magnitude magnitude NN en-wikipedia-org-2350 51 175 and and CC en-wikipedia-org-2350 51 176 position position NN en-wikipedia-org-2350 51 177 respectively respectively RB en-wikipedia-org-2350 51 178 of of IN en-wikipedia-org-2350 51 179 the the DT en-wikipedia-org-2350 51 180 ith ith NNP en-wikipedia-org-2350 51 181 charge charge NN en-wikipedia-org-2350 51 182 , , , en-wikipedia-org-2350 51 183 R r NN en-wikipedia-org-2350 51 184 ^ ^ NN en-wikipedia-org-2350 51 185 i i PRP en-wikipedia-org-2350 51 186 { { -LRB- en-wikipedia-org-2350 51 187 \textstyle \textstyle CD en-wikipedia-org-2350 51 188 { { -LRB- en-wikipedia-org-2350 51 189 \hat \hat CD en-wikipedia-org-2350 51 190 { { -LRB- en-wikipedia-org-2350 51 191 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 192 { { -LRB- en-wikipedia-org-2350 51 193 R}}}_{i R}}}_{i NNP en-wikipedia-org-2350 51 194 } } -RRB- en-wikipedia-org-2350 51 195 } } -RRB- en-wikipedia-org-2350 51 196 is be VBZ en-wikipedia-org-2350 51 197 a a DT en-wikipedia-org-2350 51 198 unit unit NN en-wikipedia-org-2350 51 199 vector vector NN en-wikipedia-org-2350 51 200 in in IN en-wikipedia-org-2350 51 201 the the DT en-wikipedia-org-2350 51 202 direction direction NN en-wikipedia-org-2350 51 203 of of IN en-wikipedia-org-2350 51 204 R r NN en-wikipedia-org-2350 51 205 i i NN en-wikipedia-org-2350 51 206 = = SYM en-wikipedia-org-2350 51 207 r r NN en-wikipedia-org-2350 51 208 − − NNP en-wikipedia-org-2350 51 209 r r NN en-wikipedia-org-2350 51 210 i i PRP en-wikipedia-org-2350 51 211 { { -LRB- en-wikipedia-org-2350 51 212 \textstyle \textstyle CD en-wikipedia-org-2350 51 213 { { -LRB- en-wikipedia-org-2350 51 214 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 51 215 { { -LRB- en-wikipedia-org-2350 51 216 R}}_{i}={\boldsymbol r}}_{i}={\boldsymbol NN en-wikipedia-org-2350 51 217 { { -LRB- en-wikipedia-org-2350 51 218 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 51 219 { { -LRB- en-wikipedia-org-2350 51 220 r}}_{i r}}_{i NNP en-wikipedia-org-2350 51 221 } } -RRB- en-wikipedia-org-2350 51 222 } } -RRB- en-wikipedia-org-2350 51 223 , , , en-wikipedia-org-2350 51 224 a a DT en-wikipedia-org-2350 51 225 vector vector NN en-wikipedia-org-2350 51 226 pointing point VBG en-wikipedia-org-2350 51 227 from from IN en-wikipedia-org-2350 51 228 charges charge NNS en-wikipedia-org-2350 51 229 q q NNP en-wikipedia-org-2350 51 230 i i NNP en-wikipedia-org-2350 51 231 { { -LRB- en-wikipedia-org-2350 51 232 \displaystyle \displaystyle CD en-wikipedia-org-2350 51 233 q_{i q_{i NN en-wikipedia-org-2350 51 234 } } -RRB- en-wikipedia-org-2350 51 235 } } -RRB- en-wikipedia-org-2350 51 236 to to IN en-wikipedia-org-2350 51 237 q q NNP en-wikipedia-org-2350 51 238 { { -LRB- en-wikipedia-org-2350 51 239 \displaystyle \displaystyle CD en-wikipedia-org-2350 51 240 q q NNP en-wikipedia-org-2350 51 241 } } -RRB- en-wikipedia-org-2350 51 242 . . . en-wikipedia-org-2350 52 1 [ [ -LRB- en-wikipedia-org-2350 52 2 20 20 CD en-wikipedia-org-2350 52 3 ] ] -RRB- en-wikipedia-org-2350 52 4 Continuous continuous JJ en-wikipedia-org-2350 52 5 charge charge NN en-wikipedia-org-2350 52 6 distribution[edit distribution[edit VBZ en-wikipedia-org-2350 52 7 ] ] -RRB- en-wikipedia-org-2350 52 8 In in IN en-wikipedia-org-2350 52 9 this this DT en-wikipedia-org-2350 52 10 case case NN en-wikipedia-org-2350 52 11 , , , en-wikipedia-org-2350 52 12 the the DT en-wikipedia-org-2350 52 13 principle principle NN en-wikipedia-org-2350 52 14 of of IN en-wikipedia-org-2350 52 15 linear linear JJ en-wikipedia-org-2350 52 16 superposition superposition NN en-wikipedia-org-2350 52 17 is be VBZ en-wikipedia-org-2350 52 18 also also RB en-wikipedia-org-2350 52 19 used use VBN en-wikipedia-org-2350 52 20 . . . en-wikipedia-org-2350 53 1 For for IN en-wikipedia-org-2350 53 2 a a DT en-wikipedia-org-2350 53 3 continuous continuous JJ en-wikipedia-org-2350 53 4 charge charge NN en-wikipedia-org-2350 53 5 distribution distribution NN en-wikipedia-org-2350 53 6 , , , en-wikipedia-org-2350 53 7 an an DT en-wikipedia-org-2350 53 8 integral integral NN en-wikipedia-org-2350 53 9 over over IN en-wikipedia-org-2350 53 10 the the DT en-wikipedia-org-2350 53 11 region region NN en-wikipedia-org-2350 53 12 containing contain VBG en-wikipedia-org-2350 53 13 the the DT en-wikipedia-org-2350 53 14 charge charge NN en-wikipedia-org-2350 53 15 is be VBZ en-wikipedia-org-2350 53 16 equivalent equivalent JJ en-wikipedia-org-2350 53 17 to to IN en-wikipedia-org-2350 53 18 an an DT en-wikipedia-org-2350 53 19 infinite infinite JJ en-wikipedia-org-2350 53 20 summation summation NN en-wikipedia-org-2350 53 21 , , , en-wikipedia-org-2350 53 22 treating treat VBG en-wikipedia-org-2350 53 23 each each DT en-wikipedia-org-2350 53 24 infinitesimal infinitesimal JJ en-wikipedia-org-2350 53 25 element element NN en-wikipedia-org-2350 53 26 of of IN en-wikipedia-org-2350 53 27 space space NN en-wikipedia-org-2350 53 28 as as IN en-wikipedia-org-2350 53 29 a a DT en-wikipedia-org-2350 53 30 point point NN en-wikipedia-org-2350 53 31 charge charge NN en-wikipedia-org-2350 53 32 d d NNP en-wikipedia-org-2350 53 33 q q NNP en-wikipedia-org-2350 53 34 { { -LRB- en-wikipedia-org-2350 53 35 \displaystyle \displaystyle CD en-wikipedia-org-2350 53 36 \mathrm \mathrm NN en-wikipedia-org-2350 53 37 { { -LRB- en-wikipedia-org-2350 53 38 d d NNP en-wikipedia-org-2350 53 39 } } -RRB- en-wikipedia-org-2350 53 40 q q NN en-wikipedia-org-2350 53 41 } } -RRB- en-wikipedia-org-2350 53 42 . . . en-wikipedia-org-2350 54 1 The the DT en-wikipedia-org-2350 54 2 distribution distribution NN en-wikipedia-org-2350 54 3 of of IN en-wikipedia-org-2350 54 4 charge charge NN en-wikipedia-org-2350 54 5 is be VBZ en-wikipedia-org-2350 54 6 usually usually RB en-wikipedia-org-2350 54 7 linear linear JJ en-wikipedia-org-2350 54 8 , , , en-wikipedia-org-2350 54 9 surface surface NN en-wikipedia-org-2350 54 10 or or CC en-wikipedia-org-2350 54 11 volumetric volumetric NN en-wikipedia-org-2350 54 12 . . . en-wikipedia-org-2350 55 1 For for IN en-wikipedia-org-2350 55 2 a a DT en-wikipedia-org-2350 55 3 linear linear JJ en-wikipedia-org-2350 55 4 charge charge NN en-wikipedia-org-2350 55 5 distribution distribution NN en-wikipedia-org-2350 55 6 ( ( -LRB- en-wikipedia-org-2350 55 7 a a DT en-wikipedia-org-2350 55 8 good good JJ en-wikipedia-org-2350 55 9 approximation approximation NN en-wikipedia-org-2350 55 10 for for IN en-wikipedia-org-2350 55 11 charge charge NN en-wikipedia-org-2350 55 12 in in IN en-wikipedia-org-2350 55 13 a a DT en-wikipedia-org-2350 55 14 wire wire NN en-wikipedia-org-2350 55 15 ) ) -RRB- en-wikipedia-org-2350 55 16 where where WRB en-wikipedia-org-2350 55 17 λ λ NNP en-wikipedia-org-2350 55 18 ( ( -LRB- en-wikipedia-org-2350 55 19 r r NN en-wikipedia-org-2350 55 20 ′ ′ ADD en-wikipedia-org-2350 55 21 ) ) -RRB- en-wikipedia-org-2350 55 22 { { -LRB- en-wikipedia-org-2350 55 23 \displaystyle \displaystyle CD en-wikipedia-org-2350 55 24 \lambda \lambda CD en-wikipedia-org-2350 55 25 ( ( -LRB- en-wikipedia-org-2350 55 26 { { -LRB- en-wikipedia-org-2350 55 27 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 55 28 { { -LRB- en-wikipedia-org-2350 55 29 r r NN en-wikipedia-org-2350 55 30 } } -RRB- en-wikipedia-org-2350 55 31 } } -RRB- en-wikipedia-org-2350 55 32 ' ' '' en-wikipedia-org-2350 55 33 ) ) -RRB- en-wikipedia-org-2350 55 34 } } -RRB- en-wikipedia-org-2350 55 35 gives give VBZ en-wikipedia-org-2350 55 36 the the DT en-wikipedia-org-2350 55 37 charge charge NN en-wikipedia-org-2350 55 38 per per IN en-wikipedia-org-2350 55 39 unit unit NN en-wikipedia-org-2350 55 40 length length NN en-wikipedia-org-2350 55 41 at at IN en-wikipedia-org-2350 55 42 position position NN en-wikipedia-org-2350 55 43 r r NNP en-wikipedia-org-2350 55 44 ′ ′ ADD en-wikipedia-org-2350 55 45 { { -LRB- en-wikipedia-org-2350 55 46 \displaystyle \displaystyle CD en-wikipedia-org-2350 55 47 { { -LRB- en-wikipedia-org-2350 55 48 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 55 49 { { -LRB- en-wikipedia-org-2350 55 50 r r NN en-wikipedia-org-2350 55 51 } } -RRB- en-wikipedia-org-2350 55 52 } } -RRB- en-wikipedia-org-2350 55 53 ' ' '' en-wikipedia-org-2350 55 54 } } -RRB- en-wikipedia-org-2350 55 55 , , , en-wikipedia-org-2350 55 56 and and CC en-wikipedia-org-2350 55 57 d d NNP en-wikipedia-org-2350 55 58 ℓ ℓ NNP en-wikipedia-org-2350 55 59 ′ ′ CD en-wikipedia-org-2350 55 60 { { -LRB- en-wikipedia-org-2350 55 61 \displaystyle \displaystyle CD en-wikipedia-org-2350 55 62 \mathrm \mathrm NN en-wikipedia-org-2350 55 63 { { -LRB- en-wikipedia-org-2350 55 64 d d NN en-wikipedia-org-2350 55 65 } } -RRB- en-wikipedia-org-2350 55 66 \ell \ell CD en-wikipedia-org-2350 55 67 ' ' '' en-wikipedia-org-2350 55 68 } } -RRB- en-wikipedia-org-2350 55 69 is be VBZ en-wikipedia-org-2350 55 70 an an DT en-wikipedia-org-2350 55 71 infinitesimal infinitesimal JJ en-wikipedia-org-2350 55 72 element element NN en-wikipedia-org-2350 55 73 of of IN en-wikipedia-org-2350 55 74 length length NN en-wikipedia-org-2350 55 75 , , , en-wikipedia-org-2350 55 76 d d NNP en-wikipedia-org-2350 55 77 q q NNP en-wikipedia-org-2350 55 78 ′ ′ ADD en-wikipedia-org-2350 55 79 = = SYM en-wikipedia-org-2350 55 80 λ λ NN en-wikipedia-org-2350 55 81 ( ( -LRB- en-wikipedia-org-2350 55 82 r r NN en-wikipedia-org-2350 55 83 ′ ′ ADD en-wikipedia-org-2350 55 84 ) ) -RRB- en-wikipedia-org-2350 55 85 d d NNP en-wikipedia-org-2350 55 86 ℓ ℓ NNP en-wikipedia-org-2350 55 87 ′ ′ XX en-wikipedia-org-2350 55 88 . . . en-wikipedia-org-2350 56 1 { { -LRB- en-wikipedia-org-2350 56 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 56 3 \mathrm \mathrm NN en-wikipedia-org-2350 56 4 { { -LRB- en-wikipedia-org-2350 56 5 d d NN en-wikipedia-org-2350 56 6 } } -RRB- en-wikipedia-org-2350 56 7 q'=\lambda q'=\lambda NNP en-wikipedia-org-2350 56 8 ( ( -LRB- en-wikipedia-org-2350 56 9 { { -LRB- en-wikipedia-org-2350 56 10 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 56 11 { { -LRB- en-wikipedia-org-2350 56 12 r'}})\,d\ell r'}})\,d\ell NN en-wikipedia-org-2350 56 13 ' ' '' en-wikipedia-org-2350 56 14 . . . en-wikipedia-org-2350 56 15 } } -RRB- en-wikipedia-org-2350 57 1 [ [ -LRB- en-wikipedia-org-2350 57 2 21 21 CD en-wikipedia-org-2350 57 3 ] ] -RRB- en-wikipedia-org-2350 57 4 For for IN en-wikipedia-org-2350 57 5 a a DT en-wikipedia-org-2350 57 6 surface surface NN en-wikipedia-org-2350 57 7 charge charge NN en-wikipedia-org-2350 57 8 distribution distribution NN en-wikipedia-org-2350 57 9 ( ( -LRB- en-wikipedia-org-2350 57 10 a a DT en-wikipedia-org-2350 57 11 good good JJ en-wikipedia-org-2350 57 12 approximation approximation NN en-wikipedia-org-2350 57 13 for for IN en-wikipedia-org-2350 57 14 charge charge NN en-wikipedia-org-2350 57 15 on on IN en-wikipedia-org-2350 57 16 a a DT en-wikipedia-org-2350 57 17 plate plate NN en-wikipedia-org-2350 57 18 in in IN en-wikipedia-org-2350 57 19 a a DT en-wikipedia-org-2350 57 20 parallel parallel JJ en-wikipedia-org-2350 57 21 plate plate NN en-wikipedia-org-2350 57 22 capacitor capacitor NN en-wikipedia-org-2350 57 23 ) ) -RRB- en-wikipedia-org-2350 57 24 where where WRB en-wikipedia-org-2350 57 25 σ σ NNP en-wikipedia-org-2350 57 26 ( ( -LRB- en-wikipedia-org-2350 57 27 r r NNP en-wikipedia-org-2350 57 28 ′ ′ ADD en-wikipedia-org-2350 57 29 ) ) -RRB- en-wikipedia-org-2350 57 30 { { -LRB- en-wikipedia-org-2350 57 31 \displaystyle \displaystyle CD en-wikipedia-org-2350 57 32 \sigma \sigma CD en-wikipedia-org-2350 57 33 ( ( -LRB- en-wikipedia-org-2350 57 34 { { -LRB- en-wikipedia-org-2350 57 35 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 57 36 { { -LRB- en-wikipedia-org-2350 57 37 r r NN en-wikipedia-org-2350 57 38 } } -RRB- en-wikipedia-org-2350 57 39 } } -RRB- en-wikipedia-org-2350 57 40 ' ' '' en-wikipedia-org-2350 57 41 ) ) -RRB- en-wikipedia-org-2350 57 42 } } -RRB- en-wikipedia-org-2350 57 43 gives give VBZ en-wikipedia-org-2350 57 44 the the DT en-wikipedia-org-2350 57 45 charge charge NN en-wikipedia-org-2350 57 46 per per IN en-wikipedia-org-2350 57 47 unit unit NN en-wikipedia-org-2350 57 48 area area NN en-wikipedia-org-2350 57 49 at at IN en-wikipedia-org-2350 57 50 position position NN en-wikipedia-org-2350 57 51 r r NNP en-wikipedia-org-2350 57 52 ′ ′ ADD en-wikipedia-org-2350 57 53 { { -LRB- en-wikipedia-org-2350 57 54 \displaystyle \displaystyle CD en-wikipedia-org-2350 57 55 { { -LRB- en-wikipedia-org-2350 57 56 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 57 57 { { -LRB- en-wikipedia-org-2350 57 58 r r NN en-wikipedia-org-2350 57 59 } } -RRB- en-wikipedia-org-2350 57 60 } } -RRB- en-wikipedia-org-2350 57 61 ' ' '' en-wikipedia-org-2350 57 62 } } -RRB- en-wikipedia-org-2350 57 63 , , , en-wikipedia-org-2350 57 64 and and CC en-wikipedia-org-2350 57 65 d d LS en-wikipedia-org-2350 57 66 A a NN en-wikipedia-org-2350 57 67 ′ ′ CD en-wikipedia-org-2350 57 68 { { -LRB- en-wikipedia-org-2350 57 69 \displaystyle \displaystyle CD en-wikipedia-org-2350 57 70 \mathrm \mathrm NN en-wikipedia-org-2350 57 71 { { -LRB- en-wikipedia-org-2350 57 72 d d NN en-wikipedia-org-2350 57 73 } } -RRB- en-wikipedia-org-2350 57 74 A a NN en-wikipedia-org-2350 57 75 ' ' '' en-wikipedia-org-2350 57 76 } } -RRB- en-wikipedia-org-2350 57 77 is be VBZ en-wikipedia-org-2350 57 78 an an DT en-wikipedia-org-2350 57 79 infinitesimal infinitesimal JJ en-wikipedia-org-2350 57 80 element element NN en-wikipedia-org-2350 57 81 of of IN en-wikipedia-org-2350 57 82 area area NN en-wikipedia-org-2350 57 83 , , , en-wikipedia-org-2350 57 84 d d NNP en-wikipedia-org-2350 57 85 q q NNP en-wikipedia-org-2350 57 86 ′ ′ ADD en-wikipedia-org-2350 57 87 = = SYM en-wikipedia-org-2350 57 88 σ σ NNP en-wikipedia-org-2350 57 89 ( ( -LRB- en-wikipedia-org-2350 57 90 r r NNP en-wikipedia-org-2350 57 91 ′ ′ ADD en-wikipedia-org-2350 57 92 ) ) -RRB- en-wikipedia-org-2350 57 93 d d LS en-wikipedia-org-2350 57 94 A a NN en-wikipedia-org-2350 57 95 ′ ′ XX en-wikipedia-org-2350 57 96 . . . en-wikipedia-org-2350 58 1 { { -LRB- en-wikipedia-org-2350 58 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 58 3 \mathrm \mathrm NN en-wikipedia-org-2350 58 4 { { -LRB- en-wikipedia-org-2350 58 5 d d NNP en-wikipedia-org-2350 58 6 } } -RRB- en-wikipedia-org-2350 58 7 q'=\sigma q'=\sigma NNP en-wikipedia-org-2350 58 8 ( ( -LRB- en-wikipedia-org-2350 58 9 { { -LRB- en-wikipedia-org-2350 58 10 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 58 11 { { -LRB- en-wikipedia-org-2350 58 12 r'}})\,dA r'}})\,da NN en-wikipedia-org-2350 58 13 ' ' '' en-wikipedia-org-2350 58 14 . . . en-wikipedia-org-2350 58 15 } } -RRB- en-wikipedia-org-2350 59 1 For for IN en-wikipedia-org-2350 59 2 a a DT en-wikipedia-org-2350 59 3 volume volume NN en-wikipedia-org-2350 59 4 charge charge NN en-wikipedia-org-2350 59 5 distribution distribution NN en-wikipedia-org-2350 59 6 ( ( -LRB- en-wikipedia-org-2350 59 7 such such JJ en-wikipedia-org-2350 59 8 as as IN en-wikipedia-org-2350 59 9 charge charge NN en-wikipedia-org-2350 59 10 within within IN en-wikipedia-org-2350 59 11 a a DT en-wikipedia-org-2350 59 12 bulk bulk JJ en-wikipedia-org-2350 59 13 metal metal NN en-wikipedia-org-2350 59 14 ) ) -RRB- en-wikipedia-org-2350 59 15 where where WRB en-wikipedia-org-2350 59 16 ρ ρ NNP en-wikipedia-org-2350 59 17 ( ( -LRB- en-wikipedia-org-2350 59 18 r r NN en-wikipedia-org-2350 59 19 ′ ′ ADD en-wikipedia-org-2350 59 20 ) ) -RRB- en-wikipedia-org-2350 59 21 { { -LRB- en-wikipedia-org-2350 59 22 \displaystyle \displaystyle CD en-wikipedia-org-2350 59 23 \rho \rho NN en-wikipedia-org-2350 59 24 ( ( -LRB- en-wikipedia-org-2350 59 25 { { -LRB- en-wikipedia-org-2350 59 26 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 59 27 { { -LRB- en-wikipedia-org-2350 59 28 r r NN en-wikipedia-org-2350 59 29 } } -RRB- en-wikipedia-org-2350 59 30 } } -RRB- en-wikipedia-org-2350 59 31 ' ' '' en-wikipedia-org-2350 59 32 ) ) -RRB- en-wikipedia-org-2350 59 33 } } -RRB- en-wikipedia-org-2350 59 34 gives give VBZ en-wikipedia-org-2350 59 35 the the DT en-wikipedia-org-2350 59 36 charge charge NN en-wikipedia-org-2350 59 37 per per IN en-wikipedia-org-2350 59 38 unit unit NN en-wikipedia-org-2350 59 39 volume volume NN en-wikipedia-org-2350 59 40 at at IN en-wikipedia-org-2350 59 41 position position NN en-wikipedia-org-2350 59 42 r r NNP en-wikipedia-org-2350 59 43 ′ ′ ADD en-wikipedia-org-2350 59 44 { { -LRB- en-wikipedia-org-2350 59 45 \displaystyle \displaystyle CD en-wikipedia-org-2350 59 46 { { -LRB- en-wikipedia-org-2350 59 47 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 59 48 { { -LRB- en-wikipedia-org-2350 59 49 r r NN en-wikipedia-org-2350 59 50 } } -RRB- en-wikipedia-org-2350 59 51 } } -RRB- en-wikipedia-org-2350 59 52 ' ' '' en-wikipedia-org-2350 59 53 } } -RRB- en-wikipedia-org-2350 59 54 , , , en-wikipedia-org-2350 59 55 and and CC en-wikipedia-org-2350 59 56 d d NN en-wikipedia-org-2350 59 57 V v NN en-wikipedia-org-2350 59 58 ′ ′ CD en-wikipedia-org-2350 59 59 { { -LRB- en-wikipedia-org-2350 59 60 \displaystyle \displaystyle CD en-wikipedia-org-2350 59 61 \mathrm \mathrm NN en-wikipedia-org-2350 59 62 { { -LRB- en-wikipedia-org-2350 59 63 d d NN en-wikipedia-org-2350 59 64 } } -RRB- en-wikipedia-org-2350 59 65 V v NN en-wikipedia-org-2350 59 66 ' ' '' en-wikipedia-org-2350 59 67 } } -RRB- en-wikipedia-org-2350 59 68 is be VBZ en-wikipedia-org-2350 59 69 an an DT en-wikipedia-org-2350 59 70 infinitesimal infinitesimal JJ en-wikipedia-org-2350 59 71 element element NN en-wikipedia-org-2350 59 72 of of IN en-wikipedia-org-2350 59 73 volume volume NN en-wikipedia-org-2350 59 74 , , , en-wikipedia-org-2350 59 75 d d NNP en-wikipedia-org-2350 59 76 q q NNP en-wikipedia-org-2350 59 77 ′ ′ ADD en-wikipedia-org-2350 59 78 = = SYM en-wikipedia-org-2350 59 79 ρ ρ FW en-wikipedia-org-2350 59 80 ( ( -LRB- en-wikipedia-org-2350 59 81 r r NN en-wikipedia-org-2350 59 82 ′ ′ ADD en-wikipedia-org-2350 59 83 ) ) -RRB- en-wikipedia-org-2350 59 84 d d NNP en-wikipedia-org-2350 59 85 V v NN en-wikipedia-org-2350 59 86 ′ ′ ADD en-wikipedia-org-2350 59 87 . . . en-wikipedia-org-2350 60 1 { { -LRB- en-wikipedia-org-2350 60 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 60 3 \mathrm \mathrm NN en-wikipedia-org-2350 60 4 { { -LRB- en-wikipedia-org-2350 60 5 d d NN en-wikipedia-org-2350 60 6 } } -RRB- en-wikipedia-org-2350 60 7 q'=\rho q'=\rho NN en-wikipedia-org-2350 60 8 ( ( -LRB- en-wikipedia-org-2350 60 9 { { -LRB- en-wikipedia-org-2350 60 10 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 60 11 { { -LRB- en-wikipedia-org-2350 60 12 r'}})\,dV r'}})\,dv NN en-wikipedia-org-2350 60 13 ' ' '' en-wikipedia-org-2350 60 14 . . . en-wikipedia-org-2350 60 15 } } -RRB- en-wikipedia-org-2350 61 1 [ [ -LRB- en-wikipedia-org-2350 61 2 20 20 CD en-wikipedia-org-2350 61 3 ] ] -RRB- en-wikipedia-org-2350 61 4 The the DT en-wikipedia-org-2350 61 5 force force NN en-wikipedia-org-2350 61 6 on on IN en-wikipedia-org-2350 61 7 a a DT en-wikipedia-org-2350 61 8 small small JJ en-wikipedia-org-2350 61 9 test test NN en-wikipedia-org-2350 61 10 charge charge NN en-wikipedia-org-2350 61 11 q q NNP en-wikipedia-org-2350 61 12 { { -LRB- en-wikipedia-org-2350 61 13 \displaystyle \displaystyle CD en-wikipedia-org-2350 61 14 q q NN en-wikipedia-org-2350 61 15 } } -RRB- en-wikipedia-org-2350 61 16 at at IN en-wikipedia-org-2350 61 17 position position NN en-wikipedia-org-2350 61 18 r r NN en-wikipedia-org-2350 61 19 { { -LRB- en-wikipedia-org-2350 61 20 \displaystyle \displaystyle CD en-wikipedia-org-2350 61 21 { { -LRB- en-wikipedia-org-2350 61 22 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 61 23 { { -LRB- en-wikipedia-org-2350 61 24 r r NN en-wikipedia-org-2350 61 25 } } -RRB- en-wikipedia-org-2350 61 26 } } -RRB- en-wikipedia-org-2350 61 27 } } -RRB- en-wikipedia-org-2350 61 28 in in IN en-wikipedia-org-2350 61 29 vacuum vacuum NN en-wikipedia-org-2350 61 30 is be VBZ en-wikipedia-org-2350 61 31 given give VBN en-wikipedia-org-2350 61 32 by by IN en-wikipedia-org-2350 61 33 the the DT en-wikipedia-org-2350 61 34 integral integral NN en-wikipedia-org-2350 61 35 over over IN en-wikipedia-org-2350 61 36 the the DT en-wikipedia-org-2350 61 37 distribution distribution NN en-wikipedia-org-2350 61 38 of of IN en-wikipedia-org-2350 61 39 charge charge NN en-wikipedia-org-2350 61 40 : : : en-wikipedia-org-2350 61 41 F F NNP en-wikipedia-org-2350 61 42 ( ( -LRB- en-wikipedia-org-2350 61 43 r r NNP en-wikipedia-org-2350 61 44 ) ) -RRB- en-wikipedia-org-2350 61 45 = = SYM en-wikipedia-org-2350 61 46 q q NNP en-wikipedia-org-2350 61 47 4 4 CD en-wikipedia-org-2350 61 48 π π NN en-wikipedia-org-2350 61 49 ε ε NN en-wikipedia-org-2350 61 50 0 0 CD en-wikipedia-org-2350 61 51 ∫ ∫ CD en-wikipedia-org-2350 61 52 d d NNP en-wikipedia-org-2350 61 53 q q NNP en-wikipedia-org-2350 61 54 ′ ′ NNP en-wikipedia-org-2350 61 55 r r NNP en-wikipedia-org-2350 61 56 − − NNP en-wikipedia-org-2350 61 57 r r NNP en-wikipedia-org-2350 61 58 ′ ′ CD en-wikipedia-org-2350 61 59 | | NNP en-wikipedia-org-2350 61 60 r r NNP en-wikipedia-org-2350 61 61 − − NNP en-wikipedia-org-2350 61 62 r r NNP en-wikipedia-org-2350 61 63 ′ ′ CD en-wikipedia-org-2350 61 64 | | NNP en-wikipedia-org-2350 61 65 3 3 CD en-wikipedia-org-2350 61 66 . . . en-wikipedia-org-2350 62 1 { { -LRB- en-wikipedia-org-2350 62 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 62 3 { { -LRB- en-wikipedia-org-2350 62 4 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 62 5 { { -LRB- en-wikipedia-org-2350 62 6 F}}({\boldsymbol F}}({\boldsymbol NNP en-wikipedia-org-2350 62 7 { { -LRB- en-wikipedia-org-2350 62 8 r}})={q r}})={q NNP en-wikipedia-org-2350 62 9 \over \over NNP en-wikipedia-org-2350 62 10 4\pi 4\pi CD en-wikipedia-org-2350 62 11 \varepsilon \varepsilon CD en-wikipedia-org-2350 62 12 _ _ NNP en-wikipedia-org-2350 62 13 { { -LRB- en-wikipedia-org-2350 62 14 0}}\int 0}}\int NN en-wikipedia-org-2350 62 15 \mathrm \mathrm CD en-wikipedia-org-2350 62 16 { { -LRB- en-wikipedia-org-2350 62 17 d d NN en-wikipedia-org-2350 62 18 } } -RRB- en-wikipedia-org-2350 62 19 q'{{\boldsymbol q'{{\boldsymbol NN en-wikipedia-org-2350 62 20 { { -LRB- en-wikipedia-org-2350 62 21 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 62 22 { { -LRB- en-wikipedia-org-2350 62 23 r r NNP en-wikipedia-org-2350 62 24 ' ' '' en-wikipedia-org-2350 62 25 } } -RRB- en-wikipedia-org-2350 62 26 } } -RRB- en-wikipedia-org-2350 62 27 \over \over CD en-wikipedia-org-2350 62 28 |{\boldsymbol |{\boldsymbol NN en-wikipedia-org-2350 62 29 { { -LRB- en-wikipedia-org-2350 62 30 r}}-{\boldsymbol r}}-{\boldsymbol NN en-wikipedia-org-2350 62 31 { { -LRB- en-wikipedia-org-2350 62 32 r'}}|^{3 r'}}|^{3 NNP en-wikipedia-org-2350 62 33 } } -RRB- en-wikipedia-org-2350 62 34 } } -RRB- en-wikipedia-org-2350 62 35 . . . en-wikipedia-org-2350 62 36 } } -RRB- en-wikipedia-org-2350 63 1 Coulomb Coulomb NNP en-wikipedia-org-2350 63 2 's 's POS en-wikipedia-org-2350 63 3 constant[edit constant[edit NN en-wikipedia-org-2350 63 4 ] ] -RRB- en-wikipedia-org-2350 63 5 Main main JJ en-wikipedia-org-2350 63 6 article article NN en-wikipedia-org-2350 63 7 : : : en-wikipedia-org-2350 63 8 Coulomb Coulomb NNP en-wikipedia-org-2350 63 9 's 's POS en-wikipedia-org-2350 63 10 constant constant JJ en-wikipedia-org-2350 63 11 Coulomb Coulomb NNP en-wikipedia-org-2350 63 12 's 's POS en-wikipedia-org-2350 63 13 constant constant NN en-wikipedia-org-2350 63 14 is be VBZ en-wikipedia-org-2350 63 15 a a DT en-wikipedia-org-2350 63 16 proportionality proportionality NN en-wikipedia-org-2350 63 17 factor factor NN en-wikipedia-org-2350 63 18 that that WDT en-wikipedia-org-2350 63 19 appears appear VBZ en-wikipedia-org-2350 63 20 in in IN en-wikipedia-org-2350 63 21 Coulomb Coulomb NNP en-wikipedia-org-2350 63 22 's 's POS en-wikipedia-org-2350 63 23 law law NN en-wikipedia-org-2350 63 24 as as RB en-wikipedia-org-2350 63 25 well well RB en-wikipedia-org-2350 63 26 as as IN en-wikipedia-org-2350 63 27 in in IN en-wikipedia-org-2350 63 28 other other JJ en-wikipedia-org-2350 63 29 electric electric NN en-wikipedia-org-2350 63 30 - - HYPH en-wikipedia-org-2350 63 31 related relate VBN en-wikipedia-org-2350 63 32 formulas formula NNS en-wikipedia-org-2350 63 33 . . . en-wikipedia-org-2350 64 1 Denoted denote VBN en-wikipedia-org-2350 64 2 k k NNP en-wikipedia-org-2350 64 3 e e NNP en-wikipedia-org-2350 64 4 { { -LRB- en-wikipedia-org-2350 64 5 \displaystyle \displaystyle CD en-wikipedia-org-2350 64 6 k_{e k_{e NNP en-wikipedia-org-2350 64 7 } } -RRB- en-wikipedia-org-2350 64 8 } } -RRB- en-wikipedia-org-2350 64 9 , , , en-wikipedia-org-2350 64 10 it -PRON- PRP en-wikipedia-org-2350 64 11 is be VBZ en-wikipedia-org-2350 64 12 also also RB en-wikipedia-org-2350 64 13 called call VBN en-wikipedia-org-2350 64 14 the the DT en-wikipedia-org-2350 64 15 electric electric JJ en-wikipedia-org-2350 64 16 force force NN en-wikipedia-org-2350 64 17 constant constant JJ en-wikipedia-org-2350 64 18 or or CC en-wikipedia-org-2350 64 19 electrostatic electrostatic JJ en-wikipedia-org-2350 64 20 constant[22 constant[22 NN en-wikipedia-org-2350 64 21 ] ] -RRB- en-wikipedia-org-2350 64 22 hence hence RB en-wikipedia-org-2350 64 23 the the DT en-wikipedia-org-2350 64 24 subscript subscript NN en-wikipedia-org-2350 64 25 e e CD en-wikipedia-org-2350 64 26 { { -LRB- en-wikipedia-org-2350 64 27 \displaystyle \displaystyle CD en-wikipedia-org-2350 64 28 e e NN en-wikipedia-org-2350 64 29 } } -RRB- en-wikipedia-org-2350 64 30 . . . en-wikipedia-org-2350 65 1 When when WRB en-wikipedia-org-2350 65 2 the the DT en-wikipedia-org-2350 65 3 electromagnetic electromagnetic JJ en-wikipedia-org-2350 65 4 theory theory NN en-wikipedia-org-2350 65 5 is be VBZ en-wikipedia-org-2350 65 6 expressed express VBN en-wikipedia-org-2350 65 7 in in IN en-wikipedia-org-2350 65 8 the the DT en-wikipedia-org-2350 65 9 International International NNP en-wikipedia-org-2350 65 10 System System NNP en-wikipedia-org-2350 65 11 of of IN en-wikipedia-org-2350 65 12 Units Units NNPS en-wikipedia-org-2350 65 13 , , , en-wikipedia-org-2350 65 14 force force NN en-wikipedia-org-2350 65 15 is be VBZ en-wikipedia-org-2350 65 16 measured measure VBN en-wikipedia-org-2350 65 17 in in IN en-wikipedia-org-2350 65 18 newtons newton NNS en-wikipedia-org-2350 65 19 , , , en-wikipedia-org-2350 65 20 charge charge NN en-wikipedia-org-2350 65 21 in in IN en-wikipedia-org-2350 65 22 coulombs coulomb NNS en-wikipedia-org-2350 65 23 and and CC en-wikipedia-org-2350 65 24 distance distance NN en-wikipedia-org-2350 65 25 in in IN en-wikipedia-org-2350 65 26 meters meter NNS en-wikipedia-org-2350 65 27 . . . en-wikipedia-org-2350 66 1 Coulomb Coulomb NNP en-wikipedia-org-2350 66 2 's 's POS en-wikipedia-org-2350 66 3 constant constant NN en-wikipedia-org-2350 66 4 is be VBZ en-wikipedia-org-2350 66 5 given give VBN en-wikipedia-org-2350 66 6 by by IN en-wikipedia-org-2350 66 7 k k NNP en-wikipedia-org-2350 66 8 e e NNP en-wikipedia-org-2350 66 9 = = SYM en-wikipedia-org-2350 66 10 1 1 CD en-wikipedia-org-2350 66 11 4 4 CD en-wikipedia-org-2350 66 12 π π NN en-wikipedia-org-2350 66 13 ε ε NN en-wikipedia-org-2350 66 14 0 0 CD en-wikipedia-org-2350 66 15 { { -LRB- en-wikipedia-org-2350 66 16 \displaystyle \displaystyle CD en-wikipedia-org-2350 66 17 k_{e}={\tfrac k_{e}={\tfrac . en-wikipedia-org-2350 66 18 { { -LRB- en-wikipedia-org-2350 66 19 1}{4\pi 1}{4\pi CD en-wikipedia-org-2350 66 20 \varepsilon \varepsilon CD en-wikipedia-org-2350 66 21 _ _ NNP en-wikipedia-org-2350 66 22 { { -LRB- en-wikipedia-org-2350 66 23 0 0 CD en-wikipedia-org-2350 66 24 } } -RRB- en-wikipedia-org-2350 66 25 } } -RRB- en-wikipedia-org-2350 66 26 } } -RRB- en-wikipedia-org-2350 66 27 } } -RRB- en-wikipedia-org-2350 66 28 . . . en-wikipedia-org-2350 67 1 The the DT en-wikipedia-org-2350 67 2 constant constant JJ en-wikipedia-org-2350 67 3 ε ε NN en-wikipedia-org-2350 67 4 0 0 CD en-wikipedia-org-2350 67 5 { { -LRB- en-wikipedia-org-2350 67 6 \displaystyle \displaystyle CD en-wikipedia-org-2350 67 7 \varepsilon \varepsilon CD en-wikipedia-org-2350 67 8 _ _ NNP en-wikipedia-org-2350 67 9 { { -LRB- en-wikipedia-org-2350 67 10 0 0 CD en-wikipedia-org-2350 67 11 } } -RRB- en-wikipedia-org-2350 67 12 } } -RRB- en-wikipedia-org-2350 67 13 is be VBZ en-wikipedia-org-2350 67 14 the the DT en-wikipedia-org-2350 67 15 vacuum vacuum NN en-wikipedia-org-2350 67 16 electric electric NNP en-wikipedia-org-2350 67 17 permittivity permittivity NN en-wikipedia-org-2350 67 18 ( ( -LRB- en-wikipedia-org-2350 67 19 also also RB en-wikipedia-org-2350 67 20 known know VBN en-wikipedia-org-2350 67 21 as as IN en-wikipedia-org-2350 67 22 " " `` en-wikipedia-org-2350 67 23 electric electric JJ en-wikipedia-org-2350 67 24 constant")[23 constant")[23 '' en-wikipedia-org-2350 67 25 ] ] -RRB- en-wikipedia-org-2350 67 26 in in IN en-wikipedia-org-2350 67 27 C C NNP en-wikipedia-org-2350 67 28 2 2 CD en-wikipedia-org-2350 67 29 ⋅ ⋅ NNP en-wikipedia-org-2350 67 30 m m NNP en-wikipedia-org-2350 67 31 − − NNP en-wikipedia-org-2350 67 32 2 2 CD en-wikipedia-org-2350 67 33 ⋅ ⋅ NNP en-wikipedia-org-2350 67 34 N N NNP en-wikipedia-org-2350 67 35 − − NNP en-wikipedia-org-2350 67 36 1 1 CD en-wikipedia-org-2350 67 37 { { -LRB- en-wikipedia-org-2350 67 38 \displaystyle \displaystyle CD en-wikipedia-org-2350 67 39 C^{2}\cdot C^{2}\cdot : en-wikipedia-org-2350 67 40 m^{-2}\cdot m^{-2}\cdot NN en-wikipedia-org-2350 67 41 N^{-1 n^{-1 ADD en-wikipedia-org-2350 67 42 } } -RRB- en-wikipedia-org-2350 67 43 } } -RRB- en-wikipedia-org-2350 67 44 . . . en-wikipedia-org-2350 68 1 It -PRON- PRP en-wikipedia-org-2350 68 2 should should MD en-wikipedia-org-2350 68 3 not not RB en-wikipedia-org-2350 68 4 be be VB en-wikipedia-org-2350 68 5 confused confuse VBN en-wikipedia-org-2350 68 6 with with IN en-wikipedia-org-2350 68 7 ε ε DT en-wikipedia-org-2350 68 8 r r NN en-wikipedia-org-2350 68 9 { { -LRB- en-wikipedia-org-2350 68 10 \displaystyle \displaystyle CD en-wikipedia-org-2350 68 11 \varepsilon \varepsilon CD en-wikipedia-org-2350 68 12 _ _ NNP en-wikipedia-org-2350 68 13 { { -LRB- en-wikipedia-org-2350 68 14 r r NN en-wikipedia-org-2350 68 15 } } -RRB- en-wikipedia-org-2350 68 16 } } -RRB- en-wikipedia-org-2350 68 17 , , , en-wikipedia-org-2350 68 18 which which WDT en-wikipedia-org-2350 68 19 is be VBZ en-wikipedia-org-2350 68 20 the the DT en-wikipedia-org-2350 68 21 dimensionless dimensionless JJ en-wikipedia-org-2350 68 22 relative relative JJ en-wikipedia-org-2350 68 23 permittivity permittivity NN en-wikipedia-org-2350 68 24 of of IN en-wikipedia-org-2350 68 25 the the DT en-wikipedia-org-2350 68 26 material material NN en-wikipedia-org-2350 68 27 in in IN en-wikipedia-org-2350 68 28 which which WDT en-wikipedia-org-2350 68 29 the the DT en-wikipedia-org-2350 68 30 charges charge NNS en-wikipedia-org-2350 68 31 are be VBP en-wikipedia-org-2350 68 32 immersed immersed JJ en-wikipedia-org-2350 68 33 , , , en-wikipedia-org-2350 68 34 or or CC en-wikipedia-org-2350 68 35 with with IN en-wikipedia-org-2350 68 36 their -PRON- PRP$ en-wikipedia-org-2350 68 37 product product NN en-wikipedia-org-2350 68 38 ε ε NN en-wikipedia-org-2350 68 39 a a NN en-wikipedia-org-2350 68 40 = = SYM en-wikipedia-org-2350 68 41 ε ε NN en-wikipedia-org-2350 68 42 0 0 CD en-wikipedia-org-2350 68 43 ε ε NN en-wikipedia-org-2350 68 44 r r NN en-wikipedia-org-2350 68 45 { { -LRB- en-wikipedia-org-2350 68 46 \displaystyle \displaystyle CD en-wikipedia-org-2350 68 47 \varepsilon \varepsilon CD en-wikipedia-org-2350 68 48 _ _ NNP en-wikipedia-org-2350 68 49 { { -LRB- en-wikipedia-org-2350 68 50 a}=\varepsilon a}=\varepsilon ADD en-wikipedia-org-2350 68 51 _ _ NNP en-wikipedia-org-2350 68 52 { { -LRB- en-wikipedia-org-2350 68 53 0}\varepsilon 0}\varepsilon CD en-wikipedia-org-2350 68 54 _ _ NNP en-wikipedia-org-2350 68 55 { { -LRB- en-wikipedia-org-2350 68 56 r r NN en-wikipedia-org-2350 68 57 } } -RRB- en-wikipedia-org-2350 68 58 } } -RRB- en-wikipedia-org-2350 68 59 , , , en-wikipedia-org-2350 68 60 which which WDT en-wikipedia-org-2350 68 61 is be VBZ en-wikipedia-org-2350 68 62 called call VBN en-wikipedia-org-2350 68 63 " " `` en-wikipedia-org-2350 68 64 absolute absolute JJ en-wikipedia-org-2350 68 65 permittivity permittivity NN en-wikipedia-org-2350 68 66 of of IN en-wikipedia-org-2350 68 67 the the DT en-wikipedia-org-2350 68 68 material material NN en-wikipedia-org-2350 68 69 " " '' en-wikipedia-org-2350 68 70 and and CC en-wikipedia-org-2350 68 71 is be VBZ en-wikipedia-org-2350 68 72 still still RB en-wikipedia-org-2350 68 73 used use VBN en-wikipedia-org-2350 68 74 in in IN en-wikipedia-org-2350 68 75 electrical electrical JJ en-wikipedia-org-2350 68 76 engineering engineering NN en-wikipedia-org-2350 68 77 . . . en-wikipedia-org-2350 69 1 Prior prior RB en-wikipedia-org-2350 69 2 to to IN en-wikipedia-org-2350 69 3 the the DT en-wikipedia-org-2350 69 4 2019 2019 CD en-wikipedia-org-2350 69 5 redefinition redefinition NN en-wikipedia-org-2350 69 6 of of IN en-wikipedia-org-2350 69 7 the the DT en-wikipedia-org-2350 69 8 SI SI NNP en-wikipedia-org-2350 69 9 base base NN en-wikipedia-org-2350 69 10 units unit NNS en-wikipedia-org-2350 69 11 , , , en-wikipedia-org-2350 69 12 the the DT en-wikipedia-org-2350 69 13 Coulomb Coulomb NNP en-wikipedia-org-2350 69 14 constant constant NN en-wikipedia-org-2350 69 15 was be VBD en-wikipedia-org-2350 69 16 considered consider VBN en-wikipedia-org-2350 69 17 to to TO en-wikipedia-org-2350 69 18 have have VB en-wikipedia-org-2350 69 19 an an DT en-wikipedia-org-2350 69 20 exact exact JJ en-wikipedia-org-2350 69 21 value value NN en-wikipedia-org-2350 69 22 : : : en-wikipedia-org-2350 69 23 k k NNP en-wikipedia-org-2350 69 24 e e NNP en-wikipedia-org-2350 69 25 = = SYM en-wikipedia-org-2350 69 26 1 1 CD en-wikipedia-org-2350 69 27 4 4 CD en-wikipedia-org-2350 69 28 π π NN en-wikipedia-org-2350 69 29 ε ε NN en-wikipedia-org-2350 69 30 0 0 CD en-wikipedia-org-2350 69 31 = = SYM en-wikipedia-org-2350 69 32 c c NN en-wikipedia-org-2350 69 33 0 0 CD en-wikipedia-org-2350 69 34 2 2 CD en-wikipedia-org-2350 69 35 μ μ SYM en-wikipedia-org-2350 69 36 0 0 CD en-wikipedia-org-2350 69 37 4 4 CD en-wikipedia-org-2350 69 38 π π NN en-wikipedia-org-2350 69 39 = = SYM en-wikipedia-org-2350 69 40 c c NN en-wikipedia-org-2350 69 41 0 0 CD en-wikipedia-org-2350 69 42 2 2 CD en-wikipedia-org-2350 69 43 × × CD en-wikipedia-org-2350 69 44 10 10 CD en-wikipedia-org-2350 69 45 − − NNP en-wikipedia-org-2350 69 46 7 7 CD en-wikipedia-org-2350 69 47     _SP en-wikipedia-org-2350 69 48 H H NNP en-wikipedia-org-2350 69 49 m m NNP en-wikipedia-org-2350 69 50 − − NNP en-wikipedia-org-2350 69 51 1 1 CD en-wikipedia-org-2350 69 52 = = SYM en-wikipedia-org-2350 69 53 8.987 8.987 CD en-wikipedia-org-2350 69 54 551 551 CD en-wikipedia-org-2350 69 55 787 787 CD en-wikipedia-org-2350 69 56 368 368 CD en-wikipedia-org-2350 69 57 176 176 CD en-wikipedia-org-2350 69 58 4 4 CD en-wikipedia-org-2350 69 59 × × CD en-wikipedia-org-2350 69 60 10 10 CD en-wikipedia-org-2350 69 61 9 9 CD en-wikipedia-org-2350 69 62     _SP en-wikipedia-org-2350 69 63 N N NNP en-wikipedia-org-2350 69 64 m m NN en-wikipedia-org-2350 69 65 2 2 CD en-wikipedia-org-2350 69 66 C C NNP en-wikipedia-org-2350 69 67 − − NNP en-wikipedia-org-2350 69 68 2 2 CD en-wikipedia-org-2350 69 69 . . . en-wikipedia-org-2350 70 1 { { -LRB- en-wikipedia-org-2350 70 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 70 3 { { -LRB- en-wikipedia-org-2350 70 4 \begin{aligned}k_{\text{e}}&={\frac \begin{aligned}k_{\text{e}}&={\frac NNP en-wikipedia-org-2350 70 5 { { -LRB- en-wikipedia-org-2350 70 6 1}{4\pi 1}{4\pi CD en-wikipedia-org-2350 70 7 \varepsilon \varepsilon CD en-wikipedia-org-2350 70 8 _ _ NNP en-wikipedia-org-2350 70 9 { { -LRB- en-wikipedia-org-2350 70 10 0}}}={\frac 0}}}={\frac . en-wikipedia-org-2350 70 11 { { -LRB- en-wikipedia-org-2350 70 12 c_{0}^{2}\mu c_{0}^{2}\mu NN en-wikipedia-org-2350 70 13 _ _ NNP en-wikipedia-org-2350 70 14 { { -LRB- en-wikipedia-org-2350 70 15 0}}{4\pi 0}}{4\pi NN en-wikipedia-org-2350 70 16 } } -RRB- en-wikipedia-org-2350 70 17 } } -RRB- en-wikipedia-org-2350 70 18 = = NFP en-wikipedia-org-2350 70 19 c_{0}^{2}\times c_{0}^{2}\times NNP en-wikipedia-org-2350 70 20 10^{-7}\ 10^{-7}\ CD en-wikipedia-org-2350 70 21 { { -LRB- en-wikipedia-org-2350 70 22 H\,m}^{-1}\\&=8.987\,551\,787\,368\,176\,4\times H\,m}^{-1}\\&=8.987\,551\,787\,368\,176\,4\times NNP en-wikipedia-org-2350 70 23 10^{9}\ 10^{9}\ CD en-wikipedia-org-2350 70 24 { { -LRB- en-wikipedia-org-2350 70 25 N\,m^{2}\,C}^{-2}.\end{aligned n\,m^{2}\,c}^{-2}.\end{aligned CD en-wikipedia-org-2350 70 26 } } -RRB- en-wikipedia-org-2350 70 27 } } -RRB- en-wikipedia-org-2350 70 28 } } -RRB- en-wikipedia-org-2350 70 29 Since since IN en-wikipedia-org-2350 70 30 the the DT en-wikipedia-org-2350 70 31 2019 2019 CD en-wikipedia-org-2350 70 32 redefinition,[24][25 redefinition,[24][25 NN en-wikipedia-org-2350 70 33 ] ] -RRB- en-wikipedia-org-2350 70 34 the the DT en-wikipedia-org-2350 70 35 Coulomb Coulomb NNP en-wikipedia-org-2350 70 36 constant constant NN en-wikipedia-org-2350 70 37 is be VBZ en-wikipedia-org-2350 70 38 no no RB en-wikipedia-org-2350 70 39 longer long RBR en-wikipedia-org-2350 70 40 exactly exactly RB en-wikipedia-org-2350 70 41 defined define VBN en-wikipedia-org-2350 70 42 and and CC en-wikipedia-org-2350 70 43 is be VBZ en-wikipedia-org-2350 70 44 subject subject JJ en-wikipedia-org-2350 70 45 to to IN en-wikipedia-org-2350 70 46 the the DT en-wikipedia-org-2350 70 47 measurement measurement NN en-wikipedia-org-2350 70 48 error error NN en-wikipedia-org-2350 70 49 in in IN en-wikipedia-org-2350 70 50 the the DT en-wikipedia-org-2350 70 51 fine fine JJ en-wikipedia-org-2350 70 52 structure structure NN en-wikipedia-org-2350 70 53 constant constant JJ en-wikipedia-org-2350 70 54 . . . en-wikipedia-org-2350 71 1 As as IN en-wikipedia-org-2350 71 2 calculated calculate VBN en-wikipedia-org-2350 71 3 from from IN en-wikipedia-org-2350 71 4 CODATA CODATA NNP en-wikipedia-org-2350 71 5 2018 2018 CD en-wikipedia-org-2350 71 6 recommended recommend VBD en-wikipedia-org-2350 71 7 values value NNS en-wikipedia-org-2350 71 8 , , , en-wikipedia-org-2350 71 9 the the DT en-wikipedia-org-2350 71 10 Coulomb Coulomb NNP en-wikipedia-org-2350 71 11 constant constant JJ en-wikipedia-org-2350 71 12 is[26 is[26 NNP en-wikipedia-org-2350 71 13 ] ] -RRB- en-wikipedia-org-2350 71 14 k k NNP en-wikipedia-org-2350 71 15 e e NN en-wikipedia-org-2350 71 16 = = SYM en-wikipedia-org-2350 71 17 8.987 8.987 CD en-wikipedia-org-2350 71 18 551 551 CD en-wikipedia-org-2350 71 19 792 792 CD en-wikipedia-org-2350 71 20 3 3 CD en-wikipedia-org-2350 71 21 ( ( -LRB- en-wikipedia-org-2350 71 22 14 14 CD en-wikipedia-org-2350 71 23 ) ) -RRB- en-wikipedia-org-2350 71 24 × × CD en-wikipedia-org-2350 71 25 10 10 CD en-wikipedia-org-2350 71 26 9 9 CD en-wikipedia-org-2350 71 27     _SP en-wikipedia-org-2350 71 28 N N NNP en-wikipedia-org-2350 71 29 m m NN en-wikipedia-org-2350 71 30 2 2 CD en-wikipedia-org-2350 71 31 C C NNP en-wikipedia-org-2350 71 32 − − NNP en-wikipedia-org-2350 71 33 2 2 CD en-wikipedia-org-2350 71 34 . . . en-wikipedia-org-2350 72 1 { { -LRB- en-wikipedia-org-2350 72 2 \displaystyle \displaystyle CD en-wikipedia-org-2350 72 3 k_{\text{e}}=8.987\,551\,792\,3\,(14)\times k_{\text{e}}=8.987\,551\,792\,3\,(14)\times CD en-wikipedia-org-2350 72 4 10^{9}\ 10^{9}\ CD en-wikipedia-org-2350 72 5 { { -LRB- en-wikipedia-org-2350 72 6 N\,m^{2}\,C}^{-2 N\,m^{2}\,C}^{-2 NNP en-wikipedia-org-2350 72 7 } } -RRB- en-wikipedia-org-2350 72 8 . . . en-wikipedia-org-2350 72 9 } } -RRB- en-wikipedia-org-2350 73 1 In in IN en-wikipedia-org-2350 73 2 Gaussian gaussian JJ en-wikipedia-org-2350 73 3 units unit NNS en-wikipedia-org-2350 73 4 and and CC en-wikipedia-org-2350 73 5 Lorentz lorentz NN en-wikipedia-org-2350 73 6 – – : en-wikipedia-org-2350 73 7 Heaviside Heaviside NNP en-wikipedia-org-2350 73 8 units unit NNS en-wikipedia-org-2350 73 9 , , , en-wikipedia-org-2350 73 10 which which WDT en-wikipedia-org-2350 73 11 are be VBP en-wikipedia-org-2350 73 12 both both DT en-wikipedia-org-2350 73 13 CGS CGS NNP en-wikipedia-org-2350 73 14 unit unit NN en-wikipedia-org-2350 73 15 systems system NNS en-wikipedia-org-2350 73 16 , , , en-wikipedia-org-2350 73 17 the the DT en-wikipedia-org-2350 73 18 constant constant NN en-wikipedia-org-2350 73 19 has have VBZ en-wikipedia-org-2350 73 20 different different JJ en-wikipedia-org-2350 73 21 , , , en-wikipedia-org-2350 73 22 dimensionless dimensionless JJ en-wikipedia-org-2350 73 23 values value NNS en-wikipedia-org-2350 73 24 . . . en-wikipedia-org-2350 74 1 In in IN en-wikipedia-org-2350 74 2 electrostatic electrostatic JJ en-wikipedia-org-2350 74 3 units unit NNS en-wikipedia-org-2350 74 4 or or CC en-wikipedia-org-2350 74 5 Gaussian gaussian JJ en-wikipedia-org-2350 74 6 units unit NNS en-wikipedia-org-2350 74 7 the the DT en-wikipedia-org-2350 74 8 unit unit NN en-wikipedia-org-2350 74 9 charge charge NN en-wikipedia-org-2350 74 10 ( ( -LRB- en-wikipedia-org-2350 74 11 esu esu NNP en-wikipedia-org-2350 74 12 or or CC en-wikipedia-org-2350 74 13 statcoulomb statcoulomb NN en-wikipedia-org-2350 74 14 ) ) -RRB- en-wikipedia-org-2350 74 15 is be VBZ en-wikipedia-org-2350 74 16 defined define VBN en-wikipedia-org-2350 74 17 in in IN en-wikipedia-org-2350 74 18 such such PDT en-wikipedia-org-2350 74 19 a a DT en-wikipedia-org-2350 74 20 way way NN en-wikipedia-org-2350 74 21 that that WDT en-wikipedia-org-2350 74 22 the the DT en-wikipedia-org-2350 74 23 Coulomb Coulomb NNP en-wikipedia-org-2350 74 24 constant constant JJ en-wikipedia-org-2350 74 25 disappears disappear NNS en-wikipedia-org-2350 74 26 , , , en-wikipedia-org-2350 74 27 as as IN en-wikipedia-org-2350 74 28 it -PRON- PRP en-wikipedia-org-2350 74 29 has have VBZ en-wikipedia-org-2350 74 30 the the DT en-wikipedia-org-2350 74 31 value value NN en-wikipedia-org-2350 74 32 of of IN en-wikipedia-org-2350 74 33 one one CD en-wikipedia-org-2350 74 34 and and CC en-wikipedia-org-2350 74 35 becomes become VBZ en-wikipedia-org-2350 74 36 dimensionless dimensionless JJ en-wikipedia-org-2350 74 37 . . . en-wikipedia-org-2350 75 1 k k NNP en-wikipedia-org-2350 75 2 e e NNP en-wikipedia-org-2350 75 3 = = SYM en-wikipedia-org-2350 75 4 1 1 CD en-wikipedia-org-2350 75 5 { { -LRB- en-wikipedia-org-2350 75 6 \displaystyle \displaystyle CD en-wikipedia-org-2350 75 7 k_{\text{e}}=1 k_{\text{e}}=1 NNP en-wikipedia-org-2350 75 8 } } -RRB- en-wikipedia-org-2350 75 9 ( ( -LRB- en-wikipedia-org-2350 75 10 Gaussian gaussian JJ en-wikipedia-org-2350 75 11 units unit NNS en-wikipedia-org-2350 75 12 ) ) -RRB- en-wikipedia-org-2350 75 13 . . . en-wikipedia-org-2350 76 1 In in IN en-wikipedia-org-2350 76 2 Lorentz Lorentz NNP en-wikipedia-org-2350 76 3 – – : en-wikipedia-org-2350 76 4 Heaviside Heaviside NNP en-wikipedia-org-2350 76 5 units unit NNS en-wikipedia-org-2350 76 6 , , , en-wikipedia-org-2350 76 7 also also RB en-wikipedia-org-2350 76 8 called call VBD en-wikipedia-org-2350 76 9 rationalized rationalized JJ en-wikipedia-org-2350 76 10 units unit NNS en-wikipedia-org-2350 76 11 , , , en-wikipedia-org-2350 76 12 the the DT en-wikipedia-org-2350 76 13 Coulomb Coulomb NNP en-wikipedia-org-2350 76 14 constant constant NN en-wikipedia-org-2350 76 15 is be VBZ en-wikipedia-org-2350 76 16 dimensionless dimensionless JJ en-wikipedia-org-2350 76 17 and and CC en-wikipedia-org-2350 76 18 is be VBZ en-wikipedia-org-2350 76 19 equal equal JJ en-wikipedia-org-2350 76 20 to to IN en-wikipedia-org-2350 76 21 k k NNP en-wikipedia-org-2350 76 22 e e NNP en-wikipedia-org-2350 76 23 = = SYM en-wikipedia-org-2350 76 24 1 1 CD en-wikipedia-org-2350 76 25 4 4 CD en-wikipedia-org-2350 76 26 π π CD en-wikipedia-org-2350 76 27 { { -LRB- en-wikipedia-org-2350 76 28 \displaystyle \displaystyle CD en-wikipedia-org-2350 76 29 k_{\text{e}}={\frac k_{\text{e}}={\frac . en-wikipedia-org-2350 76 30 { { -LRB- en-wikipedia-org-2350 76 31 1}{4\pi 1}{4\pi CD en-wikipedia-org-2350 76 32 } } -RRB- en-wikipedia-org-2350 76 33 } } -RRB- en-wikipedia-org-2350 76 34 } } -RRB- en-wikipedia-org-2350 76 35 ( ( -LRB- en-wikipedia-org-2350 76 36 Lorentz lorentz NN en-wikipedia-org-2350 76 37 – – : en-wikipedia-org-2350 76 38 Heaviside Heaviside NNP en-wikipedia-org-2350 76 39 units unit NNS en-wikipedia-org-2350 76 40 ) ) -RRB- en-wikipedia-org-2350 76 41 Gaussian gaussian JJ en-wikipedia-org-2350 76 42 units unit NNS en-wikipedia-org-2350 76 43 are be VBP en-wikipedia-org-2350 76 44 more more RBR en-wikipedia-org-2350 76 45 amenable amenable JJ en-wikipedia-org-2350 76 46 for for IN en-wikipedia-org-2350 76 47 microscopic microscopic JJ en-wikipedia-org-2350 76 48 problems problem NNS en-wikipedia-org-2350 76 49 such such JJ en-wikipedia-org-2350 76 50 as as IN en-wikipedia-org-2350 76 51 the the DT en-wikipedia-org-2350 76 52 electrodynamics electrodynamic NNS en-wikipedia-org-2350 76 53 of of IN en-wikipedia-org-2350 76 54 individual individual JJ en-wikipedia-org-2350 76 55 electrically electrically RB en-wikipedia-org-2350 76 56 charged charge VBN en-wikipedia-org-2350 76 57 particles particle NNS en-wikipedia-org-2350 76 58 . . . en-wikipedia-org-2350 77 1 [ [ -LRB- en-wikipedia-org-2350 77 2 27 27 CD en-wikipedia-org-2350 77 3 ] ] -RRB- en-wikipedia-org-2350 77 4 SI SI NNP en-wikipedia-org-2350 77 5 units unit NNS en-wikipedia-org-2350 77 6 are be VBP en-wikipedia-org-2350 77 7 more more RBR en-wikipedia-org-2350 77 8 convenient convenient JJ en-wikipedia-org-2350 77 9 for for IN en-wikipedia-org-2350 77 10 practical practical JJ en-wikipedia-org-2350 77 11 , , , en-wikipedia-org-2350 77 12 large large JJ en-wikipedia-org-2350 77 13 - - HYPH en-wikipedia-org-2350 77 14 scale scale NN en-wikipedia-org-2350 77 15 phenomena phenomenon NNS en-wikipedia-org-2350 77 16 , , , en-wikipedia-org-2350 77 17 such such JJ en-wikipedia-org-2350 77 18 as as IN en-wikipedia-org-2350 77 19 engineering engineering NN en-wikipedia-org-2350 77 20 applications application NNS en-wikipedia-org-2350 77 21 . . . en-wikipedia-org-2350 78 1 [ [ -LRB- en-wikipedia-org-2350 78 2 27 27 CD en-wikipedia-org-2350 78 3 ] ] -RRB- en-wikipedia-org-2350 78 4 Limitations[edit limitations[edit NN en-wikipedia-org-2350 78 5 ] ] -RRB- en-wikipedia-org-2350 78 6 There there EX en-wikipedia-org-2350 78 7 are be VBP en-wikipedia-org-2350 78 8 three three CD en-wikipedia-org-2350 78 9 conditions condition NNS en-wikipedia-org-2350 78 10 to to TO en-wikipedia-org-2350 78 11 be be VB en-wikipedia-org-2350 78 12 fulfilled fulfil VBN en-wikipedia-org-2350 78 13 for for IN en-wikipedia-org-2350 78 14 the the DT en-wikipedia-org-2350 78 15 validity validity NN en-wikipedia-org-2350 78 16 of of IN en-wikipedia-org-2350 78 17 Coulomb Coulomb NNP en-wikipedia-org-2350 78 18 's 's POS en-wikipedia-org-2350 78 19 inverse inverse JJ en-wikipedia-org-2350 78 20 square square JJ en-wikipedia-org-2350 78 21 law:[28 law:[28 NN en-wikipedia-org-2350 78 22 ] ] -RRB- en-wikipedia-org-2350 78 23 The the DT en-wikipedia-org-2350 78 24 charges charge NNS en-wikipedia-org-2350 78 25 must must MD en-wikipedia-org-2350 78 26 have have VB en-wikipedia-org-2350 78 27 a a DT en-wikipedia-org-2350 78 28 spherically spherically RB en-wikipedia-org-2350 78 29 symmetric symmetric JJ en-wikipedia-org-2350 78 30 distribution distribution NN en-wikipedia-org-2350 78 31 ( ( -LRB- en-wikipedia-org-2350 78 32 e.g. e.g. RB en-wikipedia-org-2350 79 1 be be VB en-wikipedia-org-2350 79 2 point point NN en-wikipedia-org-2350 79 3 charges charge NNS en-wikipedia-org-2350 79 4 , , , en-wikipedia-org-2350 79 5 or or CC en-wikipedia-org-2350 79 6 a a DT en-wikipedia-org-2350 79 7 charged charge VBN en-wikipedia-org-2350 79 8 metal metal NN en-wikipedia-org-2350 79 9 sphere sphere NN en-wikipedia-org-2350 79 10 ) ) -RRB- en-wikipedia-org-2350 79 11 . . . en-wikipedia-org-2350 80 1 The the DT en-wikipedia-org-2350 80 2 charges charge NNS en-wikipedia-org-2350 80 3 must must MD en-wikipedia-org-2350 80 4 not not RB en-wikipedia-org-2350 80 5 overlap overlap VB en-wikipedia-org-2350 80 6 ( ( -LRB- en-wikipedia-org-2350 80 7 e.g. e.g. RB en-wikipedia-org-2350 81 1 they -PRON- PRP en-wikipedia-org-2350 81 2 must must MD en-wikipedia-org-2350 81 3 be be VB en-wikipedia-org-2350 81 4 distinct distinct JJ en-wikipedia-org-2350 81 5 point point NN en-wikipedia-org-2350 81 6 charges charge NNS en-wikipedia-org-2350 81 7 ) ) -RRB- en-wikipedia-org-2350 81 8 . . . en-wikipedia-org-2350 82 1 The the DT en-wikipedia-org-2350 82 2 charges charge NNS en-wikipedia-org-2350 82 3 must must MD en-wikipedia-org-2350 82 4 be be VB en-wikipedia-org-2350 82 5 stationary stationary JJ en-wikipedia-org-2350 82 6 with with IN en-wikipedia-org-2350 82 7 respect respect NN en-wikipedia-org-2350 82 8 to to IN en-wikipedia-org-2350 82 9 each each DT en-wikipedia-org-2350 82 10 other other JJ en-wikipedia-org-2350 82 11 . . . en-wikipedia-org-2350 83 1 The the DT en-wikipedia-org-2350 83 2 last last JJ en-wikipedia-org-2350 83 3 of of IN en-wikipedia-org-2350 83 4 these these DT en-wikipedia-org-2350 83 5 is be VBZ en-wikipedia-org-2350 83 6 known know VBN en-wikipedia-org-2350 83 7 as as IN en-wikipedia-org-2350 83 8 the the DT en-wikipedia-org-2350 83 9 electrostatic electrostatic JJ en-wikipedia-org-2350 83 10 approximation approximation NN en-wikipedia-org-2350 83 11 . . . en-wikipedia-org-2350 84 1 When when WRB en-wikipedia-org-2350 84 2 movement movement NN en-wikipedia-org-2350 84 3 takes take VBZ en-wikipedia-org-2350 84 4 place place NN en-wikipedia-org-2350 84 5 , , , en-wikipedia-org-2350 84 6 Einstein Einstein NNP en-wikipedia-org-2350 84 7 's 's POS en-wikipedia-org-2350 84 8 theory theory NN en-wikipedia-org-2350 84 9 of of IN en-wikipedia-org-2350 84 10 relativity relativity NN en-wikipedia-org-2350 84 11 must must MD en-wikipedia-org-2350 84 12 be be VB en-wikipedia-org-2350 84 13 taken take VBN en-wikipedia-org-2350 84 14 into into IN en-wikipedia-org-2350 84 15 consideration consideration NN en-wikipedia-org-2350 84 16 , , , en-wikipedia-org-2350 84 17 and and CC en-wikipedia-org-2350 84 18 a a DT en-wikipedia-org-2350 84 19 result result NN en-wikipedia-org-2350 84 20 , , , en-wikipedia-org-2350 84 21 an an DT en-wikipedia-org-2350 84 22 extra extra JJ en-wikipedia-org-2350 84 23 factor factor NN en-wikipedia-org-2350 84 24 is be VBZ en-wikipedia-org-2350 84 25 introduced introduce VBN en-wikipedia-org-2350 84 26 , , , en-wikipedia-org-2350 84 27 which which WDT en-wikipedia-org-2350 84 28 alters alter VBZ en-wikipedia-org-2350 84 29 the the DT en-wikipedia-org-2350 84 30 force force NN en-wikipedia-org-2350 84 31 produced produce VBN en-wikipedia-org-2350 84 32 on on IN en-wikipedia-org-2350 84 33 the the DT en-wikipedia-org-2350 84 34 two two CD en-wikipedia-org-2350 84 35 objects object NNS en-wikipedia-org-2350 84 36 . . . en-wikipedia-org-2350 85 1 This this DT en-wikipedia-org-2350 85 2 extra extra JJ en-wikipedia-org-2350 85 3 part part NN en-wikipedia-org-2350 85 4 of of IN en-wikipedia-org-2350 85 5 the the DT en-wikipedia-org-2350 85 6 force force NN en-wikipedia-org-2350 85 7 is be VBZ en-wikipedia-org-2350 85 8 called call VBN en-wikipedia-org-2350 85 9 the the DT en-wikipedia-org-2350 85 10 magnetic magnetic JJ en-wikipedia-org-2350 85 11 force force NN en-wikipedia-org-2350 85 12 , , , en-wikipedia-org-2350 85 13 and and CC en-wikipedia-org-2350 85 14 is be VBZ en-wikipedia-org-2350 85 15 described describe VBN en-wikipedia-org-2350 85 16 by by IN en-wikipedia-org-2350 85 17 magnetic magnetic JJ en-wikipedia-org-2350 85 18 fields field NNS en-wikipedia-org-2350 85 19 . . . en-wikipedia-org-2350 86 1 For for IN en-wikipedia-org-2350 86 2 slow slow JJ en-wikipedia-org-2350 86 3 movement movement NN en-wikipedia-org-2350 86 4 , , , en-wikipedia-org-2350 86 5 the the DT en-wikipedia-org-2350 86 6 magnetic magnetic JJ en-wikipedia-org-2350 86 7 force force NN en-wikipedia-org-2350 86 8 is be VBZ en-wikipedia-org-2350 86 9 minimal minimal JJ en-wikipedia-org-2350 86 10 and and CC en-wikipedia-org-2350 86 11 Coulomb Coulomb NNP en-wikipedia-org-2350 86 12 's 's POS en-wikipedia-org-2350 86 13 law law NN en-wikipedia-org-2350 86 14 can can MD en-wikipedia-org-2350 86 15 still still RB en-wikipedia-org-2350 86 16 be be VB en-wikipedia-org-2350 86 17 considered consider VBN en-wikipedia-org-2350 86 18 approximately approximately RB en-wikipedia-org-2350 86 19 correct correct JJ en-wikipedia-org-2350 86 20 , , , en-wikipedia-org-2350 86 21 but but CC en-wikipedia-org-2350 86 22 when when WRB en-wikipedia-org-2350 86 23 the the DT en-wikipedia-org-2350 86 24 charges charge NNS en-wikipedia-org-2350 86 25 are be VBP en-wikipedia-org-2350 86 26 moving move VBG en-wikipedia-org-2350 86 27 more more RBR en-wikipedia-org-2350 86 28 quickly quickly RB en-wikipedia-org-2350 86 29 in in IN en-wikipedia-org-2350 86 30 relation relation NN en-wikipedia-org-2350 86 31 to to IN en-wikipedia-org-2350 86 32 each each DT en-wikipedia-org-2350 86 33 other other JJ en-wikipedia-org-2350 86 34 , , , en-wikipedia-org-2350 86 35 the the DT en-wikipedia-org-2350 86 36 full full JJ en-wikipedia-org-2350 86 37 electrodynamics electrodynamic NNS en-wikipedia-org-2350 86 38 rules rule NNS en-wikipedia-org-2350 86 39 ( ( -LRB- en-wikipedia-org-2350 86 40 incorporating incorporate VBG en-wikipedia-org-2350 86 41 the the DT en-wikipedia-org-2350 86 42 magnetic magnetic JJ en-wikipedia-org-2350 86 43 force force NN en-wikipedia-org-2350 86 44 ) ) -RRB- en-wikipedia-org-2350 86 45 must must MD en-wikipedia-org-2350 86 46 be be VB en-wikipedia-org-2350 86 47 considered consider VBN en-wikipedia-org-2350 86 48 . . . en-wikipedia-org-2350 87 1 Electric electric JJ en-wikipedia-org-2350 87 2 field[edit field[edit CD en-wikipedia-org-2350 87 3 ] ] -RRB- en-wikipedia-org-2350 87 4 Main main JJ en-wikipedia-org-2350 87 5 article article NN en-wikipedia-org-2350 87 6 : : : en-wikipedia-org-2350 87 7 Electric electric JJ en-wikipedia-org-2350 87 8 field field NN en-wikipedia-org-2350 87 9 If if IN en-wikipedia-org-2350 87 10 two two CD en-wikipedia-org-2350 87 11 charges charge NNS en-wikipedia-org-2350 87 12 have have VBP en-wikipedia-org-2350 87 13 the the DT en-wikipedia-org-2350 87 14 same same JJ en-wikipedia-org-2350 87 15 sign sign NN en-wikipedia-org-2350 87 16 , , , en-wikipedia-org-2350 87 17 the the DT en-wikipedia-org-2350 87 18 electrostatic electrostatic JJ en-wikipedia-org-2350 87 19 force force NN en-wikipedia-org-2350 87 20 between between IN en-wikipedia-org-2350 87 21 them -PRON- PRP en-wikipedia-org-2350 87 22 is be VBZ en-wikipedia-org-2350 87 23 repulsive repulsive JJ en-wikipedia-org-2350 87 24 ; ; : en-wikipedia-org-2350 87 25 if if IN en-wikipedia-org-2350 87 26 they -PRON- PRP en-wikipedia-org-2350 87 27 have have VBP en-wikipedia-org-2350 87 28 different different JJ en-wikipedia-org-2350 87 29 sign sign NN en-wikipedia-org-2350 87 30 , , , en-wikipedia-org-2350 87 31 the the DT en-wikipedia-org-2350 87 32 force force NN en-wikipedia-org-2350 87 33 between between IN en-wikipedia-org-2350 87 34 them -PRON- PRP en-wikipedia-org-2350 87 35 is be VBZ en-wikipedia-org-2350 87 36 attractive attractive JJ en-wikipedia-org-2350 87 37 . . . en-wikipedia-org-2350 88 1 An an DT en-wikipedia-org-2350 88 2 electric electric JJ en-wikipedia-org-2350 88 3 field field NN en-wikipedia-org-2350 88 4 is be VBZ en-wikipedia-org-2350 88 5 a a DT en-wikipedia-org-2350 88 6 vector vector NN en-wikipedia-org-2350 88 7 field field NN en-wikipedia-org-2350 88 8 that that WDT en-wikipedia-org-2350 88 9 associates associate VBZ en-wikipedia-org-2350 88 10 to to IN en-wikipedia-org-2350 88 11 each each DT en-wikipedia-org-2350 88 12 point point NN en-wikipedia-org-2350 88 13 in in IN en-wikipedia-org-2350 88 14 space space NN en-wikipedia-org-2350 88 15 the the DT en-wikipedia-org-2350 88 16 Coulomb Coulomb NNP en-wikipedia-org-2350 88 17 force force NN en-wikipedia-org-2350 88 18 experienced experience VBN en-wikipedia-org-2350 88 19 by by IN en-wikipedia-org-2350 88 20 a a DT en-wikipedia-org-2350 88 21 unit unit NN en-wikipedia-org-2350 88 22 test test NN en-wikipedia-org-2350 88 23 charge charge NN en-wikipedia-org-2350 88 24 . . . en-wikipedia-org-2350 89 1 [ [ -LRB- en-wikipedia-org-2350 89 2 19 19 CD en-wikipedia-org-2350 89 3 ] ] -RRB- en-wikipedia-org-2350 89 4 The the DT en-wikipedia-org-2350 89 5 strength strength NN en-wikipedia-org-2350 89 6 and and CC en-wikipedia-org-2350 89 7 direction direction NN en-wikipedia-org-2350 89 8 of of IN en-wikipedia-org-2350 89 9 the the DT en-wikipedia-org-2350 89 10 Coulomb Coulomb NNP en-wikipedia-org-2350 89 11 force force NN en-wikipedia-org-2350 89 12 F f NN en-wikipedia-org-2350 89 13 { { -LRB- en-wikipedia-org-2350 89 14 \textstyle \textstyle CD en-wikipedia-org-2350 89 15 \mathbf \mathbf CD en-wikipedia-org-2350 89 16 { { -LRB- en-wikipedia-org-2350 89 17 F f NN en-wikipedia-org-2350 89 18 } } -RRB- en-wikipedia-org-2350 89 19 } } -RRB- en-wikipedia-org-2350 89 20 on on IN en-wikipedia-org-2350 89 21 a a DT en-wikipedia-org-2350 89 22 charge charge NN en-wikipedia-org-2350 89 23 q q NNP en-wikipedia-org-2350 89 24 t t NN en-wikipedia-org-2350 89 25 { { -LRB- en-wikipedia-org-2350 89 26 \textstyle \textstyle CD en-wikipedia-org-2350 89 27 q_{t q_{t NNP en-wikipedia-org-2350 89 28 } } -RRB- en-wikipedia-org-2350 89 29 } } -RRB- en-wikipedia-org-2350 89 30 depends depend VBZ en-wikipedia-org-2350 89 31 on on IN en-wikipedia-org-2350 89 32 the the DT en-wikipedia-org-2350 89 33 electric electric JJ en-wikipedia-org-2350 89 34 field field NN en-wikipedia-org-2350 89 35 E E NNS en-wikipedia-org-2350 89 36 { { -LRB- en-wikipedia-org-2350 89 37 \textstyle \textstyle CD en-wikipedia-org-2350 89 38 \mathbf \mathbf CD en-wikipedia-org-2350 89 39 { { -LRB- en-wikipedia-org-2350 89 40 E e NN en-wikipedia-org-2350 89 41 } } -RRB- en-wikipedia-org-2350 89 42 } } -RRB- en-wikipedia-org-2350 89 43 established establish VBN en-wikipedia-org-2350 89 44 by by IN en-wikipedia-org-2350 89 45 other other JJ en-wikipedia-org-2350 89 46 charges charge NNS en-wikipedia-org-2350 89 47 that that IN en-wikipedia-org-2350 89 48 it -PRON- PRP en-wikipedia-org-2350 89 49 finds find VBZ en-wikipedia-org-2350 89 50 itself -PRON- PRP en-wikipedia-org-2350 89 51 in in IN en-wikipedia-org-2350 89 52 , , , en-wikipedia-org-2350 89 53 such such JJ en-wikipedia-org-2350 89 54 that that IN en-wikipedia-org-2350 89 55 F F NNP en-wikipedia-org-2350 89 56 = = SYM en-wikipedia-org-2350 89 57 q q NNP en-wikipedia-org-2350 89 58 t t NN en-wikipedia-org-2350 89 59 E e NN en-wikipedia-org-2350 89 60 { { -LRB- en-wikipedia-org-2350 89 61 \textstyle \textstyle CD en-wikipedia-org-2350 89 62 \mathbf \mathbf CD en-wikipedia-org-2350 89 63 { { -LRB- en-wikipedia-org-2350 89 64 F f NN en-wikipedia-org-2350 89 65 } } -RRB- en-wikipedia-org-2350 89 66 = = SYM en-wikipedia-org-2350 89 67 q_{t}\mathbf q_{t}\mathbf VB en-wikipedia-org-2350 89 68 { { -LRB- en-wikipedia-org-2350 89 69 E e NN en-wikipedia-org-2350 89 70 } } -RRB- en-wikipedia-org-2350 89 71 } } -RRB- en-wikipedia-org-2350 89 72 . . . en-wikipedia-org-2350 90 1 In in IN en-wikipedia-org-2350 90 2 the the DT en-wikipedia-org-2350 90 3 simplest simple JJS en-wikipedia-org-2350 90 4 case case NN en-wikipedia-org-2350 90 5 , , , en-wikipedia-org-2350 90 6 the the DT en-wikipedia-org-2350 90 7 field field NN en-wikipedia-org-2350 90 8 is be VBZ en-wikipedia-org-2350 90 9 considered consider VBN en-wikipedia-org-2350 90 10 to to TO en-wikipedia-org-2350 90 11 be be VB en-wikipedia-org-2350 90 12 generated generate VBN en-wikipedia-org-2350 90 13 solely solely RB en-wikipedia-org-2350 90 14 by by IN en-wikipedia-org-2350 90 15 a a DT en-wikipedia-org-2350 90 16 single single JJ en-wikipedia-org-2350 90 17 source source NN en-wikipedia-org-2350 90 18 point point NN en-wikipedia-org-2350 90 19 charge charge NN en-wikipedia-org-2350 90 20 . . . en-wikipedia-org-2350 91 1 More more RBR en-wikipedia-org-2350 91 2 generally generally RB en-wikipedia-org-2350 91 3 , , , en-wikipedia-org-2350 91 4 the the DT en-wikipedia-org-2350 91 5 field field NN en-wikipedia-org-2350 91 6 can can MD en-wikipedia-org-2350 91 7 be be VB en-wikipedia-org-2350 91 8 generated generate VBN en-wikipedia-org-2350 91 9 by by IN en-wikipedia-org-2350 91 10 a a DT en-wikipedia-org-2350 91 11 distribution distribution NN en-wikipedia-org-2350 91 12 of of IN en-wikipedia-org-2350 91 13 charges charge NNS en-wikipedia-org-2350 91 14 who who WP en-wikipedia-org-2350 91 15 contribute contribute VBP en-wikipedia-org-2350 91 16 to to IN en-wikipedia-org-2350 91 17 the the DT en-wikipedia-org-2350 91 18 overall overall NN en-wikipedia-org-2350 91 19 by by IN en-wikipedia-org-2350 91 20 the the DT en-wikipedia-org-2350 91 21 principle principle NN en-wikipedia-org-2350 91 22 of of IN en-wikipedia-org-2350 91 23 superposition superposition NN en-wikipedia-org-2350 91 24 . . . en-wikipedia-org-2350 92 1 If if IN en-wikipedia-org-2350 92 2 the the DT en-wikipedia-org-2350 92 3 field field NN en-wikipedia-org-2350 92 4 is be VBZ en-wikipedia-org-2350 92 5 generated generate VBN en-wikipedia-org-2350 92 6 by by IN en-wikipedia-org-2350 92 7 a a DT en-wikipedia-org-2350 92 8 positive positive JJ en-wikipedia-org-2350 92 9 source source NN en-wikipedia-org-2350 92 10 point point NN en-wikipedia-org-2350 92 11 charge charge NN en-wikipedia-org-2350 92 12 q q NNP en-wikipedia-org-2350 92 13 { { -LRB- en-wikipedia-org-2350 92 14 \textstyle \textstyle NNP en-wikipedia-org-2350 92 15 q q NNP en-wikipedia-org-2350 92 16 } } -RRB- en-wikipedia-org-2350 92 17 , , , en-wikipedia-org-2350 92 18 the the DT en-wikipedia-org-2350 92 19 direction direction NN en-wikipedia-org-2350 92 20 of of IN en-wikipedia-org-2350 92 21 the the DT en-wikipedia-org-2350 92 22 electric electric JJ en-wikipedia-org-2350 92 23 field field NN en-wikipedia-org-2350 92 24 points point VBZ en-wikipedia-org-2350 92 25 along along IN en-wikipedia-org-2350 92 26 lines line NNS en-wikipedia-org-2350 92 27 directed direct VBD en-wikipedia-org-2350 92 28 radially radially NN en-wikipedia-org-2350 92 29 outwards outward NNS en-wikipedia-org-2350 92 30 from from IN en-wikipedia-org-2350 92 31 it -PRON- PRP en-wikipedia-org-2350 92 32 , , , en-wikipedia-org-2350 92 33 i.e. i.e. FW en-wikipedia-org-2350 93 1 in in IN en-wikipedia-org-2350 93 2 the the DT en-wikipedia-org-2350 93 3 direction direction NN en-wikipedia-org-2350 93 4 that that IN en-wikipedia-org-2350 93 5 a a DT en-wikipedia-org-2350 93 6 positive positive JJ en-wikipedia-org-2350 93 7 point point NN en-wikipedia-org-2350 93 8 test test NN en-wikipedia-org-2350 93 9 charge charge NN en-wikipedia-org-2350 93 10 q q NNP en-wikipedia-org-2350 93 11 t t NNP en-wikipedia-org-2350 93 12 { { -LRB- en-wikipedia-org-2350 93 13 \textstyle \textstyle CD en-wikipedia-org-2350 93 14 q_{t q_{t NNP en-wikipedia-org-2350 93 15 } } -RRB- en-wikipedia-org-2350 93 16 } } -RRB- en-wikipedia-org-2350 93 17 would would MD en-wikipedia-org-2350 93 18 move move VB en-wikipedia-org-2350 93 19 if if IN en-wikipedia-org-2350 93 20 placed place VBN en-wikipedia-org-2350 93 21 in in IN en-wikipedia-org-2350 93 22 the the DT en-wikipedia-org-2350 93 23 field field NN en-wikipedia-org-2350 93 24 . . . en-wikipedia-org-2350 94 1 For for IN en-wikipedia-org-2350 94 2 a a DT en-wikipedia-org-2350 94 3 negative negative JJ en-wikipedia-org-2350 94 4 point point NN en-wikipedia-org-2350 94 5 source source NN en-wikipedia-org-2350 94 6 charge charge NN en-wikipedia-org-2350 94 7 , , , en-wikipedia-org-2350 94 8 the the DT en-wikipedia-org-2350 94 9 direction direction NN en-wikipedia-org-2350 94 10 is be VBZ en-wikipedia-org-2350 94 11 radially radially NN en-wikipedia-org-2350 94 12 inwards inward NNS en-wikipedia-org-2350 94 13 . . . en-wikipedia-org-2350 95 1 The the DT en-wikipedia-org-2350 95 2 magnitude magnitude NN en-wikipedia-org-2350 95 3 of of IN en-wikipedia-org-2350 95 4 the the DT en-wikipedia-org-2350 95 5 electric electric JJ en-wikipedia-org-2350 95 6 field field NN en-wikipedia-org-2350 95 7 E e NN en-wikipedia-org-2350 95 8 can can MD en-wikipedia-org-2350 95 9 be be VB en-wikipedia-org-2350 95 10 derived derive VBN en-wikipedia-org-2350 95 11 from from IN en-wikipedia-org-2350 95 12 Coulomb Coulomb NNP en-wikipedia-org-2350 95 13 's 's POS en-wikipedia-org-2350 95 14 law law NN en-wikipedia-org-2350 95 15 . . . en-wikipedia-org-2350 96 1 By by IN en-wikipedia-org-2350 96 2 choosing choose VBG en-wikipedia-org-2350 96 3 one one CD en-wikipedia-org-2350 96 4 of of IN en-wikipedia-org-2350 96 5 the the DT en-wikipedia-org-2350 96 6 point point NN en-wikipedia-org-2350 96 7 charges charge NNS en-wikipedia-org-2350 96 8 to to TO en-wikipedia-org-2350 96 9 be be VB en-wikipedia-org-2350 96 10 the the DT en-wikipedia-org-2350 96 11 source source NN en-wikipedia-org-2350 96 12 , , , en-wikipedia-org-2350 96 13 and and CC en-wikipedia-org-2350 96 14 the the DT en-wikipedia-org-2350 96 15 other other JJ en-wikipedia-org-2350 96 16 to to TO en-wikipedia-org-2350 96 17 be be VB en-wikipedia-org-2350 96 18 the the DT en-wikipedia-org-2350 96 19 test test NN en-wikipedia-org-2350 96 20 charge charge NN en-wikipedia-org-2350 96 21 , , , en-wikipedia-org-2350 96 22 it -PRON- PRP en-wikipedia-org-2350 96 23 follows follow VBZ en-wikipedia-org-2350 96 24 from from IN en-wikipedia-org-2350 96 25 Coulomb Coulomb NNP en-wikipedia-org-2350 96 26 's 's POS en-wikipedia-org-2350 96 27 law law NN en-wikipedia-org-2350 96 28 that that IN en-wikipedia-org-2350 96 29 the the DT en-wikipedia-org-2350 96 30 magnitude magnitude NN en-wikipedia-org-2350 96 31 of of IN en-wikipedia-org-2350 96 32 the the DT en-wikipedia-org-2350 96 33 electric electric JJ en-wikipedia-org-2350 96 34 field field NN en-wikipedia-org-2350 96 35 E E NNS en-wikipedia-org-2350 96 36 created create VBN en-wikipedia-org-2350 96 37 by by IN en-wikipedia-org-2350 96 38 a a DT en-wikipedia-org-2350 96 39 single single JJ en-wikipedia-org-2350 96 40 source source NN en-wikipedia-org-2350 96 41 point point NN en-wikipedia-org-2350 96 42 charge charge NN en-wikipedia-org-2350 96 43 Q Q NNP en-wikipedia-org-2350 96 44 at at IN en-wikipedia-org-2350 96 45 a a DT en-wikipedia-org-2350 96 46 certain certain JJ en-wikipedia-org-2350 96 47 distance distance NN en-wikipedia-org-2350 96 48 from from IN en-wikipedia-org-2350 96 49 it -PRON- PRP en-wikipedia-org-2350 96 50 r r NNP en-wikipedia-org-2350 96 51 in in IN en-wikipedia-org-2350 96 52 vacuum vacuum NN en-wikipedia-org-2350 96 53 is be VBZ en-wikipedia-org-2350 96 54 given give VBN en-wikipedia-org-2350 96 55 by by IN en-wikipedia-org-2350 96 56 | | NNP en-wikipedia-org-2350 96 57 E E NNP en-wikipedia-org-2350 96 58 | | NNP en-wikipedia-org-2350 96 59 = = SYM en-wikipedia-org-2350 96 60 k k NNP en-wikipedia-org-2350 96 61 e e NNP en-wikipedia-org-2350 96 62 | | NNP en-wikipedia-org-2350 96 63 q q NNP en-wikipedia-org-2350 96 64 | | NNP en-wikipedia-org-2350 96 65 r r NNP en-wikipedia-org-2350 96 66 2 2 CD en-wikipedia-org-2350 96 67 { { -LRB- en-wikipedia-org-2350 96 68 \displaystyle \displaystyle CD en-wikipedia-org-2350 96 69 |{\boldsymbol |{\boldsymbol CD en-wikipedia-org-2350 96 70 { { -LRB- en-wikipedia-org-2350 96 71 E}}|={k_{e}}{|q| E}}|={k_{e}}{|q| NNP en-wikipedia-org-2350 96 72 \over \over CD en-wikipedia-org-2350 96 73 r^{2 r^{2 NNP en-wikipedia-org-2350 96 74 } } -RRB- en-wikipedia-org-2350 96 75 } } -RRB- en-wikipedia-org-2350 96 76 } } -RRB- en-wikipedia-org-2350 96 77 A a DT en-wikipedia-org-2350 96 78 system system NN en-wikipedia-org-2350 96 79 N n CD en-wikipedia-org-2350 96 80 of of IN en-wikipedia-org-2350 96 81 charges charge NNS en-wikipedia-org-2350 96 82 q q NNP en-wikipedia-org-2350 96 83 i i PRP en-wikipedia-org-2350 96 84 { { -LRB- en-wikipedia-org-2350 96 85 \displaystyle \displaystyle CD en-wikipedia-org-2350 96 86 q_{i q_{i NN en-wikipedia-org-2350 96 87 } } -RRB- en-wikipedia-org-2350 96 88 } } -RRB- en-wikipedia-org-2350 96 89 stationed station VBN en-wikipedia-org-2350 96 90 at at IN en-wikipedia-org-2350 96 91 r r NN en-wikipedia-org-2350 96 92 i i PRP en-wikipedia-org-2350 96 93 { { -LRB- en-wikipedia-org-2350 96 94 \textstyle \textstyle CD en-wikipedia-org-2350 96 95 { { -LRB- en-wikipedia-org-2350 96 96 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 96 97 { { -LRB- en-wikipedia-org-2350 96 98 r}}_{i r}}_{i NNP en-wikipedia-org-2350 96 99 } } -RRB- en-wikipedia-org-2350 96 100 } } -RRB- en-wikipedia-org-2350 96 101 produces produce VBZ en-wikipedia-org-2350 96 102 an an DT en-wikipedia-org-2350 96 103 electric electric JJ en-wikipedia-org-2350 96 104 field field NN en-wikipedia-org-2350 96 105 whose whose WP$ en-wikipedia-org-2350 96 106 magnitude magnitude NN en-wikipedia-org-2350 96 107 and and CC en-wikipedia-org-2350 96 108 direction direction NN en-wikipedia-org-2350 96 109 is be VBZ en-wikipedia-org-2350 96 110 , , , en-wikipedia-org-2350 96 111 by by IN en-wikipedia-org-2350 96 112 superposition superposition NN en-wikipedia-org-2350 96 113 E E NNS en-wikipedia-org-2350 96 114 ( ( -LRB- en-wikipedia-org-2350 96 115 r r NN en-wikipedia-org-2350 96 116 ) ) -RRB- en-wikipedia-org-2350 96 117 = = SYM en-wikipedia-org-2350 96 118 1 1 CD en-wikipedia-org-2350 96 119 4 4 CD en-wikipedia-org-2350 96 120 π π NN en-wikipedia-org-2350 96 121 ε ε NN en-wikipedia-org-2350 96 122 0 0 CD en-wikipedia-org-2350 96 123 ∑ ∑ . en-wikipedia-org-2350 96 124 i i NN en-wikipedia-org-2350 96 125 = = SYM en-wikipedia-org-2350 96 126 1 1 CD en-wikipedia-org-2350 96 127 N n CD en-wikipedia-org-2350 96 128 q q NNP en-wikipedia-org-2350 96 129 i i NN en-wikipedia-org-2350 96 130 r r NN en-wikipedia-org-2350 96 131 − − NNP en-wikipedia-org-2350 96 132 r r NNP en-wikipedia-org-2350 96 133 i i NN en-wikipedia-org-2350 96 134 | | NNP en-wikipedia-org-2350 96 135 r r NNP en-wikipedia-org-2350 96 136 − − NNP en-wikipedia-org-2350 96 137 r r NNP en-wikipedia-org-2350 96 138 i i NN en-wikipedia-org-2350 96 139 | | CD en-wikipedia-org-2350 96 140 3 3 CD en-wikipedia-org-2350 96 141 { { -LRB- en-wikipedia-org-2350 96 142 \displaystyle \displaystyle CD en-wikipedia-org-2350 96 143 { { -LRB- en-wikipedia-org-2350 96 144 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 96 145 { { -LRB- en-wikipedia-org-2350 96 146 E}}({\boldsymbol E}}({\boldsymbol NNP en-wikipedia-org-2350 96 147 { { -LRB- en-wikipedia-org-2350 96 148 r}})={1 r}})={1 NNP en-wikipedia-org-2350 96 149 \over \over NNP en-wikipedia-org-2350 96 150 4\pi 4\pi CD en-wikipedia-org-2350 96 151 \varepsilon \varepsilon CD en-wikipedia-org-2350 96 152 _ _ NNP en-wikipedia-org-2350 96 153 { { -LRB- en-wikipedia-org-2350 96 154 0}}\sum 0}}\sum CD en-wikipedia-org-2350 96 155 _ _ NNP en-wikipedia-org-2350 96 156 { { -LRB- en-wikipedia-org-2350 96 157 i=1}^{N}q_{i}{\frac i=1}^{n}q_{i}{\frac RB en-wikipedia-org-2350 96 158 { { -LRB- en-wikipedia-org-2350 96 159 { { -LRB- en-wikipedia-org-2350 96 160 \boldsymbol \boldsymbol CD en-wikipedia-org-2350 96 161 { { -LRB- en-wikipedia-org-2350 96 162 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 96 163 { { -LRB- en-wikipedia-org-2350 96 164 r}}_{i}}{|{\boldsymbol r}}_{i}}{|{\boldsymbol NNP en-wikipedia-org-2350 96 165 { { -LRB- en-wikipedia-org-2350 96 166 r}}-{\boldsymbol r}}-{\boldsymbol NNP en-wikipedia-org-2350 96 167 { { -LRB- en-wikipedia-org-2350 96 168 r}}_{i}|^{3 r}}_{i}|^{3 NNP en-wikipedia-org-2350 96 169 } } -RRB- en-wikipedia-org-2350 96 170 } } -RRB- en-wikipedia-org-2350 96 171 } } -RRB- en-wikipedia-org-2350 96 172 } } -RRB- en-wikipedia-org-2350 96 173 Atomic Atomic NNP en-wikipedia-org-2350 96 174 forces[edit forces[edit NFP en-wikipedia-org-2350 96 175 ] ] -RRB- en-wikipedia-org-2350 96 176 See see VB en-wikipedia-org-2350 96 177 also also RB en-wikipedia-org-2350 96 178 : : : en-wikipedia-org-2350 96 179 Coulomb coulomb VB en-wikipedia-org-2350 96 180 explosion explosion NN en-wikipedia-org-2350 96 181 Coulomb Coulomb NNP en-wikipedia-org-2350 96 182 's 's POS en-wikipedia-org-2350 96 183 law law NN en-wikipedia-org-2350 96 184 holds hold VBZ en-wikipedia-org-2350 96 185 even even RB en-wikipedia-org-2350 96 186 within within IN en-wikipedia-org-2350 96 187 atoms atom NNS en-wikipedia-org-2350 96 188 , , , en-wikipedia-org-2350 96 189 correctly correctly RB en-wikipedia-org-2350 96 190 describing describe VBG en-wikipedia-org-2350 96 191 the the DT en-wikipedia-org-2350 96 192 force force NN en-wikipedia-org-2350 96 193 between between IN en-wikipedia-org-2350 96 194 the the DT en-wikipedia-org-2350 96 195 positively positively RB en-wikipedia-org-2350 96 196 charged charge VBN en-wikipedia-org-2350 96 197 atomic atomic JJ en-wikipedia-org-2350 96 198 nucleus nucleus NNP en-wikipedia-org-2350 96 199 and and CC en-wikipedia-org-2350 96 200 each each DT en-wikipedia-org-2350 96 201 of of IN en-wikipedia-org-2350 96 202 the the DT en-wikipedia-org-2350 96 203 negatively negatively RB en-wikipedia-org-2350 96 204 charged charge VBN en-wikipedia-org-2350 96 205 electrons electron NNS en-wikipedia-org-2350 96 206 . . . en-wikipedia-org-2350 97 1 This this DT en-wikipedia-org-2350 97 2 simple simple JJ en-wikipedia-org-2350 97 3 law law NN en-wikipedia-org-2350 97 4 also also RB en-wikipedia-org-2350 97 5 correctly correctly RB en-wikipedia-org-2350 97 6 accounts account VBZ en-wikipedia-org-2350 97 7 for for IN en-wikipedia-org-2350 97 8 the the DT en-wikipedia-org-2350 97 9 forces force NNS en-wikipedia-org-2350 97 10 that that WDT en-wikipedia-org-2350 97 11 bind bind VBP en-wikipedia-org-2350 97 12 atoms atom VBZ en-wikipedia-org-2350 97 13 together together RB en-wikipedia-org-2350 97 14 to to TO en-wikipedia-org-2350 97 15 form form VB en-wikipedia-org-2350 97 16 molecules molecule NNS en-wikipedia-org-2350 97 17 and and CC en-wikipedia-org-2350 97 18 for for IN en-wikipedia-org-2350 97 19 the the DT en-wikipedia-org-2350 97 20 forces force NNS en-wikipedia-org-2350 97 21 that that WDT en-wikipedia-org-2350 97 22 bind bind VBP en-wikipedia-org-2350 97 23 atoms atom NNS en-wikipedia-org-2350 97 24 and and CC en-wikipedia-org-2350 97 25 molecules molecule NNS en-wikipedia-org-2350 97 26 together together RB en-wikipedia-org-2350 97 27 to to TO en-wikipedia-org-2350 97 28 form form VB en-wikipedia-org-2350 97 29 solids solid NNS en-wikipedia-org-2350 97 30 and and CC en-wikipedia-org-2350 97 31 liquids liquid NNS en-wikipedia-org-2350 97 32 . . . en-wikipedia-org-2350 98 1 Generally generally RB en-wikipedia-org-2350 98 2 , , , en-wikipedia-org-2350 98 3 as as IN en-wikipedia-org-2350 98 4 the the DT en-wikipedia-org-2350 98 5 distance distance NN en-wikipedia-org-2350 98 6 between between IN en-wikipedia-org-2350 98 7 ions ion NNS en-wikipedia-org-2350 98 8 increases increase NNS en-wikipedia-org-2350 98 9 , , , en-wikipedia-org-2350 98 10 the the DT en-wikipedia-org-2350 98 11 force force NN en-wikipedia-org-2350 98 12 of of IN en-wikipedia-org-2350 98 13 attraction attraction NN en-wikipedia-org-2350 98 14 , , , en-wikipedia-org-2350 98 15 and and CC en-wikipedia-org-2350 98 16 binding bind VBG en-wikipedia-org-2350 98 17 energy energy NN en-wikipedia-org-2350 98 18 , , , en-wikipedia-org-2350 98 19 approach approach NN en-wikipedia-org-2350 98 20 zero zero CD en-wikipedia-org-2350 98 21 and and CC en-wikipedia-org-2350 98 22 ionic ionic JJ en-wikipedia-org-2350 98 23 bonding bonding NN en-wikipedia-org-2350 98 24 is be VBZ en-wikipedia-org-2350 98 25 less less RBR en-wikipedia-org-2350 98 26 favorable favorable JJ en-wikipedia-org-2350 98 27 . . . en-wikipedia-org-2350 99 1 As as IN en-wikipedia-org-2350 99 2 the the DT en-wikipedia-org-2350 99 3 magnitude magnitude NN en-wikipedia-org-2350 99 4 of of IN en-wikipedia-org-2350 99 5 opposing oppose VBG en-wikipedia-org-2350 99 6 charges charge NNS en-wikipedia-org-2350 99 7 increases increase NNS en-wikipedia-org-2350 99 8 , , , en-wikipedia-org-2350 99 9 energy energy NN en-wikipedia-org-2350 99 10 increases increase NNS en-wikipedia-org-2350 99 11 and and CC en-wikipedia-org-2350 99 12 ionic ionic JJ en-wikipedia-org-2350 99 13 bonding bonding NN en-wikipedia-org-2350 99 14 is be VBZ en-wikipedia-org-2350 99 15 more more RBR en-wikipedia-org-2350 99 16 favorable favorable JJ en-wikipedia-org-2350 99 17 . . . en-wikipedia-org-2350 100 1 Relation relation NN en-wikipedia-org-2350 100 2 to to IN en-wikipedia-org-2350 100 3 Gauss Gauss NNP en-wikipedia-org-2350 100 4 's 's POS en-wikipedia-org-2350 100 5 law[edit law[edit NN en-wikipedia-org-2350 100 6 ] ] -RRB- en-wikipedia-org-2350 100 7 Deriving Deriving NNP en-wikipedia-org-2350 100 8 Gauss Gauss NNP en-wikipedia-org-2350 100 9 's 's POS en-wikipedia-org-2350 100 10 law law NN en-wikipedia-org-2350 100 11 from from IN en-wikipedia-org-2350 100 12 Coulomb Coulomb NNP en-wikipedia-org-2350 100 13 's 's POS en-wikipedia-org-2350 100 14 law[edit law[edit NN en-wikipedia-org-2350 100 15 ] ] -RRB- en-wikipedia-org-2350 100 16 Strictly strictly RB en-wikipedia-org-2350 100 17 speaking speak VBG en-wikipedia-org-2350 100 18 , , , en-wikipedia-org-2350 100 19 Gauss Gauss NNP en-wikipedia-org-2350 100 20 's 's POS en-wikipedia-org-2350 100 21 law law NN en-wikipedia-org-2350 100 22 can can MD en-wikipedia-org-2350 100 23 not not RB en-wikipedia-org-2350 100 24 be be VB en-wikipedia-org-2350 100 25 derived derive VBN en-wikipedia-org-2350 100 26 from from IN en-wikipedia-org-2350 100 27 Coulomb Coulomb NNP en-wikipedia-org-2350 100 28 's 's POS en-wikipedia-org-2350 100 29 law law NN en-wikipedia-org-2350 100 30 alone alone RB en-wikipedia-org-2350 100 31 , , , en-wikipedia-org-2350 100 32 since since IN en-wikipedia-org-2350 100 33 Coulomb Coulomb NNP en-wikipedia-org-2350 100 34 's 's POS en-wikipedia-org-2350 100 35 law law NN en-wikipedia-org-2350 100 36 gives give VBZ en-wikipedia-org-2350 100 37 the the DT en-wikipedia-org-2350 100 38 electric electric JJ en-wikipedia-org-2350 100 39 field field NN en-wikipedia-org-2350 100 40 due due IN en-wikipedia-org-2350 100 41 to to IN en-wikipedia-org-2350 100 42 an an DT en-wikipedia-org-2350 100 43 individual individual JJ en-wikipedia-org-2350 100 44 point point NN en-wikipedia-org-2350 100 45 charge charge NN en-wikipedia-org-2350 100 46 only only RB en-wikipedia-org-2350 100 47 . . . en-wikipedia-org-2350 101 1 However however RB en-wikipedia-org-2350 101 2 , , , en-wikipedia-org-2350 101 3 Gauss Gauss NNP en-wikipedia-org-2350 101 4 's 's POS en-wikipedia-org-2350 101 5 law law NN en-wikipedia-org-2350 101 6 can can MD en-wikipedia-org-2350 101 7 be be VB en-wikipedia-org-2350 101 8 proven prove VBN en-wikipedia-org-2350 101 9 from from IN en-wikipedia-org-2350 101 10 Coulomb Coulomb NNP en-wikipedia-org-2350 101 11 's 's POS en-wikipedia-org-2350 101 12 law law NN en-wikipedia-org-2350 101 13 if if IN en-wikipedia-org-2350 101 14 it -PRON- PRP en-wikipedia-org-2350 101 15 is be VBZ en-wikipedia-org-2350 101 16 assumed assume VBN en-wikipedia-org-2350 101 17 , , , en-wikipedia-org-2350 101 18 in in IN en-wikipedia-org-2350 101 19 addition addition NN en-wikipedia-org-2350 101 20 , , , en-wikipedia-org-2350 101 21 that that IN en-wikipedia-org-2350 101 22 the the DT en-wikipedia-org-2350 101 23 electric electric JJ en-wikipedia-org-2350 101 24 field field NN en-wikipedia-org-2350 101 25 obeys obey VBZ en-wikipedia-org-2350 101 26 the the DT en-wikipedia-org-2350 101 27 superposition superposition NN en-wikipedia-org-2350 101 28 principle principle NN en-wikipedia-org-2350 101 29 . . . en-wikipedia-org-2350 102 1 The the DT en-wikipedia-org-2350 102 2 superposition superposition NN en-wikipedia-org-2350 102 3 principle principle NN en-wikipedia-org-2350 102 4 says say VBZ en-wikipedia-org-2350 102 5 that that IN en-wikipedia-org-2350 102 6 the the DT en-wikipedia-org-2350 102 7 resulting result VBG en-wikipedia-org-2350 102 8 field field NN en-wikipedia-org-2350 102 9 is be VBZ en-wikipedia-org-2350 102 10 the the DT en-wikipedia-org-2350 102 11 vector vector NN en-wikipedia-org-2350 102 12 sum sum NN en-wikipedia-org-2350 102 13 of of IN en-wikipedia-org-2350 102 14 fields field NNS en-wikipedia-org-2350 102 15 generated generate VBN en-wikipedia-org-2350 102 16 by by IN en-wikipedia-org-2350 102 17 each each DT en-wikipedia-org-2350 102 18 particle particle NN en-wikipedia-org-2350 102 19 ( ( -LRB- en-wikipedia-org-2350 102 20 or or CC en-wikipedia-org-2350 102 21 the the DT en-wikipedia-org-2350 102 22 integral integral JJ en-wikipedia-org-2350 102 23 , , , en-wikipedia-org-2350 102 24 if if IN en-wikipedia-org-2350 102 25 the the DT en-wikipedia-org-2350 102 26 charges charge NNS en-wikipedia-org-2350 102 27 are be VBP en-wikipedia-org-2350 102 28 distributed distribute VBN en-wikipedia-org-2350 102 29 smoothly smoothly RB en-wikipedia-org-2350 102 30 in in IN en-wikipedia-org-2350 102 31 space space NN en-wikipedia-org-2350 102 32 ) ) -RRB- en-wikipedia-org-2350 102 33 . . . en-wikipedia-org-2350 103 1 Outline outline NN en-wikipedia-org-2350 103 2 of of IN en-wikipedia-org-2350 103 3 proof proof NN en-wikipedia-org-2350 103 4 Coulomb Coulomb NNP en-wikipedia-org-2350 103 5 's 's POS en-wikipedia-org-2350 103 6 law law NN en-wikipedia-org-2350 103 7 states state VBZ en-wikipedia-org-2350 103 8 that that IN en-wikipedia-org-2350 103 9 the the DT en-wikipedia-org-2350 103 10 electric electric JJ en-wikipedia-org-2350 103 11 field field NN en-wikipedia-org-2350 103 12 due due IN en-wikipedia-org-2350 103 13 to to IN en-wikipedia-org-2350 103 14 a a DT en-wikipedia-org-2350 103 15 stationary stationary JJ en-wikipedia-org-2350 103 16 point point NN en-wikipedia-org-2350 103 17 charge charge NN en-wikipedia-org-2350 103 18 is be VBZ en-wikipedia-org-2350 103 19 : : : en-wikipedia-org-2350 103 20 E E NNP en-wikipedia-org-2350 103 21 ( ( -LRB- en-wikipedia-org-2350 103 22 r r NN en-wikipedia-org-2350 103 23 ) ) -RRB- en-wikipedia-org-2350 103 24 = = SYM en-wikipedia-org-2350 103 25 q q NNP en-wikipedia-org-2350 103 26 4 4 CD en-wikipedia-org-2350 103 27 π π NN en-wikipedia-org-2350 103 28 ε ε NN en-wikipedia-org-2350 103 29 0 0 CD en-wikipedia-org-2350 103 30 e e NN en-wikipedia-org-2350 103 31 r r NN en-wikipedia-org-2350 103 32 r r NN en-wikipedia-org-2350 103 33 2 2 CD en-wikipedia-org-2350 103 34 { { -LRB- en-wikipedia-org-2350 103 35 \displaystyle \displaystyle CD en-wikipedia-org-2350 103 36 \mathbf \mathbf CD en-wikipedia-org-2350 103 37 { { -LRB- en-wikipedia-org-2350 103 38 E e NN en-wikipedia-org-2350 103 39 } } -RRB- en-wikipedia-org-2350 103 40 ( ( -LRB- en-wikipedia-org-2350 103 41 \mathbf \mathbf CD en-wikipedia-org-2350 103 42 { { -LRB- en-wikipedia-org-2350 103 43 r r NN en-wikipedia-org-2350 103 44 } } -RRB- en-wikipedia-org-2350 103 45 ) ) -RRB- en-wikipedia-org-2350 103 46 = = NFP en-wikipedia-org-2350 103 47 { { -LRB- en-wikipedia-org-2350 103 48 \frac \frac NNP en-wikipedia-org-2350 103 49 { { -LRB- en-wikipedia-org-2350 103 50 q}{4\pi q}{4\pi NNP en-wikipedia-org-2350 103 51 \varepsilon \varepsilon NNP en-wikipedia-org-2350 103 52 _ _ NNP en-wikipedia-org-2350 103 53 { { -LRB- en-wikipedia-org-2350 103 54 0}}}{\frac 0}}}{\frac NFP en-wikipedia-org-2350 103 55 { { -LRB- en-wikipedia-org-2350 103 56 \mathbf \mathbf CD en-wikipedia-org-2350 103 57 { { -LRB- en-wikipedia-org-2350 103 58 e e NN en-wikipedia-org-2350 103 59 } } -RRB- en-wikipedia-org-2350 103 60 _ _ NNP en-wikipedia-org-2350 103 61 { { -LRB- en-wikipedia-org-2350 103 62 r}}{r^{2 r}}{r^{2 , en-wikipedia-org-2350 103 63 } } -RRB- en-wikipedia-org-2350 103 64 } } -RRB- en-wikipedia-org-2350 103 65 } } -RRB- en-wikipedia-org-2350 103 66 } } -RRB- en-wikipedia-org-2350 103 67 where where WRB en-wikipedia-org-2350 103 68 er er UH en-wikipedia-org-2350 103 69 is be VBZ en-wikipedia-org-2350 103 70 the the DT en-wikipedia-org-2350 103 71 radial radial JJ en-wikipedia-org-2350 103 72 unit unit NN en-wikipedia-org-2350 103 73 vector vector NN en-wikipedia-org-2350 103 74 , , , en-wikipedia-org-2350 103 75 r r NNP en-wikipedia-org-2350 103 76 is be VBZ en-wikipedia-org-2350 103 77 the the DT en-wikipedia-org-2350 103 78 radius radius NN en-wikipedia-org-2350 103 79 , , , en-wikipedia-org-2350 103 80 |r| |r| NNP en-wikipedia-org-2350 103 81 , , , en-wikipedia-org-2350 103 82 ε0 ε0 NN en-wikipedia-org-2350 103 83 is be VBZ en-wikipedia-org-2350 103 84 the the DT en-wikipedia-org-2350 103 85 electric electric JJ en-wikipedia-org-2350 103 86 constant constant NN en-wikipedia-org-2350 103 87 , , , en-wikipedia-org-2350 103 88 q q NNP en-wikipedia-org-2350 103 89 is be VBZ en-wikipedia-org-2350 103 90 the the DT en-wikipedia-org-2350 103 91 charge charge NN en-wikipedia-org-2350 103 92 of of IN en-wikipedia-org-2350 103 93 the the DT en-wikipedia-org-2350 103 94 particle particle NN en-wikipedia-org-2350 103 95 , , , en-wikipedia-org-2350 103 96 which which WDT en-wikipedia-org-2350 103 97 is be VBZ en-wikipedia-org-2350 103 98 assumed assume VBN en-wikipedia-org-2350 103 99 to to TO en-wikipedia-org-2350 103 100 be be VB en-wikipedia-org-2350 103 101 located locate VBN en-wikipedia-org-2350 103 102 at at IN en-wikipedia-org-2350 103 103 the the DT en-wikipedia-org-2350 103 104 origin origin NN en-wikipedia-org-2350 103 105 . . . en-wikipedia-org-2350 104 1 Using use VBG en-wikipedia-org-2350 104 2 the the DT en-wikipedia-org-2350 104 3 expression expression NN en-wikipedia-org-2350 104 4 from from IN en-wikipedia-org-2350 104 5 Coulomb Coulomb NNP en-wikipedia-org-2350 104 6 's 's POS en-wikipedia-org-2350 104 7 law law NN en-wikipedia-org-2350 104 8 , , , en-wikipedia-org-2350 104 9 we -PRON- PRP en-wikipedia-org-2350 104 10 get get VBP en-wikipedia-org-2350 104 11 the the DT en-wikipedia-org-2350 104 12 total total JJ en-wikipedia-org-2350 104 13 field field NN en-wikipedia-org-2350 104 14 at at IN en-wikipedia-org-2350 104 15 r r NN en-wikipedia-org-2350 104 16 by by IN en-wikipedia-org-2350 104 17 using use VBG en-wikipedia-org-2350 104 18 an an DT en-wikipedia-org-2350 104 19 integral integral NN en-wikipedia-org-2350 104 20 to to TO en-wikipedia-org-2350 104 21 sum sum VB en-wikipedia-org-2350 104 22 the the DT en-wikipedia-org-2350 104 23 field field NN en-wikipedia-org-2350 104 24 at at IN en-wikipedia-org-2350 104 25 r r NN en-wikipedia-org-2350 104 26 due due IN en-wikipedia-org-2350 104 27 to to IN en-wikipedia-org-2350 104 28 the the DT en-wikipedia-org-2350 104 29 infinitesimal infinitesimal JJ en-wikipedia-org-2350 104 30 charge charge NN en-wikipedia-org-2350 104 31 at at IN en-wikipedia-org-2350 104 32 each each DT en-wikipedia-org-2350 104 33 other other JJ en-wikipedia-org-2350 104 34 point point NN en-wikipedia-org-2350 104 35 s s VBZ en-wikipedia-org-2350 104 36 in in IN en-wikipedia-org-2350 104 37 space space NN en-wikipedia-org-2350 104 38 , , , en-wikipedia-org-2350 104 39 to to TO en-wikipedia-org-2350 104 40 give give VB en-wikipedia-org-2350 104 41 E E NNP en-wikipedia-org-2350 104 42 ( ( -LRB- en-wikipedia-org-2350 104 43 r r NN en-wikipedia-org-2350 104 44 ) ) -RRB- en-wikipedia-org-2350 104 45 = = SYM en-wikipedia-org-2350 104 46 1 1 CD en-wikipedia-org-2350 104 47 4 4 CD en-wikipedia-org-2350 104 48 π π NN en-wikipedia-org-2350 104 49 ε ε NN en-wikipedia-org-2350 104 50 0 0 CD en-wikipedia-org-2350 104 51 ∫ ∫ CD en-wikipedia-org-2350 104 52 ρ ρ NN en-wikipedia-org-2350 104 53 ( ( -LRB- en-wikipedia-org-2350 104 54 s s NNP en-wikipedia-org-2350 104 55 ) ) -RRB- en-wikipedia-org-2350 104 56 ( ( -LRB- en-wikipedia-org-2350 104 57 r r NN en-wikipedia-org-2350 104 58 − − NNP en-wikipedia-org-2350 104 59 s s POS en-wikipedia-org-2350 104 60 ) ) -RRB- en-wikipedia-org-2350 104 61 | | NNP en-wikipedia-org-2350 104 62 r r NNP en-wikipedia-org-2350 104 63 − − NNP en-wikipedia-org-2350 104 64 s s NNP en-wikipedia-org-2350 104 65 | | NNP en-wikipedia-org-2350 104 66 3 3 CD en-wikipedia-org-2350 104 67 d d NN en-wikipedia-org-2350 104 68 3 3 CD en-wikipedia-org-2350 104 69 s s NN en-wikipedia-org-2350 104 70 { { -LRB- en-wikipedia-org-2350 104 71 \displaystyle \displaystyle CD en-wikipedia-org-2350 104 72 \mathbf \mathbf CD en-wikipedia-org-2350 104 73 { { -LRB- en-wikipedia-org-2350 104 74 E e NN en-wikipedia-org-2350 104 75 } } -RRB- en-wikipedia-org-2350 104 76 ( ( -LRB- en-wikipedia-org-2350 104 77 \mathbf \mathbf CD en-wikipedia-org-2350 104 78 { { -LRB- en-wikipedia-org-2350 104 79 r r NN en-wikipedia-org-2350 104 80 } } -RRB- en-wikipedia-org-2350 104 81 ) ) -RRB- en-wikipedia-org-2350 104 82 = = NFP en-wikipedia-org-2350 104 83 { { -LRB- en-wikipedia-org-2350 104 84 \frac \frac CD en-wikipedia-org-2350 104 85 { { -LRB- en-wikipedia-org-2350 104 86 1}{4\pi 1}{4\pi CD en-wikipedia-org-2350 104 87 \varepsilon \varepsilon CD en-wikipedia-org-2350 104 88 _ _ NNP en-wikipedia-org-2350 104 89 { { -LRB- en-wikipedia-org-2350 104 90 0}}}\int 0}}}\int NNP en-wikipedia-org-2350 104 91 { { -LRB- en-wikipedia-org-2350 104 92 \frac \frac CD en-wikipedia-org-2350 104 93 { { -LRB- en-wikipedia-org-2350 104 94 \rho \rho NN en-wikipedia-org-2350 104 95 ( ( -LRB- en-wikipedia-org-2350 104 96 \mathbf \mathbf CD en-wikipedia-org-2350 104 97 { { -LRB- en-wikipedia-org-2350 104 98 s s NN en-wikipedia-org-2350 104 99 } } -RRB- en-wikipedia-org-2350 104 100 ) ) -RRB- en-wikipedia-org-2350 104 101 ( ( -LRB- en-wikipedia-org-2350 104 102 \mathbf \mathbf CD en-wikipedia-org-2350 104 103 { { -LRB- en-wikipedia-org-2350 104 104 r r NN en-wikipedia-org-2350 104 105 } } -RRB- en-wikipedia-org-2350 104 106 -\mathbf -\mathbf NFP en-wikipedia-org-2350 104 107 { { -LRB- en-wikipedia-org-2350 104 108 s s NN en-wikipedia-org-2350 104 109 } } -RRB- en-wikipedia-org-2350 104 110 ) ) -RRB- en-wikipedia-org-2350 104 111 } } -RRB- en-wikipedia-org-2350 104 112 { { -LRB- en-wikipedia-org-2350 104 113 |\mathbf |\mathbf NNP en-wikipedia-org-2350 104 114 { { -LRB- en-wikipedia-org-2350 104 115 r r NNP en-wikipedia-org-2350 104 116 } } -RRB- en-wikipedia-org-2350 104 117 -\mathbf -\mathbf NFP en-wikipedia-org-2350 104 118 { { -LRB- en-wikipedia-org-2350 104 119 s s NNP en-wikipedia-org-2350 104 120 } } -RRB- en-wikipedia-org-2350 104 121 |^{3}}}\,\mathbf |^{3}}}\,\mathbf NNP en-wikipedia-org-2350 104 122 { { -LRB- en-wikipedia-org-2350 104 123 d d NN en-wikipedia-org-2350 104 124 } } -RRB- en-wikipedia-org-2350 104 125 ^{3}\mathbf ^{3}\mathbf NNP en-wikipedia-org-2350 104 126 { { -LRB- en-wikipedia-org-2350 104 127 s s NN en-wikipedia-org-2350 104 128 } } -RRB- en-wikipedia-org-2350 104 129 } } -RRB- en-wikipedia-org-2350 104 130 where where WRB en-wikipedia-org-2350 104 131 ρ ρ PRP en-wikipedia-org-2350 104 132 is be VBZ en-wikipedia-org-2350 104 133 the the DT en-wikipedia-org-2350 104 134 charge charge NN en-wikipedia-org-2350 104 135 density density NN en-wikipedia-org-2350 104 136 . . . en-wikipedia-org-2350 105 1 If if IN en-wikipedia-org-2350 105 2 we -PRON- PRP en-wikipedia-org-2350 105 3 take take VBP en-wikipedia-org-2350 105 4 the the DT en-wikipedia-org-2350 105 5 divergence divergence NN en-wikipedia-org-2350 105 6 of of IN en-wikipedia-org-2350 105 7 both both DT en-wikipedia-org-2350 105 8 sides side NNS en-wikipedia-org-2350 105 9 of of IN en-wikipedia-org-2350 105 10 this this DT en-wikipedia-org-2350 105 11 equation equation NN en-wikipedia-org-2350 105 12 with with IN en-wikipedia-org-2350 105 13 respect respect NN en-wikipedia-org-2350 105 14 to to IN en-wikipedia-org-2350 105 15 r r NN en-wikipedia-org-2350 105 16 , , , en-wikipedia-org-2350 105 17 and and CC en-wikipedia-org-2350 105 18 use use VB en-wikipedia-org-2350 105 19 the the DT en-wikipedia-org-2350 105 20 known known JJ en-wikipedia-org-2350 105 21 theorem[29 theorem[29 NN en-wikipedia-org-2350 105 22 ] ] -RRB- en-wikipedia-org-2350 105 23 ∇ ∇ NNP en-wikipedia-org-2350 105 24 ⋅ ⋅ NNP en-wikipedia-org-2350 105 25 ( ( -LRB- en-wikipedia-org-2350 105 26 r r NNP en-wikipedia-org-2350 105 27 | | NNP en-wikipedia-org-2350 105 28 r r NNP en-wikipedia-org-2350 105 29 | | CD en-wikipedia-org-2350 105 30 3 3 CD en-wikipedia-org-2350 105 31 ) ) -RRB- en-wikipedia-org-2350 105 32 = = SYM en-wikipedia-org-2350 105 33 4 4 CD en-wikipedia-org-2350 105 34 π π NN en-wikipedia-org-2350 105 35 δ δ NN en-wikipedia-org-2350 105 36 ( ( -LRB- en-wikipedia-org-2350 105 37 r r NN en-wikipedia-org-2350 105 38 ) ) -RRB- en-wikipedia-org-2350 105 39 { { -LRB- en-wikipedia-org-2350 105 40 \displaystyle \displaystyle CD en-wikipedia-org-2350 105 41 \nabla \nabla CD en-wikipedia-org-2350 105 42 \cdot \cdot CD en-wikipedia-org-2350 105 43 \left({\frac \left({\frac CD en-wikipedia-org-2350 105 44 { { -LRB- en-wikipedia-org-2350 105 45 \mathbf \mathbf CD en-wikipedia-org-2350 105 46 { { -LRB- en-wikipedia-org-2350 105 47 r r NN en-wikipedia-org-2350 105 48 } } -RRB- en-wikipedia-org-2350 105 49 } } -RRB- en-wikipedia-org-2350 105 50 { { -LRB- en-wikipedia-org-2350 105 51 |\mathbf |\mathbf NNP en-wikipedia-org-2350 105 52 { { -LRB- en-wikipedia-org-2350 105 53 r r NNP en-wikipedia-org-2350 105 54 } } -RRB- en-wikipedia-org-2350 105 55 |^{3}}}\right)=4\pi |^{3}}}\right)=4\pi NNP en-wikipedia-org-2350 105 56 \delta \delta NN en-wikipedia-org-2350 105 57 ( ( -LRB- en-wikipedia-org-2350 105 58 \mathbf \mathbf CD en-wikipedia-org-2350 105 59 { { -LRB- en-wikipedia-org-2350 105 60 r r NN en-wikipedia-org-2350 105 61 } } -RRB- en-wikipedia-org-2350 105 62 ) ) -RRB- en-wikipedia-org-2350 105 63 } } -RRB- en-wikipedia-org-2350 105 64 where where WRB en-wikipedia-org-2350 105 65 δ(r δ(r NNP en-wikipedia-org-2350 105 66 ) ) -RRB- en-wikipedia-org-2350 105 67 is be VBZ en-wikipedia-org-2350 105 68 the the DT en-wikipedia-org-2350 105 69 Dirac Dirac NNP en-wikipedia-org-2350 105 70 delta delta NN en-wikipedia-org-2350 105 71 function function NN en-wikipedia-org-2350 105 72 , , , en-wikipedia-org-2350 105 73 the the DT en-wikipedia-org-2350 105 74 result result NN en-wikipedia-org-2350 105 75 is be VBZ en-wikipedia-org-2350 105 76 ∇ ∇ NNP en-wikipedia-org-2350 105 77 ⋅ ⋅ NNP en-wikipedia-org-2350 105 78 E E NNP en-wikipedia-org-2350 105 79 ( ( -LRB- en-wikipedia-org-2350 105 80 r r NN en-wikipedia-org-2350 105 81 ) ) -RRB- en-wikipedia-org-2350 105 82 = = NN en-wikipedia-org-2350 105 83 1 1 CD en-wikipedia-org-2350 105 84 ε ε NN en-wikipedia-org-2350 105 85 0 0 CD en-wikipedia-org-2350 105 86 ∫ ∫ CD en-wikipedia-org-2350 105 87 ρ ρ NN en-wikipedia-org-2350 105 88 ( ( -LRB- en-wikipedia-org-2350 105 89 s s NNP en-wikipedia-org-2350 105 90 ) ) -RRB- en-wikipedia-org-2350 105 91 δ δ NN en-wikipedia-org-2350 105 92 ( ( -LRB- en-wikipedia-org-2350 105 93 r r NNP en-wikipedia-org-2350 105 94 − − NNP en-wikipedia-org-2350 105 95 s s POS en-wikipedia-org-2350 105 96 ) ) -RRB- en-wikipedia-org-2350 105 97 d d NNP en-wikipedia-org-2350 105 98 3 3 CD en-wikipedia-org-2350 105 99 s s NN en-wikipedia-org-2350 105 100 { { -LRB- en-wikipedia-org-2350 105 101 \displaystyle \displaystyle CD en-wikipedia-org-2350 105 102 \nabla \nabla CD en-wikipedia-org-2350 105 103 \cdot \cdot CD en-wikipedia-org-2350 105 104 \mathbf \mathbf CD en-wikipedia-org-2350 105 105 { { -LRB- en-wikipedia-org-2350 105 106 E e NN en-wikipedia-org-2350 105 107 } } -RRB- en-wikipedia-org-2350 105 108 ( ( -LRB- en-wikipedia-org-2350 105 109 \mathbf \mathbf CD en-wikipedia-org-2350 105 110 { { -LRB- en-wikipedia-org-2350 105 111 r r NN en-wikipedia-org-2350 105 112 } } -RRB- en-wikipedia-org-2350 105 113 ) ) -RRB- en-wikipedia-org-2350 105 114 = = NFP en-wikipedia-org-2350 105 115 { { -LRB- en-wikipedia-org-2350 105 116 \frac \frac CD en-wikipedia-org-2350 105 117 { { -LRB- en-wikipedia-org-2350 105 118 1}{\varepsilon 1}{\varepsilon CD en-wikipedia-org-2350 105 119 _ _ NNP en-wikipedia-org-2350 105 120 { { -LRB- en-wikipedia-org-2350 105 121 0}}}\int 0}}}\int NN en-wikipedia-org-2350 105 122 \rho \rho NN en-wikipedia-org-2350 105 123 ( ( -LRB- en-wikipedia-org-2350 105 124 \mathbf \mathbf CD en-wikipedia-org-2350 105 125 { { -LRB- en-wikipedia-org-2350 105 126 s s NN en-wikipedia-org-2350 105 127 } } -RRB- en-wikipedia-org-2350 105 128 ) ) -RRB- en-wikipedia-org-2350 105 129 \,\delta \,\delta NNP en-wikipedia-org-2350 105 130 ( ( -LRB- en-wikipedia-org-2350 105 131 \mathbf \mathbf CD en-wikipedia-org-2350 105 132 { { -LRB- en-wikipedia-org-2350 105 133 r r NN en-wikipedia-org-2350 105 134 } } -RRB- en-wikipedia-org-2350 105 135 -\mathbf -\mathbf NFP en-wikipedia-org-2350 105 136 { { -LRB- en-wikipedia-org-2350 105 137 s s NNP en-wikipedia-org-2350 105 138 } } -RRB- en-wikipedia-org-2350 105 139 ) ) -RRB- en-wikipedia-org-2350 105 140 \,\mathbf \,\mathbf CD en-wikipedia-org-2350 105 141 { { -LRB- en-wikipedia-org-2350 105 142 d d NN en-wikipedia-org-2350 105 143 } } -RRB- en-wikipedia-org-2350 105 144 ^{3}\mathbf ^{3}\mathbf NN en-wikipedia-org-2350 105 145 { { -LRB- en-wikipedia-org-2350 105 146 s s NN en-wikipedia-org-2350 105 147 } } -RRB- en-wikipedia-org-2350 105 148 } } -RRB- en-wikipedia-org-2350 105 149 Using use VBG en-wikipedia-org-2350 105 150 the the DT en-wikipedia-org-2350 105 151 " " `` en-wikipedia-org-2350 105 152 sifting sift VBG en-wikipedia-org-2350 105 153 property property NN en-wikipedia-org-2350 105 154 " " '' en-wikipedia-org-2350 105 155 of of IN en-wikipedia-org-2350 105 156 the the DT en-wikipedia-org-2350 105 157 Dirac Dirac NNP en-wikipedia-org-2350 105 158 delta delta NN en-wikipedia-org-2350 105 159 function function NN en-wikipedia-org-2350 105 160 , , , en-wikipedia-org-2350 105 161 we -PRON- PRP en-wikipedia-org-2350 105 162 arrive arrive VBP en-wikipedia-org-2350 105 163 at at IN en-wikipedia-org-2350 105 164 ∇ ∇ NNP en-wikipedia-org-2350 105 165 ⋅ ⋅ NNP en-wikipedia-org-2350 105 166 E E NNP en-wikipedia-org-2350 105 167 ( ( -LRB- en-wikipedia-org-2350 105 168 r r NN en-wikipedia-org-2350 105 169 ) ) -RRB- en-wikipedia-org-2350 105 170 = = NFP en-wikipedia-org-2350 105 171 ρ ρ FW en-wikipedia-org-2350 105 172 ( ( -LRB- en-wikipedia-org-2350 105 173 r r NN en-wikipedia-org-2350 105 174 ) ) -RRB- en-wikipedia-org-2350 105 175 ε ε NN en-wikipedia-org-2350 105 176 0 0 CD en-wikipedia-org-2350 105 177 , , , en-wikipedia-org-2350 105 178 { { -LRB- en-wikipedia-org-2350 105 179 \displaystyle \displaystyle CD en-wikipedia-org-2350 105 180 \nabla \nabla CD en-wikipedia-org-2350 105 181 \cdot \cdot CD en-wikipedia-org-2350 105 182 \mathbf \mathbf CD en-wikipedia-org-2350 105 183 { { -LRB- en-wikipedia-org-2350 105 184 E e NN en-wikipedia-org-2350 105 185 } } -RRB- en-wikipedia-org-2350 105 186 ( ( -LRB- en-wikipedia-org-2350 105 187 \mathbf \mathbf CD en-wikipedia-org-2350 105 188 { { -LRB- en-wikipedia-org-2350 105 189 r r NN en-wikipedia-org-2350 105 190 } } -RRB- en-wikipedia-org-2350 105 191 ) ) -RRB- en-wikipedia-org-2350 105 192 = = NFP en-wikipedia-org-2350 105 193 { { -LRB- en-wikipedia-org-2350 105 194 \frac \frac CD en-wikipedia-org-2350 105 195 { { -LRB- en-wikipedia-org-2350 105 196 \rho \rho NN en-wikipedia-org-2350 105 197 ( ( -LRB- en-wikipedia-org-2350 105 198 \mathbf \mathbf CD en-wikipedia-org-2350 105 199 { { -LRB- en-wikipedia-org-2350 105 200 r r NN en-wikipedia-org-2350 105 201 } } -RRB- en-wikipedia-org-2350 105 202 ) ) -RRB- en-wikipedia-org-2350 105 203 } } -RRB- en-wikipedia-org-2350 105 204 { { -LRB- en-wikipedia-org-2350 105 205 \varepsilon \varepsilon CD en-wikipedia-org-2350 105 206 _ _ NNP en-wikipedia-org-2350 105 207 { { -LRB- en-wikipedia-org-2350 105 208 0 0 CD en-wikipedia-org-2350 105 209 } } -RRB- en-wikipedia-org-2350 105 210 } } -RRB- en-wikipedia-org-2350 105 211 } } -RRB- en-wikipedia-org-2350 105 212 , , , en-wikipedia-org-2350 105 213 } } -RRB- en-wikipedia-org-2350 105 214 which which WDT en-wikipedia-org-2350 105 215 is be VBZ en-wikipedia-org-2350 105 216 the the DT en-wikipedia-org-2350 105 217 differential differential JJ en-wikipedia-org-2350 105 218 form form NN en-wikipedia-org-2350 105 219 of of IN en-wikipedia-org-2350 105 220 Gauss Gauss NNP en-wikipedia-org-2350 105 221 ' ' POS en-wikipedia-org-2350 105 222 law law NN en-wikipedia-org-2350 105 223 , , , en-wikipedia-org-2350 105 224 as as IN en-wikipedia-org-2350 105 225 desired desire VBN en-wikipedia-org-2350 105 226 . . . en-wikipedia-org-2350 106 1 Note note VB en-wikipedia-org-2350 106 2 that that IN en-wikipedia-org-2350 106 3 since since IN en-wikipedia-org-2350 106 4 Coulomb Coulomb NNP en-wikipedia-org-2350 106 5 's 's POS en-wikipedia-org-2350 106 6 law law NN en-wikipedia-org-2350 106 7 only only RB en-wikipedia-org-2350 106 8 applies apply VBZ en-wikipedia-org-2350 106 9 to to IN en-wikipedia-org-2350 106 10 stationary stationary JJ en-wikipedia-org-2350 106 11 charges charge NNS en-wikipedia-org-2350 106 12 , , , en-wikipedia-org-2350 106 13 there there EX en-wikipedia-org-2350 106 14 is be VBZ en-wikipedia-org-2350 106 15 no no DT en-wikipedia-org-2350 106 16 reason reason NN en-wikipedia-org-2350 106 17 to to TO en-wikipedia-org-2350 106 18 expect expect VB en-wikipedia-org-2350 106 19 Gauss Gauss NNP en-wikipedia-org-2350 106 20 's 's POS en-wikipedia-org-2350 106 21 law law NN en-wikipedia-org-2350 106 22 to to TO en-wikipedia-org-2350 106 23 hold hold VB en-wikipedia-org-2350 106 24 for for IN en-wikipedia-org-2350 106 25 moving move VBG en-wikipedia-org-2350 106 26 charges charge NNS en-wikipedia-org-2350 106 27 based base VBN en-wikipedia-org-2350 106 28 on on IN en-wikipedia-org-2350 106 29 this this DT en-wikipedia-org-2350 106 30 derivation derivation NN en-wikipedia-org-2350 106 31 alone alone RB en-wikipedia-org-2350 106 32 . . . en-wikipedia-org-2350 107 1 In in IN en-wikipedia-org-2350 107 2 fact fact NN en-wikipedia-org-2350 107 3 , , , en-wikipedia-org-2350 107 4 Gauss Gauss NNP en-wikipedia-org-2350 107 5 's 's POS en-wikipedia-org-2350 107 6 law law NN en-wikipedia-org-2350 107 7 does do VBZ en-wikipedia-org-2350 107 8 hold hold VB en-wikipedia-org-2350 107 9 for for IN en-wikipedia-org-2350 107 10 moving move VBG en-wikipedia-org-2350 107 11 charges charge NNS en-wikipedia-org-2350 107 12 , , , en-wikipedia-org-2350 107 13 and and CC en-wikipedia-org-2350 107 14 in in IN en-wikipedia-org-2350 107 15 this this DT en-wikipedia-org-2350 107 16 respect respect NN en-wikipedia-org-2350 107 17 Gauss Gauss NNP en-wikipedia-org-2350 107 18 's 's POS en-wikipedia-org-2350 107 19 law law NN en-wikipedia-org-2350 107 20 is be VBZ en-wikipedia-org-2350 107 21 more more RBR en-wikipedia-org-2350 107 22 general general JJ en-wikipedia-org-2350 107 23 than than IN en-wikipedia-org-2350 107 24 Coulomb Coulomb NNP en-wikipedia-org-2350 107 25 's 's POS en-wikipedia-org-2350 107 26 law law NN en-wikipedia-org-2350 107 27 . . . en-wikipedia-org-2350 108 1 Deriving derive VBG en-wikipedia-org-2350 108 2 Coulomb Coulomb NNP en-wikipedia-org-2350 108 3 's 's POS en-wikipedia-org-2350 108 4 law law NN en-wikipedia-org-2350 108 5 from from IN en-wikipedia-org-2350 108 6 Gauss Gauss NNP en-wikipedia-org-2350 108 7 's 's POS en-wikipedia-org-2350 108 8 law[edit law[edit NN en-wikipedia-org-2350 108 9 ] ] -RRB- en-wikipedia-org-2350 108 10 Strictly strictly RB en-wikipedia-org-2350 108 11 speaking speak VBG en-wikipedia-org-2350 108 12 , , , en-wikipedia-org-2350 108 13 Coulomb Coulomb NNP en-wikipedia-org-2350 108 14 's 's POS en-wikipedia-org-2350 108 15 law law NN en-wikipedia-org-2350 108 16 can can MD en-wikipedia-org-2350 108 17 not not RB en-wikipedia-org-2350 108 18 be be VB en-wikipedia-org-2350 108 19 derived derive VBN en-wikipedia-org-2350 108 20 from from IN en-wikipedia-org-2350 108 21 Gauss Gauss NNP en-wikipedia-org-2350 108 22 's 's POS en-wikipedia-org-2350 108 23 law law NN en-wikipedia-org-2350 108 24 alone alone RB en-wikipedia-org-2350 108 25 , , , en-wikipedia-org-2350 108 26 since since IN en-wikipedia-org-2350 108 27 Gauss Gauss NNP en-wikipedia-org-2350 108 28 's 's POS en-wikipedia-org-2350 108 29 law law NN en-wikipedia-org-2350 108 30 does do VBZ en-wikipedia-org-2350 108 31 not not RB en-wikipedia-org-2350 108 32 give give VB en-wikipedia-org-2350 108 33 any any DT en-wikipedia-org-2350 108 34 information information NN en-wikipedia-org-2350 108 35 regarding regard VBG en-wikipedia-org-2350 108 36 the the DT en-wikipedia-org-2350 108 37 curl curl NN en-wikipedia-org-2350 108 38 of of IN en-wikipedia-org-2350 108 39 E E NNP en-wikipedia-org-2350 108 40 ( ( -LRB- en-wikipedia-org-2350 108 41 see see VB en-wikipedia-org-2350 108 42 Helmholtz Helmholtz NNP en-wikipedia-org-2350 108 43 decomposition decomposition NN en-wikipedia-org-2350 108 44 and and CC en-wikipedia-org-2350 108 45 Faraday Faraday NNP en-wikipedia-org-2350 108 46 's 's POS en-wikipedia-org-2350 108 47 law law NN en-wikipedia-org-2350 108 48 ) ) -RRB- en-wikipedia-org-2350 108 49 . . . en-wikipedia-org-2350 109 1 However however RB en-wikipedia-org-2350 109 2 , , , en-wikipedia-org-2350 109 3 Coulomb Coulomb NNP en-wikipedia-org-2350 109 4 's 's POS en-wikipedia-org-2350 109 5 law law NN en-wikipedia-org-2350 109 6 can can MD en-wikipedia-org-2350 109 7 be be VB en-wikipedia-org-2350 109 8 proven prove VBN en-wikipedia-org-2350 109 9 from from IN en-wikipedia-org-2350 109 10 Gauss Gauss NNP en-wikipedia-org-2350 109 11 's 's POS en-wikipedia-org-2350 109 12 law law NN en-wikipedia-org-2350 109 13 if if IN en-wikipedia-org-2350 109 14 it -PRON- PRP en-wikipedia-org-2350 109 15 is be VBZ en-wikipedia-org-2350 109 16 assumed assume VBN en-wikipedia-org-2350 109 17 , , , en-wikipedia-org-2350 109 18 in in IN en-wikipedia-org-2350 109 19 addition addition NN en-wikipedia-org-2350 109 20 , , , en-wikipedia-org-2350 109 21 that that IN en-wikipedia-org-2350 109 22 the the DT en-wikipedia-org-2350 109 23 electric electric JJ en-wikipedia-org-2350 109 24 field field NN en-wikipedia-org-2350 109 25 from from IN en-wikipedia-org-2350 109 26 a a DT en-wikipedia-org-2350 109 27 point point NN en-wikipedia-org-2350 109 28 charge charge NN en-wikipedia-org-2350 109 29 is be VBZ en-wikipedia-org-2350 109 30 spherically spherically RB en-wikipedia-org-2350 109 31 symmetric symmetric JJ en-wikipedia-org-2350 109 32 ( ( -LRB- en-wikipedia-org-2350 109 33 this this DT en-wikipedia-org-2350 109 34 assumption assumption NN en-wikipedia-org-2350 109 35 , , , en-wikipedia-org-2350 109 36 like like IN en-wikipedia-org-2350 109 37 Coulomb Coulomb NNP en-wikipedia-org-2350 109 38 's 's POS en-wikipedia-org-2350 109 39 law law NN en-wikipedia-org-2350 109 40 itself -PRON- PRP en-wikipedia-org-2350 109 41 , , , en-wikipedia-org-2350 109 42 is be VBZ en-wikipedia-org-2350 109 43 exactly exactly RB en-wikipedia-org-2350 109 44 true true JJ en-wikipedia-org-2350 109 45 if if IN en-wikipedia-org-2350 109 46 the the DT en-wikipedia-org-2350 109 47 charge charge NN en-wikipedia-org-2350 109 48 is be VBZ en-wikipedia-org-2350 109 49 stationary stationary JJ en-wikipedia-org-2350 109 50 , , , en-wikipedia-org-2350 109 51 and and CC en-wikipedia-org-2350 109 52 approximately approximately RB en-wikipedia-org-2350 109 53 true true JJ en-wikipedia-org-2350 109 54 if if IN en-wikipedia-org-2350 109 55 the the DT en-wikipedia-org-2350 109 56 charge charge NN en-wikipedia-org-2350 109 57 is be VBZ en-wikipedia-org-2350 109 58 in in IN en-wikipedia-org-2350 109 59 motion motion NN en-wikipedia-org-2350 109 60 ) ) -RRB- en-wikipedia-org-2350 109 61 . . . en-wikipedia-org-2350 110 1 Outline outline NN en-wikipedia-org-2350 110 2 of of IN en-wikipedia-org-2350 110 3 proof proof NN en-wikipedia-org-2350 110 4 Taking Taking NNP en-wikipedia-org-2350 110 5 S S NNP en-wikipedia-org-2350 110 6 in in IN en-wikipedia-org-2350 110 7 the the DT en-wikipedia-org-2350 110 8 integral integral JJ en-wikipedia-org-2350 110 9 form form NN en-wikipedia-org-2350 110 10 of of IN en-wikipedia-org-2350 110 11 Gauss Gauss NNP en-wikipedia-org-2350 110 12 ' ' POS en-wikipedia-org-2350 110 13 law law NN en-wikipedia-org-2350 110 14 to to TO en-wikipedia-org-2350 110 15 be be VB en-wikipedia-org-2350 110 16 a a DT en-wikipedia-org-2350 110 17 spherical spherical JJ en-wikipedia-org-2350 110 18 surface surface NN en-wikipedia-org-2350 110 19 of of IN en-wikipedia-org-2350 110 20 radius radius NN en-wikipedia-org-2350 110 21 r r NNP en-wikipedia-org-2350 110 22 , , , en-wikipedia-org-2350 110 23 centered center VBN en-wikipedia-org-2350 110 24 at at IN en-wikipedia-org-2350 110 25 the the DT en-wikipedia-org-2350 110 26 point point NN en-wikipedia-org-2350 110 27 charge charge NN en-wikipedia-org-2350 110 28 Q Q NNP en-wikipedia-org-2350 110 29 , , , en-wikipedia-org-2350 110 30 we -PRON- PRP en-wikipedia-org-2350 110 31 have have VBP en-wikipedia-org-2350 110 32 ∮ ∮ VBN en-wikipedia-org-2350 110 33 S s NN en-wikipedia-org-2350 110 34 E e NN en-wikipedia-org-2350 110 35 ⋅ ⋅ NNP en-wikipedia-org-2350 110 36 d d NNP en-wikipedia-org-2350 110 37 A a NN en-wikipedia-org-2350 110 38 = = SYM en-wikipedia-org-2350 110 39 Q q NN en-wikipedia-org-2350 110 40 ε ε NN en-wikipedia-org-2350 110 41 0 0 CD en-wikipedia-org-2350 110 42 { { -LRB- en-wikipedia-org-2350 110 43 \displaystyle \displaystyle CD en-wikipedia-org-2350 110 44 \oint \oint CD en-wikipedia-org-2350 110 45 _ _ NNP en-wikipedia-org-2350 110 46 { { -LRB- en-wikipedia-org-2350 110 47 S}\mathbf S}\mathbf NNP en-wikipedia-org-2350 110 48 { { -LRB- en-wikipedia-org-2350 110 49 E e NN en-wikipedia-org-2350 110 50 } } -RRB- en-wikipedia-org-2350 110 51 \cdot \cdot CD en-wikipedia-org-2350 110 52 d\mathbf d\mathbf NNP en-wikipedia-org-2350 110 53 { { -LRB- en-wikipedia-org-2350 110 54 A a NN en-wikipedia-org-2350 110 55 } } -RRB- en-wikipedia-org-2350 110 56 = = NFP en-wikipedia-org-2350 110 57 { { -LRB- en-wikipedia-org-2350 110 58 \frac \frac NNP en-wikipedia-org-2350 110 59 { { -LRB- en-wikipedia-org-2350 110 60 Q}{\varepsilon q}{\varepsilon CD en-wikipedia-org-2350 110 61 _ _ NNP en-wikipedia-org-2350 110 62 { { -LRB- en-wikipedia-org-2350 110 63 0 0 CD en-wikipedia-org-2350 110 64 } } -RRB- en-wikipedia-org-2350 110 65 } } -RRB- en-wikipedia-org-2350 110 66 } } -RRB- en-wikipedia-org-2350 110 67 } } -RRB- en-wikipedia-org-2350 110 68 By by IN en-wikipedia-org-2350 110 69 the the DT en-wikipedia-org-2350 110 70 assumption assumption NN en-wikipedia-org-2350 110 71 of of IN en-wikipedia-org-2350 110 72 spherical spherical JJ en-wikipedia-org-2350 110 73 symmetry symmetry NN en-wikipedia-org-2350 110 74 , , , en-wikipedia-org-2350 110 75 the the DT en-wikipedia-org-2350 110 76 integrand integrand NN en-wikipedia-org-2350 110 77 is be VBZ en-wikipedia-org-2350 110 78 a a DT en-wikipedia-org-2350 110 79 constant constant JJ en-wikipedia-org-2350 110 80 which which WDT en-wikipedia-org-2350 110 81 can can MD en-wikipedia-org-2350 110 82 be be VB en-wikipedia-org-2350 110 83 taken take VBN en-wikipedia-org-2350 110 84 out out IN en-wikipedia-org-2350 110 85 of of IN en-wikipedia-org-2350 110 86 the the DT en-wikipedia-org-2350 110 87 integral integral NN en-wikipedia-org-2350 110 88 . . . en-wikipedia-org-2350 111 1 The the DT en-wikipedia-org-2350 111 2 result result NN en-wikipedia-org-2350 111 3 is be VBZ en-wikipedia-org-2350 111 4 4 4 CD en-wikipedia-org-2350 111 5 π π NN en-wikipedia-org-2350 111 6 r r NN en-wikipedia-org-2350 111 7 2 2 CD en-wikipedia-org-2350 111 8 r r NN en-wikipedia-org-2350 111 9 ^ ^ NNP en-wikipedia-org-2350 111 10 ⋅ ⋅ NNP en-wikipedia-org-2350 111 11 E E NNP en-wikipedia-org-2350 111 12 ( ( -LRB- en-wikipedia-org-2350 111 13 r r NN en-wikipedia-org-2350 111 14 ) ) -RRB- en-wikipedia-org-2350 111 15 = = NFP en-wikipedia-org-2350 111 16 Q q NN en-wikipedia-org-2350 111 17 ε ε NN en-wikipedia-org-2350 111 18 0 0 CD en-wikipedia-org-2350 111 19 { { -LRB- en-wikipedia-org-2350 111 20 \displaystyle \displaystyle CD en-wikipedia-org-2350 111 21 4\pi 4\pi CD en-wikipedia-org-2350 111 22 r^{2}{\hat r^{2}{\hat DT en-wikipedia-org-2350 111 23 { { -LRB- en-wikipedia-org-2350 111 24 \mathbf \mathbf CD en-wikipedia-org-2350 111 25 { { -LRB- en-wikipedia-org-2350 111 26 r r NN en-wikipedia-org-2350 111 27 } } -RRB- en-wikipedia-org-2350 111 28 } } -RRB- en-wikipedia-org-2350 111 29 } } -RRB- en-wikipedia-org-2350 111 30 \cdot \cdot CD en-wikipedia-org-2350 111 31 \mathbf \mathbf CD en-wikipedia-org-2350 111 32 { { -LRB- en-wikipedia-org-2350 111 33 E e NN en-wikipedia-org-2350 111 34 } } -RRB- en-wikipedia-org-2350 111 35 ( ( -LRB- en-wikipedia-org-2350 111 36 \mathbf \mathbf CD en-wikipedia-org-2350 111 37 { { -LRB- en-wikipedia-org-2350 111 38 r r NN en-wikipedia-org-2350 111 39 } } -RRB- en-wikipedia-org-2350 111 40 ) ) -RRB- en-wikipedia-org-2350 111 41 = = NFP en-wikipedia-org-2350 111 42 { { -LRB- en-wikipedia-org-2350 111 43 \frac \frac NNP en-wikipedia-org-2350 111 44 { { -LRB- en-wikipedia-org-2350 111 45 Q}{\varepsilon q}{\varepsilon CD en-wikipedia-org-2350 111 46 _ _ NNP en-wikipedia-org-2350 111 47 { { -LRB- en-wikipedia-org-2350 111 48 0 0 CD en-wikipedia-org-2350 111 49 } } -RRB- en-wikipedia-org-2350 111 50 } } -RRB- en-wikipedia-org-2350 111 51 } } -RRB- en-wikipedia-org-2350 111 52 } } -RRB- en-wikipedia-org-2350 111 53 where where WRB en-wikipedia-org-2350 111 54 r̂ r̂ NNP en-wikipedia-org-2350 111 55 is be VBZ en-wikipedia-org-2350 111 56 a a DT en-wikipedia-org-2350 111 57 unit unit NN en-wikipedia-org-2350 111 58 vector vector NN en-wikipedia-org-2350 111 59 pointing pointing NN en-wikipedia-org-2350 111 60 radially radially NNP en-wikipedia-org-2350 111 61 away away RB en-wikipedia-org-2350 111 62 from from IN en-wikipedia-org-2350 111 63 the the DT en-wikipedia-org-2350 111 64 charge charge NN en-wikipedia-org-2350 111 65 . . . en-wikipedia-org-2350 112 1 Again again RB en-wikipedia-org-2350 112 2 by by IN en-wikipedia-org-2350 112 3 spherical spherical JJ en-wikipedia-org-2350 112 4 symmetry symmetry NN en-wikipedia-org-2350 112 5 , , , en-wikipedia-org-2350 112 6 E E NNP en-wikipedia-org-2350 112 7 points point NNS en-wikipedia-org-2350 112 8 in in IN en-wikipedia-org-2350 112 9 the the DT en-wikipedia-org-2350 112 10 radial radial JJ en-wikipedia-org-2350 112 11 direction direction NN en-wikipedia-org-2350 112 12 , , , en-wikipedia-org-2350 112 13 and and CC en-wikipedia-org-2350 112 14 so so RB en-wikipedia-org-2350 112 15 we -PRON- PRP en-wikipedia-org-2350 112 16 get get VBP en-wikipedia-org-2350 112 17 E e NN en-wikipedia-org-2350 112 18 ( ( -LRB- en-wikipedia-org-2350 112 19 r r NN en-wikipedia-org-2350 112 20 ) ) -RRB- en-wikipedia-org-2350 112 21 = = NFP en-wikipedia-org-2350 112 22 Q q NN en-wikipedia-org-2350 112 23 4 4 CD en-wikipedia-org-2350 112 24 π π NN en-wikipedia-org-2350 112 25 ε ε NN en-wikipedia-org-2350 112 26 0 0 CD en-wikipedia-org-2350 112 27 r r NN en-wikipedia-org-2350 112 28 ^ ^ NN en-wikipedia-org-2350 112 29 r r NNP en-wikipedia-org-2350 112 30 2 2 CD en-wikipedia-org-2350 112 31 { { -LRB- en-wikipedia-org-2350 112 32 \displaystyle \displaystyle CD en-wikipedia-org-2350 112 33 \mathbf \mathbf CD en-wikipedia-org-2350 112 34 { { -LRB- en-wikipedia-org-2350 112 35 E e NN en-wikipedia-org-2350 112 36 } } -RRB- en-wikipedia-org-2350 112 37 ( ( -LRB- en-wikipedia-org-2350 112 38 \mathbf \mathbf CD en-wikipedia-org-2350 112 39 { { -LRB- en-wikipedia-org-2350 112 40 r r NN en-wikipedia-org-2350 112 41 } } -RRB- en-wikipedia-org-2350 112 42 ) ) -RRB- en-wikipedia-org-2350 112 43 = = NFP en-wikipedia-org-2350 112 44 { { -LRB- en-wikipedia-org-2350 112 45 \frac \frac CD en-wikipedia-org-2350 112 46 { { -LRB- en-wikipedia-org-2350 112 47 Q}{4\pi q}{4\pi CD en-wikipedia-org-2350 112 48 \varepsilon \varepsilon CD en-wikipedia-org-2350 112 49 _ _ NNP en-wikipedia-org-2350 112 50 { { -LRB- en-wikipedia-org-2350 112 51 0}}}{\frac 0}}}{\frac NFP en-wikipedia-org-2350 112 52 { { -LRB- en-wikipedia-org-2350 112 53 \hat \hat CD en-wikipedia-org-2350 112 54 { { -LRB- en-wikipedia-org-2350 112 55 \mathbf \mathbf CD en-wikipedia-org-2350 112 56 { { -LRB- en-wikipedia-org-2350 112 57 r r NN en-wikipedia-org-2350 112 58 } } -RRB- en-wikipedia-org-2350 112 59 } } -RRB- en-wikipedia-org-2350 112 60 } } -RRB- en-wikipedia-org-2350 112 61 { { -LRB- en-wikipedia-org-2350 112 62 r^{2 r^{2 NNP en-wikipedia-org-2350 112 63 } } -RRB- en-wikipedia-org-2350 112 64 } } -RRB- en-wikipedia-org-2350 112 65 } } -RRB- en-wikipedia-org-2350 112 66 } } -RRB- en-wikipedia-org-2350 112 67 which which WDT en-wikipedia-org-2350 112 68 is be VBZ en-wikipedia-org-2350 112 69 essentially essentially RB en-wikipedia-org-2350 112 70 equivalent equivalent JJ en-wikipedia-org-2350 112 71 to to IN en-wikipedia-org-2350 112 72 Coulomb Coulomb NNP en-wikipedia-org-2350 112 73 's 's POS en-wikipedia-org-2350 112 74 law law NN en-wikipedia-org-2350 112 75 . . . en-wikipedia-org-2350 113 1 Thus thus RB en-wikipedia-org-2350 113 2 the the DT en-wikipedia-org-2350 113 3 inverse inverse NN en-wikipedia-org-2350 113 4 - - HYPH en-wikipedia-org-2350 113 5 square square JJ en-wikipedia-org-2350 113 6 law law NN en-wikipedia-org-2350 113 7 dependence dependence NN en-wikipedia-org-2350 113 8 of of IN en-wikipedia-org-2350 113 9 the the DT en-wikipedia-org-2350 113 10 electric electric JJ en-wikipedia-org-2350 113 11 field field NN en-wikipedia-org-2350 113 12 in in IN en-wikipedia-org-2350 113 13 Coulomb Coulomb NNP en-wikipedia-org-2350 113 14 's 's POS en-wikipedia-org-2350 113 15 law law NN en-wikipedia-org-2350 113 16 follows follow VBZ en-wikipedia-org-2350 113 17 from from IN en-wikipedia-org-2350 113 18 Gauss Gauss NNP en-wikipedia-org-2350 113 19 ' ' POS en-wikipedia-org-2350 113 20 law law NN en-wikipedia-org-2350 113 21 . . . en-wikipedia-org-2350 114 1 Coulomb Coulomb NNP en-wikipedia-org-2350 114 2 potential[edit potential[edit NFP en-wikipedia-org-2350 114 3 ] ] -RRB- en-wikipedia-org-2350 114 4 See see VB en-wikipedia-org-2350 114 5 also also RB en-wikipedia-org-2350 114 6 : : : en-wikipedia-org-2350 114 7 Electric electric JJ en-wikipedia-org-2350 114 8 potential potential JJ en-wikipedia-org-2350 114 9 Quantum Quantum NNP en-wikipedia-org-2350 114 10 field field NN en-wikipedia-org-2350 114 11 theory[edit theory[edit CD en-wikipedia-org-2350 114 12 ] ] -RRB- en-wikipedia-org-2350 114 13 This this DT en-wikipedia-org-2350 114 14 article article NN en-wikipedia-org-2350 114 15 may may MD en-wikipedia-org-2350 114 16 be be VB en-wikipedia-org-2350 114 17 too too RB en-wikipedia-org-2350 114 18 technical technical JJ en-wikipedia-org-2350 114 19 for for IN en-wikipedia-org-2350 114 20 most most JJS en-wikipedia-org-2350 114 21 readers reader NNS en-wikipedia-org-2350 114 22 to to TO en-wikipedia-org-2350 114 23 understand understand VB en-wikipedia-org-2350 114 24 . . . en-wikipedia-org-2350 115 1 Please please UH en-wikipedia-org-2350 115 2 help help VB en-wikipedia-org-2350 115 3 improve improve VB en-wikipedia-org-2350 115 4 it -PRON- PRP en-wikipedia-org-2350 115 5 to to TO en-wikipedia-org-2350 115 6 make make VB en-wikipedia-org-2350 115 7 it -PRON- PRP en-wikipedia-org-2350 115 8 understandable understandable JJ en-wikipedia-org-2350 115 9 to to IN en-wikipedia-org-2350 115 10 non non JJ en-wikipedia-org-2350 115 11 - - NNS en-wikipedia-org-2350 115 12 experts expert NNS en-wikipedia-org-2350 115 13 , , , en-wikipedia-org-2350 115 14 without without IN en-wikipedia-org-2350 115 15 removing remove VBG en-wikipedia-org-2350 115 16 the the DT en-wikipedia-org-2350 115 17 technical technical JJ en-wikipedia-org-2350 115 18 details detail NNS en-wikipedia-org-2350 115 19 . . . en-wikipedia-org-2350 116 1 ( ( -LRB- en-wikipedia-org-2350 116 2 October October NNP en-wikipedia-org-2350 116 3 2020 2020 CD en-wikipedia-org-2350 116 4 ) ) -RRB- en-wikipedia-org-2350 116 5 ( ( -LRB- en-wikipedia-org-2350 116 6 Learn learn VB en-wikipedia-org-2350 116 7 how how WRB en-wikipedia-org-2350 116 8 and and CC en-wikipedia-org-2350 116 9 when when WRB en-wikipedia-org-2350 116 10 to to TO en-wikipedia-org-2350 116 11 remove remove VB en-wikipedia-org-2350 116 12 this this DT en-wikipedia-org-2350 116 13 template template NN en-wikipedia-org-2350 116 14 message message NN en-wikipedia-org-2350 116 15 ) ) -RRB- en-wikipedia-org-2350 116 16 The the DT en-wikipedia-org-2350 116 17 most most RBS en-wikipedia-org-2350 116 18 basic basic JJ en-wikipedia-org-2350 116 19 Feynman Feynman NNP en-wikipedia-org-2350 116 20 diagram diagram NN en-wikipedia-org-2350 116 21 for for IN en-wikipedia-org-2350 116 22 QED QED NNP en-wikipedia-org-2350 116 23 interaction interaction NN en-wikipedia-org-2350 116 24 between between IN en-wikipedia-org-2350 116 25 two two CD en-wikipedia-org-2350 116 26 fermions fermion NNS en-wikipedia-org-2350 116 27 The the DT en-wikipedia-org-2350 116 28 Coulomb Coulomb NNP en-wikipedia-org-2350 116 29 potential potential NN en-wikipedia-org-2350 116 30 admits admit VBZ en-wikipedia-org-2350 116 31 continuum continuum JJ en-wikipedia-org-2350 116 32 states state NNS en-wikipedia-org-2350 116 33 ( ( -LRB- en-wikipedia-org-2350 116 34 with with IN en-wikipedia-org-2350 116 35 E e NN en-wikipedia-org-2350 116 36 > > NN en-wikipedia-org-2350 116 37 0 0 CD en-wikipedia-org-2350 116 38 ) ) -RRB- en-wikipedia-org-2350 116 39 , , , en-wikipedia-org-2350 116 40 describing describe VBG en-wikipedia-org-2350 116 41 electron electron NNP en-wikipedia-org-2350 116 42 - - HYPH en-wikipedia-org-2350 116 43 proton proton NNP en-wikipedia-org-2350 116 44 scattering scattering NN en-wikipedia-org-2350 116 45 , , , en-wikipedia-org-2350 116 46 as as RB en-wikipedia-org-2350 116 47 well well RB en-wikipedia-org-2350 116 48 as as IN en-wikipedia-org-2350 116 49 discrete discrete JJ en-wikipedia-org-2350 116 50 bound bind VBN en-wikipedia-org-2350 116 51 states state NNS en-wikipedia-org-2350 116 52 , , , en-wikipedia-org-2350 116 53 representing represent VBG en-wikipedia-org-2350 116 54 the the DT en-wikipedia-org-2350 116 55 hydrogen hydrogen NN en-wikipedia-org-2350 116 56 atom atom NN en-wikipedia-org-2350 116 57 . . . en-wikipedia-org-2350 117 1 [ [ -LRB- en-wikipedia-org-2350 117 2 30 30 CD en-wikipedia-org-2350 117 3 ] ] -RRB- en-wikipedia-org-2350 117 4 It -PRON- PRP en-wikipedia-org-2350 117 5 can can MD en-wikipedia-org-2350 117 6 also also RB en-wikipedia-org-2350 117 7 be be VB en-wikipedia-org-2350 117 8 derived derive VBN en-wikipedia-org-2350 117 9 within within IN en-wikipedia-org-2350 117 10 the the DT en-wikipedia-org-2350 117 11 non non JJ en-wikipedia-org-2350 117 12 - - JJ en-wikipedia-org-2350 117 13 relativistic relativistic JJ en-wikipedia-org-2350 117 14 limit limit NN en-wikipedia-org-2350 117 15 between between IN en-wikipedia-org-2350 117 16 two two CD en-wikipedia-org-2350 117 17 charged charge VBN en-wikipedia-org-2350 117 18 particles particle NNS en-wikipedia-org-2350 117 19 , , , en-wikipedia-org-2350 117 20 as as IN en-wikipedia-org-2350 117 21 follows follow VBZ en-wikipedia-org-2350 117 22 : : : en-wikipedia-org-2350 117 23 Under under IN en-wikipedia-org-2350 117 24 Born Born NNP en-wikipedia-org-2350 117 25 approximation approximation NN en-wikipedia-org-2350 117 26 , , , en-wikipedia-org-2350 117 27 in in IN en-wikipedia-org-2350 117 28 non non JJ en-wikipedia-org-2350 117 29 - - JJ en-wikipedia-org-2350 117 30 relativistic relativistic JJ en-wikipedia-org-2350 117 31 quantum quantum NN en-wikipedia-org-2350 117 32 mechanics mechanic NNS en-wikipedia-org-2350 117 33 , , , en-wikipedia-org-2350 117 34 the the DT en-wikipedia-org-2350 117 35 scattering scatter VBG en-wikipedia-org-2350 117 36 amplitude amplitude NN en-wikipedia-org-2350 117 37 A a DT en-wikipedia-org-2350 117 38 ( ( -LRB- en-wikipedia-org-2350 117 39 | | NNP en-wikipedia-org-2350 117 40 p p NN en-wikipedia-org-2350 117 41 → → SYM en-wikipedia-org-2350 117 42 ⟩ ⟩ NN en-wikipedia-org-2350 117 43 → → SYM en-wikipedia-org-2350 117 44 | | CD en-wikipedia-org-2350 117 45 p p NN en-wikipedia-org-2350 117 46 → → SYM en-wikipedia-org-2350 117 47 ′ ′ ADD en-wikipedia-org-2350 117 48 ⟩ ⟩ UH en-wikipedia-org-2350 117 49 ) ) -RRB- en-wikipedia-org-2350 117 50 { { -LRB- en-wikipedia-org-2350 117 51 \textstyle \textstyle CD en-wikipedia-org-2350 117 52 { { -LRB- en-wikipedia-org-2350 117 53 \mathcal \mathcal NNP en-wikipedia-org-2350 117 54 { { -LRB- en-wikipedia-org-2350 117 55 A}}(|{\overrightarrow A}}(|{\overrightarrow NNP en-wikipedia-org-2350 117 56 { { -LRB- en-wikipedia-org-2350 117 57 p}}\rangle p}}\rangle NNP en-wikipedia-org-2350 117 58 \to \to NNP en-wikipedia-org-2350 117 59 |{\overrightarrow |{\overrightarrow , en-wikipedia-org-2350 117 60 { { -LRB- en-wikipedia-org-2350 117 61 p}}'\rangle p}}'\rangle NNP en-wikipedia-org-2350 117 62 ) ) -RRB- en-wikipedia-org-2350 117 63 } } -RRB- en-wikipedia-org-2350 117 64 is be VBZ en-wikipedia-org-2350 117 65 : : : en-wikipedia-org-2350 117 66 A a DT en-wikipedia-org-2350 117 67 ( ( -LRB- en-wikipedia-org-2350 117 68 | | CD en-wikipedia-org-2350 117 69 p p NN en-wikipedia-org-2350 117 70 → → SYM en-wikipedia-org-2350 117 71 ⟩ ⟩ NN en-wikipedia-org-2350 117 72 → → SYM en-wikipedia-org-2350 117 73 | | CD en-wikipedia-org-2350 117 74 p p NN en-wikipedia-org-2350 117 75 → → SYM en-wikipedia-org-2350 117 76 ′ ′ ADD en-wikipedia-org-2350 117 77 ⟩ ⟩ UH en-wikipedia-org-2350 117 78 ) ) -RRB- en-wikipedia-org-2350 117 79 − − NNP en-wikipedia-org-2350 117 80 1 1 CD en-wikipedia-org-2350 117 81 = = SYM en-wikipedia-org-2350 117 82 2 2 CD en-wikipedia-org-2350 117 83 π π NN en-wikipedia-org-2350 117 84 δ δ NN en-wikipedia-org-2350 117 85 ( ( -LRB- en-wikipedia-org-2350 117 86 E E NNP en-wikipedia-org-2350 117 87 p p NN en-wikipedia-org-2350 117 88 − − NNP en-wikipedia-org-2350 117 89 E e NN en-wikipedia-org-2350 117 90 p p NN en-wikipedia-org-2350 117 91 ′ ′ CD en-wikipedia-org-2350 117 92 ) ) -RRB- en-wikipedia-org-2350 117 93 ( ( -LRB- en-wikipedia-org-2350 117 94 − − NNP en-wikipedia-org-2350 117 95 i i NNP en-wikipedia-org-2350 117 96 ) ) -RRB- en-wikipedia-org-2350 117 97 ∫ ∫ . en-wikipedia-org-2350 117 98 d d NN en-wikipedia-org-2350 117 99 3 3 CD en-wikipedia-org-2350 117 100 r r NN en-wikipedia-org-2350 117 101 V v NN en-wikipedia-org-2350 117 102 ( ( -LRB- en-wikipedia-org-2350 117 103 r r NN en-wikipedia-org-2350 117 104 → → SYM en-wikipedia-org-2350 117 105 ) ) -RRB- en-wikipedia-org-2350 117 106 e e LS en-wikipedia-org-2350 117 107 − − NNP en-wikipedia-org-2350 117 108 i i PRP en-wikipedia-org-2350 117 109 ( ( -LRB- en-wikipedia-org-2350 117 110 p p NN en-wikipedia-org-2350 117 111 → → SYM en-wikipedia-org-2350 117 112 − − NNP en-wikipedia-org-2350 117 113 p p NN en-wikipedia-org-2350 117 114 → → SYM en-wikipedia-org-2350 117 115 ′ ′ ADD en-wikipedia-org-2350 117 116 ) ) -RRB- en-wikipedia-org-2350 117 117 r r NN en-wikipedia-org-2350 117 118 → → SYM en-wikipedia-org-2350 117 119 { { -LRB- en-wikipedia-org-2350 117 120 \displaystyle \displaystyle CD en-wikipedia-org-2350 117 121 { { -LRB- en-wikipedia-org-2350 117 122 \mathcal \mathcal CD en-wikipedia-org-2350 117 123 { { -LRB- en-wikipedia-org-2350 117 124 A}}(|{\overrightarrow a}}(|{\overrightarrow JJ en-wikipedia-org-2350 117 125 { { -LRB- en-wikipedia-org-2350 117 126 p}}\rangle p}}\rangle NNP en-wikipedia-org-2350 117 127 \to \to NNP en-wikipedia-org-2350 117 128 |{\overrightarrow |{\overrightarrow , en-wikipedia-org-2350 117 129 { { -LRB- en-wikipedia-org-2350 117 130 p}}'\rangle p}}'\rangle NNP en-wikipedia-org-2350 117 131 ) ) -RRB- en-wikipedia-org-2350 117 132 -1=2\pi -1=2\pi NFP en-wikipedia-org-2350 117 133 \delta \delta NNP en-wikipedia-org-2350 117 134 ( ( -LRB- en-wikipedia-org-2350 117 135 E_{p}-E_{p'})(-\mathrm E_{p}-E_{p'})(-\mathrm NNP en-wikipedia-org-2350 117 136 { { -LRB- en-wikipedia-org-2350 117 137 i i NN en-wikipedia-org-2350 117 138 } } -RRB- en-wikipedia-org-2350 117 139 ) ) -RRB- en-wikipedia-org-2350 117 140 \int \int NFP en-wikipedia-org-2350 117 141 \mathrm \mathrm CD en-wikipedia-org-2350 117 142 { { -LRB- en-wikipedia-org-2350 117 143 d d NN en-wikipedia-org-2350 117 144 } } -RRB- en-wikipedia-org-2350 117 145 ^{3}rV({\vec ^{3}rV({\vec NFP en-wikipedia-org-2350 117 146 { { -LRB- en-wikipedia-org-2350 117 147 r}})\mathrm r}})\mathrm UH en-wikipedia-org-2350 117 148 { { -LRB- en-wikipedia-org-2350 117 149 e e NN en-wikipedia-org-2350 117 150 } } -RRB- en-wikipedia-org-2350 117 151 ^{-\mathrm ^{-\mathrm NFP en-wikipedia-org-2350 117 152 { { -LRB- en-wikipedia-org-2350 117 153 i i NN en-wikipedia-org-2350 117 154 } } -RRB- en-wikipedia-org-2350 117 155 ( ( -LRB- en-wikipedia-org-2350 117 156 { { -LRB- en-wikipedia-org-2350 117 157 \vec \vec CD en-wikipedia-org-2350 117 158 { { -LRB- en-wikipedia-org-2350 117 159 p}}-{\vec p}}-{\vec NNP en-wikipedia-org-2350 117 160 { { -LRB- en-wikipedia-org-2350 117 161 p}}'){\vec p}}'){\vec NN en-wikipedia-org-2350 117 162 { { -LRB- en-wikipedia-org-2350 117 163 r r NN en-wikipedia-org-2350 117 164 } } -RRB- en-wikipedia-org-2350 117 165 } } -RRB- en-wikipedia-org-2350 117 166 } } -RRB- en-wikipedia-org-2350 117 167 } } -RRB- en-wikipedia-org-2350 117 168 This this DT en-wikipedia-org-2350 117 169 is be VBZ en-wikipedia-org-2350 117 170 to to TO en-wikipedia-org-2350 117 171 be be VB en-wikipedia-org-2350 117 172 compared compare VBN en-wikipedia-org-2350 117 173 to to IN en-wikipedia-org-2350 117 174 the the DT en-wikipedia-org-2350 117 175   _SP en-wikipedia-org-2350 117 176 : : : en-wikipedia-org-2350 117 177 ∫ ∫ . en-wikipedia-org-2350 117 178 d d NN en-wikipedia-org-2350 117 179 3 3 CD en-wikipedia-org-2350 117 180 k k NN en-wikipedia-org-2350 117 181 ( ( -LRB- en-wikipedia-org-2350 117 182 2 2 CD en-wikipedia-org-2350 117 183 π π CD en-wikipedia-org-2350 117 184 ) ) -RRB- en-wikipedia-org-2350 117 185 3 3 CD en-wikipedia-org-2350 117 186 e e NN en-wikipedia-org-2350 117 187 i i NN en-wikipedia-org-2350 117 188 k k NNP en-wikipedia-org-2350 117 189 r r NNP en-wikipedia-org-2350 117 190 0 0 CD en-wikipedia-org-2350 117 191 ⟨ ⟨ NNP en-wikipedia-org-2350 117 192 p p NN en-wikipedia-org-2350 117 193 ′ ′ XX en-wikipedia-org-2350 117 194 , , , en-wikipedia-org-2350 117 195 k k NNP en-wikipedia-org-2350 117 196 | | NNP en-wikipedia-org-2350 117 197 S S NNP en-wikipedia-org-2350 117 198 | | NNP en-wikipedia-org-2350 117 199 p p NNP en-wikipedia-org-2350 117 200 , , , en-wikipedia-org-2350 117 201 k k NN en-wikipedia-org-2350 117 202 ⟩ ⟩ `` en-wikipedia-org-2350 117 203 { { -LRB- en-wikipedia-org-2350 117 204 \displaystyle \displaystyle CD en-wikipedia-org-2350 117 205 \int \int CD en-wikipedia-org-2350 117 206 { { -LRB- en-wikipedia-org-2350 117 207 \frac \frac CD en-wikipedia-org-2350 117 208 { { -LRB- en-wikipedia-org-2350 117 209 \mathrm \mathrm CD en-wikipedia-org-2350 117 210 { { -LRB- en-wikipedia-org-2350 117 211 d d NNP en-wikipedia-org-2350 117 212 } } -RRB- en-wikipedia-org-2350 117 213 ^{3}k}{(2\pi ^{3}k}{(2\pi NFP en-wikipedia-org-2350 117 214 ) ) -RRB- en-wikipedia-org-2350 117 215 ^{3}}}\mathrm ^{3}}}\mathrm NFP en-wikipedia-org-2350 117 216 { { -LRB- en-wikipedia-org-2350 117 217 e e NNP en-wikipedia-org-2350 117 218 } } -RRB- en-wikipedia-org-2350 117 219 ^{\mathrm ^{\mathrm UH en-wikipedia-org-2350 117 220 { { -LRB- en-wikipedia-org-2350 117 221 i i NN en-wikipedia-org-2350 117 222 } } -RRB- en-wikipedia-org-2350 117 223 kr_{0}}\langle kr_{0}}\langle NNP en-wikipedia-org-2350 117 224 p',k|S|p p',k|s|p CD en-wikipedia-org-2350 117 225 , , , en-wikipedia-org-2350 117 226 k\rangle k\rangle NNP en-wikipedia-org-2350 117 227 } } -RRB- en-wikipedia-org-2350 117 228 where where WRB en-wikipedia-org-2350 117 229 we -PRON- PRP en-wikipedia-org-2350 117 230 look look VBP en-wikipedia-org-2350 117 231 at at IN en-wikipedia-org-2350 117 232 the the DT en-wikipedia-org-2350 117 233 ( ( -LRB- en-wikipedia-org-2350 117 234 connected connected JJ en-wikipedia-org-2350 117 235 ) ) -RRB- en-wikipedia-org-2350 117 236 S S NNP en-wikipedia-org-2350 117 237 - - HYPH en-wikipedia-org-2350 117 238 matrix matrix NN en-wikipedia-org-2350 117 239 entry entry NN en-wikipedia-org-2350 117 240 for for IN en-wikipedia-org-2350 117 241 two two CD en-wikipedia-org-2350 117 242 electrons electron NNS en-wikipedia-org-2350 117 243 scattering scatter VBG en-wikipedia-org-2350 117 244 off off RP en-wikipedia-org-2350 117 245 each each DT en-wikipedia-org-2350 117 246 other other JJ en-wikipedia-org-2350 117 247 , , , en-wikipedia-org-2350 117 248 treating treat VBG en-wikipedia-org-2350 117 249 one one CD en-wikipedia-org-2350 117 250 with with IN en-wikipedia-org-2350 117 251 " " `` en-wikipedia-org-2350 117 252 fixed fix VBN en-wikipedia-org-2350 117 253 " " '' en-wikipedia-org-2350 117 254 momentum momentum NN en-wikipedia-org-2350 117 255 as as IN en-wikipedia-org-2350 117 256 the the DT en-wikipedia-org-2350 117 257 source source NN en-wikipedia-org-2350 117 258 of of IN en-wikipedia-org-2350 117 259 the the DT en-wikipedia-org-2350 117 260 potential potential NN en-wikipedia-org-2350 117 261 , , , en-wikipedia-org-2350 117 262 and and CC en-wikipedia-org-2350 117 263 the the DT en-wikipedia-org-2350 117 264 other other JJ en-wikipedia-org-2350 117 265 scattering scattering NN en-wikipedia-org-2350 117 266 off off RP en-wikipedia-org-2350 117 267 that that DT en-wikipedia-org-2350 117 268 potential potential NN en-wikipedia-org-2350 117 269 . . . en-wikipedia-org-2350 118 1 Using use VBG en-wikipedia-org-2350 118 2 the the DT en-wikipedia-org-2350 118 3 Feynman Feynman NNP en-wikipedia-org-2350 118 4 rules rule NNS en-wikipedia-org-2350 118 5 to to TO en-wikipedia-org-2350 118 6 compute compute VB en-wikipedia-org-2350 118 7 the the DT en-wikipedia-org-2350 118 8 S S NNP en-wikipedia-org-2350 118 9 - - HYPH en-wikipedia-org-2350 118 10 matrix matrix NN en-wikipedia-org-2350 118 11 element element NN en-wikipedia-org-2350 118 12 , , , en-wikipedia-org-2350 118 13 we -PRON- PRP en-wikipedia-org-2350 118 14 obtain obtain VBP en-wikipedia-org-2350 118 15 in in IN en-wikipedia-org-2350 118 16 the the DT en-wikipedia-org-2350 118 17 non non JJ en-wikipedia-org-2350 118 18 - - JJ en-wikipedia-org-2350 118 19 relativistic relativistic JJ en-wikipedia-org-2350 118 20 limit limit NN en-wikipedia-org-2350 118 21 with with IN en-wikipedia-org-2350 118 22 m m NNP en-wikipedia-org-2350 118 23 0 0 CD en-wikipedia-org-2350 118 24 ≫ ≫ NNP en-wikipedia-org-2350 118 25 | | NNP en-wikipedia-org-2350 118 26 p p NN en-wikipedia-org-2350 118 27 → → SYM en-wikipedia-org-2350 118 28 | | NNS en-wikipedia-org-2350 118 29 { { -LRB- en-wikipedia-org-2350 118 30 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 31 m_{0}\gg m_{0}\gg NN en-wikipedia-org-2350 118 32 |{\vec |{\vec NN en-wikipedia-org-2350 118 33 { { -LRB- en-wikipedia-org-2350 118 34 p}}| p}}| NNP en-wikipedia-org-2350 118 35 } } -RRB- en-wikipedia-org-2350 118 36 ⟨ ⟨ NNP en-wikipedia-org-2350 118 37 p p NN en-wikipedia-org-2350 118 38 ′ ′ CD en-wikipedia-org-2350 118 39 , , , en-wikipedia-org-2350 118 40 k k NNP en-wikipedia-org-2350 118 41 | | NNP en-wikipedia-org-2350 118 42 S S NNP en-wikipedia-org-2350 118 43 | | NNP en-wikipedia-org-2350 118 44 p p NNP en-wikipedia-org-2350 118 45 , , , en-wikipedia-org-2350 118 46 k k NNP en-wikipedia-org-2350 118 47 ⟩ ⟩ `` en-wikipedia-org-2350 118 48 | | NNP en-wikipedia-org-2350 118 49 c c NNP en-wikipedia-org-2350 118 50 o o NN en-wikipedia-org-2350 118 51 n n CC en-wikipedia-org-2350 118 52 n n NNP en-wikipedia-org-2350 118 53 = = SYM en-wikipedia-org-2350 118 54 − − NNP en-wikipedia-org-2350 118 55 i i PRP en-wikipedia-org-2350 118 56 e e DT en-wikipedia-org-2350 118 57 2 2 CD en-wikipedia-org-2350 118 58 | | CD en-wikipedia-org-2350 118 59 p p NN en-wikipedia-org-2350 118 60 → → SYM en-wikipedia-org-2350 118 61 − − NNP en-wikipedia-org-2350 118 62 p p NN en-wikipedia-org-2350 118 63 → → SYM en-wikipedia-org-2350 118 64 ′ ′ CD en-wikipedia-org-2350 118 65 | | CD en-wikipedia-org-2350 118 66 2 2 CD en-wikipedia-org-2350 118 67 − − NNP en-wikipedia-org-2350 118 68 i i PRP en-wikipedia-org-2350 118 69 ϵ ϵ NN en-wikipedia-org-2350 118 70 ( ( -LRB- en-wikipedia-org-2350 118 71 2 2 CD en-wikipedia-org-2350 118 72 m m NNP en-wikipedia-org-2350 118 73 ) ) -RRB- en-wikipedia-org-2350 118 74 2 2 CD en-wikipedia-org-2350 118 75 δ δ NN en-wikipedia-org-2350 118 76 ( ( -LRB- en-wikipedia-org-2350 118 77 E E NNP en-wikipedia-org-2350 118 78 p p NN en-wikipedia-org-2350 118 79 , , , en-wikipedia-org-2350 118 80 k k NN en-wikipedia-org-2350 118 81 − − NNP en-wikipedia-org-2350 118 82 E E NNP en-wikipedia-org-2350 118 83 p p NNP en-wikipedia-org-2350 118 84 ′ ′ CD en-wikipedia-org-2350 118 85 , , , en-wikipedia-org-2350 118 86 k k NN en-wikipedia-org-2350 118 87 ) ) -RRB- en-wikipedia-org-2350 118 88 ( ( -LRB- en-wikipedia-org-2350 118 89 2 2 CD en-wikipedia-org-2350 118 90 π π NN en-wikipedia-org-2350 118 91 ) ) -RRB- en-wikipedia-org-2350 118 92 4 4 CD en-wikipedia-org-2350 118 93 δ δ NN en-wikipedia-org-2350 118 94 ( ( -LRB- en-wikipedia-org-2350 118 95 p p NN en-wikipedia-org-2350 118 96 → → SYM en-wikipedia-org-2350 118 97 − − NNP en-wikipedia-org-2350 118 98 p p NN en-wikipedia-org-2350 118 99 → → SYM en-wikipedia-org-2350 118 100 ′ ′ ADD en-wikipedia-org-2350 118 101 ) ) -RRB- en-wikipedia-org-2350 118 102 { { -LRB- en-wikipedia-org-2350 118 103 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 104 \langle \langle CD en-wikipedia-org-2350 118 105 p',k|S|p p',k|s|p CD en-wikipedia-org-2350 118 106 , , , en-wikipedia-org-2350 118 107 k\rangle k\rangle NNP en-wikipedia-org-2350 118 108 |_{conn}=-\mathrm |_{conn}=-\mathrm NNP en-wikipedia-org-2350 118 109 { { -LRB- en-wikipedia-org-2350 118 110 i i NN en-wikipedia-org-2350 118 111 } } -RRB- en-wikipedia-org-2350 118 112 { { -LRB- en-wikipedia-org-2350 118 113 \frac \frac CD en-wikipedia-org-2350 118 114 { { -LRB- en-wikipedia-org-2350 118 115 e^{2}}{|{\vec e^{2}}{|{\vec NNP en-wikipedia-org-2350 118 116 { { -LRB- en-wikipedia-org-2350 118 117 p}}-{\vec p}}-{\vec NNP en-wikipedia-org-2350 118 118 { { -LRB- en-wikipedia-org-2350 118 119 p}}'|^{2}-\mathrm p}}'|^{2}-\mathrm NNP en-wikipedia-org-2350 118 120 { { -LRB- en-wikipedia-org-2350 118 121 i i NN en-wikipedia-org-2350 118 122 } } -RRB- en-wikipedia-org-2350 118 123 \epsilon \epsilon CD en-wikipedia-org-2350 118 124 } } -RRB- en-wikipedia-org-2350 118 125 } } -RRB- en-wikipedia-org-2350 118 126 ( ( -LRB- en-wikipedia-org-2350 118 127 2m)^{2}\delta 2m)^{2}\delta NNP en-wikipedia-org-2350 118 128 ( ( -LRB- en-wikipedia-org-2350 118 129 E_{p e_{p UH en-wikipedia-org-2350 118 130 , , , en-wikipedia-org-2350 118 131 k}-E_{p',k})(2\pi k}-e_{p',k})(2\pi NN en-wikipedia-org-2350 118 132 ) ) -RRB- en-wikipedia-org-2350 118 133 ^{4}\delta ^{4}\delta . en-wikipedia-org-2350 118 134 ( ( -LRB- en-wikipedia-org-2350 118 135 { { -LRB- en-wikipedia-org-2350 118 136 \vec \vec CD en-wikipedia-org-2350 118 137 { { -LRB- en-wikipedia-org-2350 118 138 p}}-{\vec p}}-{\vec NNP en-wikipedia-org-2350 118 139 { { -LRB- en-wikipedia-org-2350 118 140 p p NN en-wikipedia-org-2350 118 141 } } -RRB- en-wikipedia-org-2350 118 142 } } -RRB- en-wikipedia-org-2350 118 143 ' ' '' en-wikipedia-org-2350 118 144 ) ) -RRB- en-wikipedia-org-2350 118 145 } } -RRB- en-wikipedia-org-2350 118 146 Comparing compare VBG en-wikipedia-org-2350 118 147 with with IN en-wikipedia-org-2350 118 148 the the DT en-wikipedia-org-2350 118 149 QM QM NNP en-wikipedia-org-2350 118 150 scattering scattering NN en-wikipedia-org-2350 118 151 , , , en-wikipedia-org-2350 118 152 we -PRON- PRP en-wikipedia-org-2350 118 153 have have VBP en-wikipedia-org-2350 118 154 to to TO en-wikipedia-org-2350 118 155 discard discard VB en-wikipedia-org-2350 118 156 the the DT en-wikipedia-org-2350 118 157 ( ( -LRB- en-wikipedia-org-2350 118 158 2 2 CD en-wikipedia-org-2350 118 159 m m CD en-wikipedia-org-2350 118 160 ) ) -RRB- en-wikipedia-org-2350 118 161 2 2 CD en-wikipedia-org-2350 118 162 { { -LRB- en-wikipedia-org-2350 118 163 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 164 ( ( -LRB- en-wikipedia-org-2350 118 165 2m)^{2 2m)^{2 NN en-wikipedia-org-2350 118 166 } } -RRB- en-wikipedia-org-2350 118 167 } } -RRB- en-wikipedia-org-2350 118 168 as as IN en-wikipedia-org-2350 118 169 they -PRON- PRP en-wikipedia-org-2350 118 170 arise arise VBP en-wikipedia-org-2350 118 171 due due IN en-wikipedia-org-2350 118 172 to to IN en-wikipedia-org-2350 118 173 differing differ VBG en-wikipedia-org-2350 118 174 normalizations normalization NNS en-wikipedia-org-2350 118 175 of of IN en-wikipedia-org-2350 118 176 momentum momentum NN en-wikipedia-org-2350 118 177 eigenstate eigenstate NN en-wikipedia-org-2350 118 178 in in IN en-wikipedia-org-2350 118 179 QFT QFT NNP en-wikipedia-org-2350 118 180 compared compare VBN en-wikipedia-org-2350 118 181 to to IN en-wikipedia-org-2350 118 182 QM QM NNP en-wikipedia-org-2350 118 183 and and CC en-wikipedia-org-2350 118 184 obtain obtain VB en-wikipedia-org-2350 118 185 : : : en-wikipedia-org-2350 118 186 ∫ ∫ NFP en-wikipedia-org-2350 118 187 V v NN en-wikipedia-org-2350 118 188 ( ( -LRB- en-wikipedia-org-2350 118 189 r r NNP en-wikipedia-org-2350 118 190 → → SYM en-wikipedia-org-2350 118 191 ) ) -RRB- en-wikipedia-org-2350 118 192 e e LS en-wikipedia-org-2350 118 193 − − NNP en-wikipedia-org-2350 118 194 i i PRP en-wikipedia-org-2350 118 195 ( ( -LRB- en-wikipedia-org-2350 118 196 p p NN en-wikipedia-org-2350 118 197 → → SYM en-wikipedia-org-2350 118 198 − − NNP en-wikipedia-org-2350 118 199 p p NN en-wikipedia-org-2350 118 200 → → SYM en-wikipedia-org-2350 118 201 ′ ′ ADD en-wikipedia-org-2350 118 202 ) ) -RRB- en-wikipedia-org-2350 118 203 r r NN en-wikipedia-org-2350 118 204 → → SYM en-wikipedia-org-2350 118 205 d d NN en-wikipedia-org-2350 118 206 3 3 CD en-wikipedia-org-2350 118 207 r r NN en-wikipedia-org-2350 118 208 = = SYM en-wikipedia-org-2350 118 209 e e NNP en-wikipedia-org-2350 118 210 2 2 CD en-wikipedia-org-2350 118 211 | | CD en-wikipedia-org-2350 118 212 p p NN en-wikipedia-org-2350 118 213 → → SYM en-wikipedia-org-2350 118 214 − − NNP en-wikipedia-org-2350 118 215 p p NN en-wikipedia-org-2350 118 216 → → SYM en-wikipedia-org-2350 118 217 ′ ′ CD en-wikipedia-org-2350 118 218 | | CD en-wikipedia-org-2350 118 219 2 2 CD en-wikipedia-org-2350 118 220 − − NNP en-wikipedia-org-2350 118 221 i i PRP en-wikipedia-org-2350 118 222 ϵ ϵ NN en-wikipedia-org-2350 118 223 { { -LRB- en-wikipedia-org-2350 118 224 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 225 \int \int CD en-wikipedia-org-2350 118 226 V({\vec v({\vec FW en-wikipedia-org-2350 118 227 { { -LRB- en-wikipedia-org-2350 118 228 r}})\mathbf r}})\mathbf NNP en-wikipedia-org-2350 118 229 { { -LRB- en-wikipedia-org-2350 118 230 e e NNP en-wikipedia-org-2350 118 231 } } -RRB- en-wikipedia-org-2350 118 232 ^{-\mathbf ^{-\mathbf NNP en-wikipedia-org-2350 118 233 { { -LRB- en-wikipedia-org-2350 118 234 i i NN en-wikipedia-org-2350 118 235 } } -RRB- en-wikipedia-org-2350 118 236 ( ( -LRB- en-wikipedia-org-2350 118 237 { { -LRB- en-wikipedia-org-2350 118 238 \vec \vec CD en-wikipedia-org-2350 118 239 { { -LRB- en-wikipedia-org-2350 118 240 p}}-{\vec p}}-{\vec NNP en-wikipedia-org-2350 118 241 { { -LRB- en-wikipedia-org-2350 118 242 p}}'){\vec p}}'){\vec NN en-wikipedia-org-2350 118 243 { { -LRB- en-wikipedia-org-2350 118 244 r}}}\mathbf r}}}\mathbf NNP en-wikipedia-org-2350 118 245 { { -LRB- en-wikipedia-org-2350 118 246 d d NNP en-wikipedia-org-2350 118 247 } } -RRB- en-wikipedia-org-2350 118 248 ^{3}r={\frac ^{3}r={\frac SYM en-wikipedia-org-2350 118 249 { { -LRB- en-wikipedia-org-2350 118 250 e^{2}}{|{\vec e^{2}}{|{\vec NN en-wikipedia-org-2350 118 251 { { -LRB- en-wikipedia-org-2350 118 252 p}}-{\vec p}}-{\vec NNP en-wikipedia-org-2350 118 253 { { -LRB- en-wikipedia-org-2350 118 254 p}}'|^{2}-\mathbf p}}'|^{2}-\mathbf NNP en-wikipedia-org-2350 118 255 { { -LRB- en-wikipedia-org-2350 118 256 i i NN en-wikipedia-org-2350 118 257 } } -RRB- en-wikipedia-org-2350 118 258 \epsilon \epsilon CD en-wikipedia-org-2350 118 259 } } -RRB- en-wikipedia-org-2350 118 260 } } -RRB- en-wikipedia-org-2350 118 261 } } -RRB- en-wikipedia-org-2350 118 262 where where WRB en-wikipedia-org-2350 118 263 Fourier Fourier NNP en-wikipedia-org-2350 118 264 transforming transform VBG en-wikipedia-org-2350 118 265 both both DT en-wikipedia-org-2350 118 266 sides side NNS en-wikipedia-org-2350 118 267 , , , en-wikipedia-org-2350 118 268 solving solve VBG en-wikipedia-org-2350 118 269 the the DT en-wikipedia-org-2350 118 270 integral integral NN en-wikipedia-org-2350 118 271 and and CC en-wikipedia-org-2350 118 272 taking take VBG en-wikipedia-org-2350 118 273 ϵ ϵ NN en-wikipedia-org-2350 118 274 → → SYM en-wikipedia-org-2350 118 275 0 0 CD en-wikipedia-org-2350 118 276 { { -LRB- en-wikipedia-org-2350 118 277 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 278 \epsilon \epsilon CD en-wikipedia-org-2350 118 279 \to \to NNP en-wikipedia-org-2350 118 280 0 0 NFP en-wikipedia-org-2350 118 281 } } -RRB- en-wikipedia-org-2350 118 282 at at IN en-wikipedia-org-2350 118 283 the the DT en-wikipedia-org-2350 118 284 end end NN en-wikipedia-org-2350 118 285 will will MD en-wikipedia-org-2350 118 286 yield yield VB en-wikipedia-org-2350 118 287 V V NNP en-wikipedia-org-2350 118 288 ( ( -LRB- en-wikipedia-org-2350 118 289 r r NN en-wikipedia-org-2350 118 290 ) ) -RRB- en-wikipedia-org-2350 118 291 = = NFP en-wikipedia-org-2350 118 292 e e NNP en-wikipedia-org-2350 118 293 2 2 CD en-wikipedia-org-2350 118 294 4 4 CD en-wikipedia-org-2350 118 295 π π NN en-wikipedia-org-2350 118 296 r r NN en-wikipedia-org-2350 118 297 { { -LRB- en-wikipedia-org-2350 118 298 \displaystyle \displaystyle CD en-wikipedia-org-2350 118 299 V(r)={\frac v(r)={\frac CD en-wikipedia-org-2350 118 300 { { -LRB- en-wikipedia-org-2350 118 301 e^{2}}{4\pi e^{2}}{4\pi NNP en-wikipedia-org-2350 118 302 r r NNP en-wikipedia-org-2350 118 303 } } -RRB- en-wikipedia-org-2350 118 304 } } -RRB- en-wikipedia-org-2350 118 305 } } -RRB- en-wikipedia-org-2350 118 306 as as IN en-wikipedia-org-2350 118 307 the the DT en-wikipedia-org-2350 118 308 Coulomb Coulomb NNP en-wikipedia-org-2350 118 309 potential potential NN en-wikipedia-org-2350 118 310 . . . en-wikipedia-org-2350 119 1 [ [ -LRB- en-wikipedia-org-2350 119 2 31 31 CD en-wikipedia-org-2350 119 3 ] ] -RRB- en-wikipedia-org-2350 119 4 However however RB en-wikipedia-org-2350 119 5 , , , en-wikipedia-org-2350 119 6 the the DT en-wikipedia-org-2350 119 7 equivalent equivalent JJ en-wikipedia-org-2350 119 8 results result NNS en-wikipedia-org-2350 119 9 of of IN en-wikipedia-org-2350 119 10 the the DT en-wikipedia-org-2350 119 11 classical classical JJ en-wikipedia-org-2350 119 12 Born Born NNP en-wikipedia-org-2350 119 13 derivations derivation NNS en-wikipedia-org-2350 119 14 for for IN en-wikipedia-org-2350 119 15 the the DT en-wikipedia-org-2350 119 16 Coulomb Coulomb NNP en-wikipedia-org-2350 119 17 problem problem NN en-wikipedia-org-2350 119 18 are be VBP en-wikipedia-org-2350 119 19 thought think VBN en-wikipedia-org-2350 119 20 to to TO en-wikipedia-org-2350 119 21 be be VB en-wikipedia-org-2350 119 22 strictly strictly RB en-wikipedia-org-2350 119 23 accidental accidental JJ en-wikipedia-org-2350 119 24 . . . en-wikipedia-org-2350 120 1 [ [ -LRB- en-wikipedia-org-2350 120 2 32][33 32][33 LS en-wikipedia-org-2350 120 3 ] ] -RRB- en-wikipedia-org-2350 120 4 The the DT en-wikipedia-org-2350 120 5 Coulomb Coulomb NNP en-wikipedia-org-2350 120 6 potential potential NN en-wikipedia-org-2350 120 7 , , , en-wikipedia-org-2350 120 8 and and CC en-wikipedia-org-2350 120 9 its -PRON- PRP$ en-wikipedia-org-2350 120 10 derivation derivation NN en-wikipedia-org-2350 120 11 , , , en-wikipedia-org-2350 120 12 can can MD en-wikipedia-org-2350 120 13 be be VB en-wikipedia-org-2350 120 14 seen see VBN en-wikipedia-org-2350 120 15 as as IN en-wikipedia-org-2350 120 16 a a DT en-wikipedia-org-2350 120 17 special special JJ en-wikipedia-org-2350 120 18 case case NN en-wikipedia-org-2350 120 19 of of IN en-wikipedia-org-2350 120 20 the the DT en-wikipedia-org-2350 120 21 Yukawa Yukawa NNP en-wikipedia-org-2350 120 22 potential potential NN en-wikipedia-org-2350 120 23 , , , en-wikipedia-org-2350 120 24 which which WDT en-wikipedia-org-2350 120 25 is be VBZ en-wikipedia-org-2350 120 26 the the DT en-wikipedia-org-2350 120 27 case case NN en-wikipedia-org-2350 120 28 where where WRB en-wikipedia-org-2350 120 29 the the DT en-wikipedia-org-2350 120 30 exchanged exchanged JJ en-wikipedia-org-2350 120 31 boson boson NN en-wikipedia-org-2350 120 32 – – : en-wikipedia-org-2350 120 33 the the DT en-wikipedia-org-2350 120 34 photon photon NN en-wikipedia-org-2350 120 35 – – : en-wikipedia-org-2350 120 36 has have VBZ en-wikipedia-org-2350 120 37 no no DT en-wikipedia-org-2350 120 38 rest rest NN en-wikipedia-org-2350 120 39 mass mass NN en-wikipedia-org-2350 120 40 . . . en-wikipedia-org-2350 121 1 [ [ -LRB- en-wikipedia-org-2350 121 2 30 30 CD en-wikipedia-org-2350 121 3 ] ] -RRB- en-wikipedia-org-2350 121 4 Simple simple JJ en-wikipedia-org-2350 121 5 experiment experiment NN en-wikipedia-org-2350 121 6 to to TO en-wikipedia-org-2350 121 7 verify verify VB en-wikipedia-org-2350 121 8 Coulomb Coulomb NNP en-wikipedia-org-2350 121 9 's 's POS en-wikipedia-org-2350 121 10 law[edit law[edit NN en-wikipedia-org-2350 121 11 ] ] -RRB- en-wikipedia-org-2350 121 12 This this DT en-wikipedia-org-2350 121 13 section section NN en-wikipedia-org-2350 121 14 may may MD en-wikipedia-org-2350 121 15 contain contain VB en-wikipedia-org-2350 121 16 an an DT en-wikipedia-org-2350 121 17 excessive excessive JJ en-wikipedia-org-2350 121 18 amount amount NN en-wikipedia-org-2350 121 19 of of IN en-wikipedia-org-2350 121 20 intricate intricate JJ en-wikipedia-org-2350 121 21 detail detail NN en-wikipedia-org-2350 121 22 that that WDT en-wikipedia-org-2350 121 23 may may MD en-wikipedia-org-2350 121 24 interest interest VB en-wikipedia-org-2350 121 25 only only RB en-wikipedia-org-2350 121 26 a a DT en-wikipedia-org-2350 121 27 particular particular JJ en-wikipedia-org-2350 121 28 audience audience NN en-wikipedia-org-2350 121 29 . . . en-wikipedia-org-2350 122 1 Please please UH en-wikipedia-org-2350 122 2 help help VB en-wikipedia-org-2350 122 3 by by IN en-wikipedia-org-2350 122 4 spinning spin VBG en-wikipedia-org-2350 122 5 off off RP en-wikipedia-org-2350 122 6 or or CC en-wikipedia-org-2350 122 7 relocating relocate VBG en-wikipedia-org-2350 122 8 any any DT en-wikipedia-org-2350 122 9 relevant relevant JJ en-wikipedia-org-2350 122 10 information information NN en-wikipedia-org-2350 122 11 , , , en-wikipedia-org-2350 122 12 and and CC en-wikipedia-org-2350 122 13 removing remove VBG en-wikipedia-org-2350 122 14 excessive excessive JJ en-wikipedia-org-2350 122 15 detail detail NN en-wikipedia-org-2350 122 16 that that WDT en-wikipedia-org-2350 122 17 may may MD en-wikipedia-org-2350 122 18 be be VB en-wikipedia-org-2350 122 19 against against IN en-wikipedia-org-2350 122 20 Wikipedia Wikipedia NNP en-wikipedia-org-2350 122 21 's 's POS en-wikipedia-org-2350 122 22 inclusion inclusion NN en-wikipedia-org-2350 122 23 policy policy NN en-wikipedia-org-2350 122 24 . . . en-wikipedia-org-2350 123 1 ( ( -LRB- en-wikipedia-org-2350 123 2 October October NNP en-wikipedia-org-2350 123 3 2020 2020 CD en-wikipedia-org-2350 123 4 ) ) -RRB- en-wikipedia-org-2350 123 5 ( ( -LRB- en-wikipedia-org-2350 123 6 Learn learn VB en-wikipedia-org-2350 123 7 how how WRB en-wikipedia-org-2350 123 8 and and CC en-wikipedia-org-2350 123 9 when when WRB en-wikipedia-org-2350 123 10 to to TO en-wikipedia-org-2350 123 11 remove remove VB en-wikipedia-org-2350 123 12 this this DT en-wikipedia-org-2350 123 13 template template NN en-wikipedia-org-2350 123 14 message message NN en-wikipedia-org-2350 123 15 ) ) -RRB- en-wikipedia-org-2350 123 16 Experiment experiment NN en-wikipedia-org-2350 123 17 to to TO en-wikipedia-org-2350 123 18 verify verify VB en-wikipedia-org-2350 123 19 Coulomb Coulomb NNP en-wikipedia-org-2350 123 20 's 's POS en-wikipedia-org-2350 123 21 law law NN en-wikipedia-org-2350 123 22 . . . en-wikipedia-org-2350 124 1 It -PRON- PRP en-wikipedia-org-2350 124 2 is be VBZ en-wikipedia-org-2350 124 3 possible possible JJ en-wikipedia-org-2350 124 4 to to TO en-wikipedia-org-2350 124 5 verify verify VB en-wikipedia-org-2350 124 6 Coulomb Coulomb NNP en-wikipedia-org-2350 124 7 's 's POS en-wikipedia-org-2350 124 8 law law NN en-wikipedia-org-2350 124 9 with with IN en-wikipedia-org-2350 124 10 a a DT en-wikipedia-org-2350 124 11 simple simple JJ en-wikipedia-org-2350 124 12 experiment experiment NN en-wikipedia-org-2350 124 13 . . . en-wikipedia-org-2350 125 1 Consider consider VB en-wikipedia-org-2350 125 2 two two CD en-wikipedia-org-2350 125 3 small small JJ en-wikipedia-org-2350 125 4 spheres sphere NNS en-wikipedia-org-2350 125 5 of of IN en-wikipedia-org-2350 125 6 mass mass NNP en-wikipedia-org-2350 125 7 m m NN en-wikipedia-org-2350 125 8 { { -LRB- en-wikipedia-org-2350 125 9 \displaystyle \displaystyle CD en-wikipedia-org-2350 125 10 m m NN en-wikipedia-org-2350 125 11 } } -RRB- en-wikipedia-org-2350 125 12 and and CC en-wikipedia-org-2350 125 13 same same JJ en-wikipedia-org-2350 125 14 - - HYPH en-wikipedia-org-2350 125 15 sign sign NN en-wikipedia-org-2350 125 16 charge charge NN en-wikipedia-org-2350 125 17 q q NN en-wikipedia-org-2350 125 18 { { -LRB- en-wikipedia-org-2350 125 19 \displaystyle \displaystyle CD en-wikipedia-org-2350 125 20 q q NNP en-wikipedia-org-2350 125 21 } } -RRB- en-wikipedia-org-2350 125 22 , , , en-wikipedia-org-2350 125 23 hanging hang VBG en-wikipedia-org-2350 125 24 from from IN en-wikipedia-org-2350 125 25 two two CD en-wikipedia-org-2350 125 26 ropes rope NNS en-wikipedia-org-2350 125 27 of of IN en-wikipedia-org-2350 125 28 negligible negligible JJ en-wikipedia-org-2350 125 29 mass mass NN en-wikipedia-org-2350 125 30 of of IN en-wikipedia-org-2350 125 31 length length NN en-wikipedia-org-2350 125 32 l l NN en-wikipedia-org-2350 125 33 { { -LRB- en-wikipedia-org-2350 125 34 \displaystyle \displaystyle CD en-wikipedia-org-2350 125 35 l l NN en-wikipedia-org-2350 125 36 } } -RRB- en-wikipedia-org-2350 125 37 . . . en-wikipedia-org-2350 126 1 The the DT en-wikipedia-org-2350 126 2 forces force NNS en-wikipedia-org-2350 126 3 acting act VBG en-wikipedia-org-2350 126 4 on on IN en-wikipedia-org-2350 126 5 each each DT en-wikipedia-org-2350 126 6 sphere sphere NN en-wikipedia-org-2350 126 7 are be VBP en-wikipedia-org-2350 126 8 three three CD en-wikipedia-org-2350 126 9 : : : en-wikipedia-org-2350 126 10 the the DT en-wikipedia-org-2350 126 11 weight weight NN en-wikipedia-org-2350 126 12 m m NNP en-wikipedia-org-2350 126 13 g g NNP en-wikipedia-org-2350 126 14 { { -LRB- en-wikipedia-org-2350 126 15 \displaystyle \displaystyle CD en-wikipedia-org-2350 126 16 mg mg NNP en-wikipedia-org-2350 126 17 } } -RRB- en-wikipedia-org-2350 126 18 , , , en-wikipedia-org-2350 126 19 the the DT en-wikipedia-org-2350 126 20 rope rope NN en-wikipedia-org-2350 126 21 tension tension NN en-wikipedia-org-2350 126 22 T T NNP en-wikipedia-org-2350 126 23 { { -LRB- en-wikipedia-org-2350 126 24 \displaystyle \displaystyle CD en-wikipedia-org-2350 126 25 \mathbf \mathbf CD en-wikipedia-org-2350 126 26 { { -LRB- en-wikipedia-org-2350 126 27 T t NN en-wikipedia-org-2350 126 28 } } -RRB- en-wikipedia-org-2350 126 29 } } -RRB- en-wikipedia-org-2350 126 30 and and CC en-wikipedia-org-2350 126 31 the the DT en-wikipedia-org-2350 126 32 electric electric JJ en-wikipedia-org-2350 126 33 force force NN en-wikipedia-org-2350 126 34 F F NNP en-wikipedia-org-2350 126 35 { { -LRB- en-wikipedia-org-2350 126 36 \displaystyle \displaystyle CD en-wikipedia-org-2350 126 37 \mathbf \mathbf CD en-wikipedia-org-2350 126 38 { { -LRB- en-wikipedia-org-2350 126 39 F f NN en-wikipedia-org-2350 126 40 } } -RRB- en-wikipedia-org-2350 126 41 } } -RRB- en-wikipedia-org-2350 126 42 . . . en-wikipedia-org-2350 127 1 In in IN en-wikipedia-org-2350 127 2 the the DT en-wikipedia-org-2350 127 3 equilibrium equilibrium NN en-wikipedia-org-2350 127 4 state state NN en-wikipedia-org-2350 127 5 : : : en-wikipedia-org-2350 127 6 T T NNP en-wikipedia-org-2350 127 7 sin sin NN en-wikipedia-org-2350 127 8 ⁡ ⁡ NNP en-wikipedia-org-2350 127 9 θ θ NNP en-wikipedia-org-2350 127 10 1 1 CD en-wikipedia-org-2350 127 11 = = SYM en-wikipedia-org-2350 127 12 F f NN en-wikipedia-org-2350 127 13 1 1 CD en-wikipedia-org-2350 127 14 { { -LRB- en-wikipedia-org-2350 127 15 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 16 \mathbf \mathbf CD en-wikipedia-org-2350 127 17 { { -LRB- en-wikipedia-org-2350 127 18 T t NN en-wikipedia-org-2350 127 19 } } -RRB- en-wikipedia-org-2350 127 20 \sin \sin CD en-wikipedia-org-2350 127 21 \theta \theta NN en-wikipedia-org-2350 127 22 _ _ NNP en-wikipedia-org-2350 127 23 { { -LRB- en-wikipedia-org-2350 127 24 1}=\mathbf 1}=\mathbf NNP en-wikipedia-org-2350 127 25 { { -LRB- en-wikipedia-org-2350 127 26 F F NNP en-wikipedia-org-2350 127 27 } } -RRB- en-wikipedia-org-2350 127 28 _ _ NNP en-wikipedia-org-2350 127 29 { { -LRB- en-wikipedia-org-2350 127 30 1 1 CD en-wikipedia-org-2350 127 31 } } -RRB- en-wikipedia-org-2350 127 32 } } -RRB- en-wikipedia-org-2350 127 33                 _SP en-wikipedia-org-2350 127 34 ( ( -LRB- en-wikipedia-org-2350 127 35 1 1 CD en-wikipedia-org-2350 127 36 ) ) -RRB- en-wikipedia-org-2350 127 37 and and CC en-wikipedia-org-2350 127 38 T T NNP en-wikipedia-org-2350 127 39 cos cos NNP en-wikipedia-org-2350 127 40 ⁡ ⁡ NNP en-wikipedia-org-2350 127 41 θ θ NNP en-wikipedia-org-2350 127 42 1 1 CD en-wikipedia-org-2350 127 43 = = SYM en-wikipedia-org-2350 127 44 m m NNP en-wikipedia-org-2350 127 45 g g NN en-wikipedia-org-2350 127 46 { { -LRB- en-wikipedia-org-2350 127 47 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 48 \mathbf \mathbf CD en-wikipedia-org-2350 127 49 { { -LRB- en-wikipedia-org-2350 127 50 T t NN en-wikipedia-org-2350 127 51 } } -RRB- en-wikipedia-org-2350 127 52 \cos \cos CD en-wikipedia-org-2350 127 53 \theta \theta CD en-wikipedia-org-2350 127 54 _ _ NNP en-wikipedia-org-2350 127 55 { { -LRB- en-wikipedia-org-2350 127 56 1}=mg 1}=mg NNP en-wikipedia-org-2350 127 57 } } -RRB- en-wikipedia-org-2350 127 58                 _SP en-wikipedia-org-2350 127 59 ( ( -LRB- en-wikipedia-org-2350 127 60 2 2 LS en-wikipedia-org-2350 127 61 ) ) -RRB- en-wikipedia-org-2350 127 62 Dividing divide VBG en-wikipedia-org-2350 127 63 ( ( -LRB- en-wikipedia-org-2350 127 64 1 1 CD en-wikipedia-org-2350 127 65 ) ) -RRB- en-wikipedia-org-2350 127 66 by by IN en-wikipedia-org-2350 127 67 ( ( -LRB- en-wikipedia-org-2350 127 68 2 2 CD en-wikipedia-org-2350 127 69 ) ) -RRB- en-wikipedia-org-2350 127 70 : : : en-wikipedia-org-2350 127 71 sin sin NN en-wikipedia-org-2350 127 72 ⁡ ⁡ NNP en-wikipedia-org-2350 127 73 θ θ NNP en-wikipedia-org-2350 127 74 1 1 CD en-wikipedia-org-2350 127 75 cos cos NNP en-wikipedia-org-2350 127 76 ⁡ ⁡ NNP en-wikipedia-org-2350 127 77 θ θ NNP en-wikipedia-org-2350 127 78 1 1 CD en-wikipedia-org-2350 127 79 = = SYM en-wikipedia-org-2350 127 80 F f NN en-wikipedia-org-2350 127 81 1 1 CD en-wikipedia-org-2350 127 82 m m NN en-wikipedia-org-2350 127 83 g g NN en-wikipedia-org-2350 127 84 ⇒ ⇒ CD en-wikipedia-org-2350 127 85 F F NNP en-wikipedia-org-2350 127 86 1 1 CD en-wikipedia-org-2350 127 87 = = SYM en-wikipedia-org-2350 127 88 m m NNP en-wikipedia-org-2350 127 89 g g NNP en-wikipedia-org-2350 127 90 tan tan NNP en-wikipedia-org-2350 127 91 ⁡ ⁡ NNP en-wikipedia-org-2350 127 92 θ θ NNP en-wikipedia-org-2350 127 93 1 1 CD en-wikipedia-org-2350 127 94 { { -LRB- en-wikipedia-org-2350 127 95 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 96 { { -LRB- en-wikipedia-org-2350 127 97 \frac \frac CD en-wikipedia-org-2350 127 98 { { -LRB- en-wikipedia-org-2350 127 99 \sin \sin CD en-wikipedia-org-2350 127 100 \theta \theta VBN en-wikipedia-org-2350 127 101 _ _ NNP en-wikipedia-org-2350 127 102 { { -LRB- en-wikipedia-org-2350 127 103 1}}{\cos 1}}{\cos NNP en-wikipedia-org-2350 127 104 \theta \theta NN en-wikipedia-org-2350 127 105 _ _ IN en-wikipedia-org-2350 127 106 { { -LRB- en-wikipedia-org-2350 127 107 1}}}={\frac 1}}}={\frac CD en-wikipedia-org-2350 127 108 { { -LRB- en-wikipedia-org-2350 127 109 F_{1}}{mg}}\Rightarrow f_{1}}{mg}}\rightarrow NN en-wikipedia-org-2350 127 110 F_{1}=mg\tan f_{1}=mg\tan UH en-wikipedia-org-2350 127 111 \theta \theta XX en-wikipedia-org-2350 127 112 _ _ NNP en-wikipedia-org-2350 127 113 { { -LRB- en-wikipedia-org-2350 127 114 1 1 CD en-wikipedia-org-2350 127 115 } } -RRB- en-wikipedia-org-2350 127 116 } } -RRB- en-wikipedia-org-2350 127 117                 _SP en-wikipedia-org-2350 127 118 ( ( -LRB- en-wikipedia-org-2350 127 119 3 3 LS en-wikipedia-org-2350 127 120 ) ) -RRB- en-wikipedia-org-2350 127 121 Let let VB en-wikipedia-org-2350 127 122 L l NN en-wikipedia-org-2350 127 123 1 1 CD en-wikipedia-org-2350 127 124 { { -LRB- en-wikipedia-org-2350 127 125 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 126 \mathbf \mathbf CD en-wikipedia-org-2350 127 127 { { -LRB- en-wikipedia-org-2350 127 128 L L NNP en-wikipedia-org-2350 127 129 } } -RRB- en-wikipedia-org-2350 127 130 _ _ NNP en-wikipedia-org-2350 127 131 { { -LRB- en-wikipedia-org-2350 127 132 1 1 CD en-wikipedia-org-2350 127 133 } } -RRB- en-wikipedia-org-2350 127 134 } } -RRB- en-wikipedia-org-2350 127 135 be be VB en-wikipedia-org-2350 127 136 the the DT en-wikipedia-org-2350 127 137 distance distance NN en-wikipedia-org-2350 127 138 between between IN en-wikipedia-org-2350 127 139 the the DT en-wikipedia-org-2350 127 140 charged charge VBN en-wikipedia-org-2350 127 141 spheres sphere NNS en-wikipedia-org-2350 127 142 ; ; : en-wikipedia-org-2350 127 143 the the DT en-wikipedia-org-2350 127 144 repulsion repulsion NN en-wikipedia-org-2350 127 145 force force NN en-wikipedia-org-2350 127 146 between between IN en-wikipedia-org-2350 127 147 them -PRON- PRP en-wikipedia-org-2350 127 148 F F NNP en-wikipedia-org-2350 127 149 1 1 CD en-wikipedia-org-2350 127 150 { { -LRB- en-wikipedia-org-2350 127 151 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 152 \mathbf \mathbf CD en-wikipedia-org-2350 127 153 { { -LRB- en-wikipedia-org-2350 127 154 F F NNP en-wikipedia-org-2350 127 155 } } -RRB- en-wikipedia-org-2350 127 156 _ _ NNP en-wikipedia-org-2350 127 157 { { -LRB- en-wikipedia-org-2350 127 158 1 1 CD en-wikipedia-org-2350 127 159 } } -RRB- en-wikipedia-org-2350 127 160 } } -RRB- en-wikipedia-org-2350 127 161 , , , en-wikipedia-org-2350 127 162 assuming assume VBG en-wikipedia-org-2350 127 163 Coulomb Coulomb NNP en-wikipedia-org-2350 127 164 's 's POS en-wikipedia-org-2350 127 165 law law NN en-wikipedia-org-2350 127 166 is be VBZ en-wikipedia-org-2350 127 167 correct correct JJ en-wikipedia-org-2350 127 168 , , , en-wikipedia-org-2350 127 169 is be VBZ en-wikipedia-org-2350 127 170 equal equal JJ en-wikipedia-org-2350 127 171 to to IN en-wikipedia-org-2350 127 172 F F NNP en-wikipedia-org-2350 127 173 1 1 CD en-wikipedia-org-2350 127 174 = = SYM en-wikipedia-org-2350 127 175 q q NNP en-wikipedia-org-2350 127 176 2 2 CD en-wikipedia-org-2350 127 177 4 4 CD en-wikipedia-org-2350 127 178 π π NN en-wikipedia-org-2350 127 179 ε ε NN en-wikipedia-org-2350 127 180 0 0 CD en-wikipedia-org-2350 127 181 L l NN en-wikipedia-org-2350 127 182 1 1 CD en-wikipedia-org-2350 127 183 2 2 CD en-wikipedia-org-2350 127 184 { { -LRB- en-wikipedia-org-2350 127 185 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 186 F_{1}={\frac f_{1}={\frac NN en-wikipedia-org-2350 127 187 { { -LRB- en-wikipedia-org-2350 127 188 q^{2}}{4\pi q^{2}}{4\pi NNP en-wikipedia-org-2350 127 189 \varepsilon \varepsilon NNP en-wikipedia-org-2350 127 190 _ _ NNP en-wikipedia-org-2350 127 191 { { -LRB- en-wikipedia-org-2350 127 192 0}L_{1}^{2 0}l_{1}^{2 CD en-wikipedia-org-2350 127 193 } } -RRB- en-wikipedia-org-2350 127 194 } } -RRB- en-wikipedia-org-2350 127 195 } } -RRB- en-wikipedia-org-2350 127 196 } } -RRB- en-wikipedia-org-2350 127 197                 _SP en-wikipedia-org-2350 127 198 ( ( -LRB- en-wikipedia-org-2350 127 199 Coulomb Coulomb NNP en-wikipedia-org-2350 127 200 's 's POS en-wikipedia-org-2350 127 201 law law NN en-wikipedia-org-2350 127 202 ) ) -RRB- en-wikipedia-org-2350 127 203 so so RB en-wikipedia-org-2350 127 204 : : : en-wikipedia-org-2350 127 205 q q NNP en-wikipedia-org-2350 127 206 2 2 CD en-wikipedia-org-2350 127 207 4 4 CD en-wikipedia-org-2350 127 208 π π NN en-wikipedia-org-2350 127 209 ε ε NN en-wikipedia-org-2350 127 210 0 0 CD en-wikipedia-org-2350 127 211 L l NN en-wikipedia-org-2350 127 212 1 1 CD en-wikipedia-org-2350 127 213 2 2 CD en-wikipedia-org-2350 127 214 = = SYM en-wikipedia-org-2350 127 215 m m NNP en-wikipedia-org-2350 127 216 g g NNP en-wikipedia-org-2350 127 217 tan tan NNP en-wikipedia-org-2350 127 218 ⁡ ⁡ NNP en-wikipedia-org-2350 127 219 θ θ NNP en-wikipedia-org-2350 127 220 1 1 CD en-wikipedia-org-2350 127 221 { { -LRB- en-wikipedia-org-2350 127 222 \displaystyle \displaystyle CD en-wikipedia-org-2350 127 223 { { -LRB- en-wikipedia-org-2350 127 224 \frac \frac CD en-wikipedia-org-2350 127 225 { { -LRB- en-wikipedia-org-2350 127 226 q^{2}}{4\pi q^{2}}{4\pi NNP en-wikipedia-org-2350 127 227 \varepsilon \varepsilon NNP en-wikipedia-org-2350 127 228 _ _ NNP en-wikipedia-org-2350 127 229 { { -LRB- en-wikipedia-org-2350 127 230 0}L_{1}^{2}}}=mg\tan 0}l_{1}^{2}}}=mg\tan CD en-wikipedia-org-2350 127 231 \theta \theta XX en-wikipedia-org-2350 127 232 _ _ NNP en-wikipedia-org-2350 127 233 { { -LRB- en-wikipedia-org-2350 127 234 1}\,\ 1}\,\ CD en-wikipedia-org-2350 127 235 ! ! . en-wikipedia-org-2350 127 236 } } -RRB- en-wikipedia-org-2350 128 1 ( ( -LRB- en-wikipedia-org-2350 128 2 4 4 LS en-wikipedia-org-2350 128 3 ) ) -RRB- en-wikipedia-org-2350 128 4 If if IN en-wikipedia-org-2350 128 5 we -PRON- PRP en-wikipedia-org-2350 128 6 now now RB en-wikipedia-org-2350 128 7 discharge discharge VBP en-wikipedia-org-2350 128 8 one one CD en-wikipedia-org-2350 128 9 of of IN en-wikipedia-org-2350 128 10 the the DT en-wikipedia-org-2350 128 11 spheres sphere NNS en-wikipedia-org-2350 128 12 , , , en-wikipedia-org-2350 128 13 and and CC en-wikipedia-org-2350 128 14 we -PRON- PRP en-wikipedia-org-2350 128 15 put put VBP en-wikipedia-org-2350 128 16 it -PRON- PRP en-wikipedia-org-2350 128 17 in in IN en-wikipedia-org-2350 128 18 contact contact NN en-wikipedia-org-2350 128 19 with with IN en-wikipedia-org-2350 128 20 the the DT en-wikipedia-org-2350 128 21 charged charge VBN en-wikipedia-org-2350 128 22 sphere sphere NN en-wikipedia-org-2350 128 23 , , , en-wikipedia-org-2350 128 24 each each DT en-wikipedia-org-2350 128 25 one one CD en-wikipedia-org-2350 128 26 of of IN en-wikipedia-org-2350 128 27 them -PRON- PRP en-wikipedia-org-2350 128 28 acquires acquire VBZ en-wikipedia-org-2350 128 29 a a DT en-wikipedia-org-2350 128 30 charge charge NN en-wikipedia-org-2350 128 31 q q NNP en-wikipedia-org-2350 128 32 2 2 CD en-wikipedia-org-2350 128 33 { { -LRB- en-wikipedia-org-2350 128 34 \textstyle \textstyle CD en-wikipedia-org-2350 128 35 { { -LRB- en-wikipedia-org-2350 128 36 \frac \frac CD en-wikipedia-org-2350 128 37 { { -LRB- en-wikipedia-org-2350 128 38 q}{2 q}{2 NNP en-wikipedia-org-2350 128 39 } } -RRB- en-wikipedia-org-2350 128 40 } } -RRB- en-wikipedia-org-2350 128 41 } } -RRB- en-wikipedia-org-2350 128 42 . . . en-wikipedia-org-2350 129 1 In in IN en-wikipedia-org-2350 129 2 the the DT en-wikipedia-org-2350 129 3 equilibrium equilibrium NN en-wikipedia-org-2350 129 4 state state NN en-wikipedia-org-2350 129 5 , , , en-wikipedia-org-2350 129 6 the the DT en-wikipedia-org-2350 129 7 distance distance NN en-wikipedia-org-2350 129 8 between between IN en-wikipedia-org-2350 129 9 the the DT en-wikipedia-org-2350 129 10 charges charge NNS en-wikipedia-org-2350 129 11 will will MD en-wikipedia-org-2350 129 12 be be VB en-wikipedia-org-2350 129 13 L l NN en-wikipedia-org-2350 129 14 2 2 CD en-wikipedia-org-2350 129 15 < < NN en-wikipedia-org-2350 129 16 L l NN en-wikipedia-org-2350 129 17 1 1 CD en-wikipedia-org-2350 129 18 { { -LRB- en-wikipedia-org-2350 129 19 \textstyle \textstyle CD en-wikipedia-org-2350 129 20 \mathbf \mathbf CD en-wikipedia-org-2350 129 21 { { -LRB- en-wikipedia-org-2350 129 22 L L NNP en-wikipedia-org-2350 129 23 } } -RRB- en-wikipedia-org-2350 129 24 _ _ NNP en-wikipedia-org-2350 129 25 { { -LRB- en-wikipedia-org-2350 129 26 2}<\mathbf 2}<\mathbf CD en-wikipedia-org-2350 129 27 { { -LRB- en-wikipedia-org-2350 129 28 L L NNP en-wikipedia-org-2350 129 29 } } -RRB- en-wikipedia-org-2350 129 30 _ _ NNP en-wikipedia-org-2350 129 31 { { -LRB- en-wikipedia-org-2350 129 32 1 1 CD en-wikipedia-org-2350 129 33 } } -RRB- en-wikipedia-org-2350 129 34 } } -RRB- en-wikipedia-org-2350 129 35 and and CC en-wikipedia-org-2350 129 36 the the DT en-wikipedia-org-2350 129 37 repulsion repulsion NN en-wikipedia-org-2350 129 38 force force NN en-wikipedia-org-2350 129 39 between between IN en-wikipedia-org-2350 129 40 them -PRON- PRP en-wikipedia-org-2350 129 41 will will MD en-wikipedia-org-2350 129 42 be be VB en-wikipedia-org-2350 129 43 : : : en-wikipedia-org-2350 129 44 F f NN en-wikipedia-org-2350 129 45 2 2 CD en-wikipedia-org-2350 129 46 = = SYM en-wikipedia-org-2350 129 47 ( ( -LRB- en-wikipedia-org-2350 129 48 q q NNP en-wikipedia-org-2350 129 49 2 2 CD en-wikipedia-org-2350 129 50 ) ) -RRB- en-wikipedia-org-2350 129 51 2 2 CD en-wikipedia-org-2350 129 52 4 4 CD en-wikipedia-org-2350 129 53 π π NN en-wikipedia-org-2350 129 54 ε ε NN en-wikipedia-org-2350 129 55 0 0 CD en-wikipedia-org-2350 129 56 L l NN en-wikipedia-org-2350 129 57 2 2 CD en-wikipedia-org-2350 129 58 2 2 CD en-wikipedia-org-2350 129 59 = = SYM en-wikipedia-org-2350 129 60 q q NNP en-wikipedia-org-2350 129 61 2 2 CD en-wikipedia-org-2350 129 62 4 4 CD en-wikipedia-org-2350 129 63 4 4 CD en-wikipedia-org-2350 129 64 π π NN en-wikipedia-org-2350 129 65 ε ε NN en-wikipedia-org-2350 129 66 0 0 CD en-wikipedia-org-2350 129 67 L l NN en-wikipedia-org-2350 129 68 2 2 CD en-wikipedia-org-2350 129 69 2 2 CD en-wikipedia-org-2350 129 70 { { -LRB- en-wikipedia-org-2350 129 71 \displaystyle \displaystyle CD en-wikipedia-org-2350 129 72 F_{2}={\frac f_{2}={\frac UH en-wikipedia-org-2350 129 73 { { -LRB- en-wikipedia-org-2350 129 74 { { -LRB- en-wikipedia-org-2350 129 75 ( ( -LRB- en-wikipedia-org-2350 129 76 { { -LRB- en-wikipedia-org-2350 129 77 \frac \frac CD en-wikipedia-org-2350 129 78 { { -LRB- en-wikipedia-org-2350 129 79 q}{2}})}^{2}}{4\pi q}{2}})}^{2}}{4\pi CD en-wikipedia-org-2350 129 80 \varepsilon \varepsilon CD en-wikipedia-org-2350 129 81 _ _ NNP en-wikipedia-org-2350 129 82 { { -LRB- en-wikipedia-org-2350 129 83 0}L_{2}^{2}}}={\frac 0}l_{2}^{2}}}={\frac NN en-wikipedia-org-2350 129 84 { { -LRB- en-wikipedia-org-2350 129 85 \frac \frac CD en-wikipedia-org-2350 129 86 { { -LRB- en-wikipedia-org-2350 129 87 q^{2}}{4}}{4\pi q^{2}}{4}}{4\pi NNP en-wikipedia-org-2350 129 88 \varepsilon \varepsilon CD en-wikipedia-org-2350 129 89 _ _ NNP en-wikipedia-org-2350 129 90 { { -LRB- en-wikipedia-org-2350 129 91 0}L_{2}^{2}}}\,\ 0}l_{2}^{2}}}\,\ CD en-wikipedia-org-2350 129 92 ! ! . en-wikipedia-org-2350 129 93 } } -RRB- en-wikipedia-org-2350 130 1 ( ( -LRB- en-wikipedia-org-2350 130 2 5 5 LS en-wikipedia-org-2350 130 3 ) ) -RRB- en-wikipedia-org-2350 130 4 We -PRON- PRP en-wikipedia-org-2350 130 5 know know VBP en-wikipedia-org-2350 130 6 that that IN en-wikipedia-org-2350 130 7 F F NNP en-wikipedia-org-2350 130 8 2 2 CD en-wikipedia-org-2350 130 9 = = SYM en-wikipedia-org-2350 130 10 m m NNP en-wikipedia-org-2350 130 11 g g NNP en-wikipedia-org-2350 130 12 tan tan NNP en-wikipedia-org-2350 130 13 ⁡ ⁡ NNP en-wikipedia-org-2350 130 14 θ θ NNP en-wikipedia-org-2350 130 15 2 2 CD en-wikipedia-org-2350 130 16 { { -LRB- en-wikipedia-org-2350 130 17 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 18 \mathbf \mathbf CD en-wikipedia-org-2350 130 19 { { -LRB- en-wikipedia-org-2350 130 20 F F NNP en-wikipedia-org-2350 130 21 } } -RRB- en-wikipedia-org-2350 130 22 _ _ NNP en-wikipedia-org-2350 130 23 { { -LRB- en-wikipedia-org-2350 130 24 2}=mg\tan 2}=mg\tan CD en-wikipedia-org-2350 130 25 \theta \theta CD en-wikipedia-org-2350 130 26 _ _ IN en-wikipedia-org-2350 130 27 { { -LRB- en-wikipedia-org-2350 130 28 2 2 CD en-wikipedia-org-2350 130 29 } } -RRB- en-wikipedia-org-2350 130 30 } } -RRB- en-wikipedia-org-2350 130 31 and and CC en-wikipedia-org-2350 130 32 : : : en-wikipedia-org-2350 130 33 q q NNP en-wikipedia-org-2350 130 34 2 2 CD en-wikipedia-org-2350 130 35 4 4 CD en-wikipedia-org-2350 130 36 4 4 CD en-wikipedia-org-2350 130 37 π π NN en-wikipedia-org-2350 130 38 ε ε NN en-wikipedia-org-2350 130 39 0 0 CD en-wikipedia-org-2350 130 40 L l NN en-wikipedia-org-2350 130 41 2 2 CD en-wikipedia-org-2350 130 42 2 2 CD en-wikipedia-org-2350 130 43 = = SYM en-wikipedia-org-2350 130 44 m m NNP en-wikipedia-org-2350 130 45 g g NNP en-wikipedia-org-2350 130 46 tan tan NNP en-wikipedia-org-2350 130 47 ⁡ ⁡ NNP en-wikipedia-org-2350 130 48 θ θ NNP en-wikipedia-org-2350 130 49 2 2 CD en-wikipedia-org-2350 130 50 { { -LRB- en-wikipedia-org-2350 130 51 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 52 { { -LRB- en-wikipedia-org-2350 130 53 \frac \frac CD en-wikipedia-org-2350 130 54 { { -LRB- en-wikipedia-org-2350 130 55 \frac \frac NNP en-wikipedia-org-2350 130 56 { { -LRB- en-wikipedia-org-2350 130 57 q^{2}}{4}}{4\pi q^{2}}{4}}{4\pi NNP en-wikipedia-org-2350 130 58 \varepsilon \varepsilon CD en-wikipedia-org-2350 130 59 _ _ NNP en-wikipedia-org-2350 130 60 { { -LRB- en-wikipedia-org-2350 130 61 0}L_{2}^{2}}}=mg\tan 0}l_{2}^{2}}}=mg\tan CD en-wikipedia-org-2350 130 62 \theta \theta XX en-wikipedia-org-2350 130 63 _ _ NNP en-wikipedia-org-2350 130 64 { { -LRB- en-wikipedia-org-2350 130 65 2 2 CD en-wikipedia-org-2350 130 66 } } -RRB- en-wikipedia-org-2350 130 67 } } -RRB- en-wikipedia-org-2350 130 68 Dividing dividing NN en-wikipedia-org-2350 130 69 ( ( -LRB- en-wikipedia-org-2350 130 70 4 4 CD en-wikipedia-org-2350 130 71 ) ) -RRB- en-wikipedia-org-2350 130 72 by by IN en-wikipedia-org-2350 130 73 ( ( -LRB- en-wikipedia-org-2350 130 74 5 5 CD en-wikipedia-org-2350 130 75 ) ) -RRB- en-wikipedia-org-2350 130 76 , , , en-wikipedia-org-2350 130 77 we -PRON- PRP en-wikipedia-org-2350 130 78 get get VBP en-wikipedia-org-2350 130 79 : : : en-wikipedia-org-2350 130 80 ( ( -LRB- en-wikipedia-org-2350 130 81 q q NNP en-wikipedia-org-2350 130 82 2 2 CD en-wikipedia-org-2350 130 83 4 4 CD en-wikipedia-org-2350 130 84 π π NN en-wikipedia-org-2350 130 85 ε ε NN en-wikipedia-org-2350 130 86 0 0 CD en-wikipedia-org-2350 130 87 L l NN en-wikipedia-org-2350 130 88 1 1 CD en-wikipedia-org-2350 130 89 2 2 CD en-wikipedia-org-2350 130 90 ) ) -RRB- en-wikipedia-org-2350 130 91 ( ( -LRB- en-wikipedia-org-2350 130 92 q q NNP en-wikipedia-org-2350 130 93 2 2 CD en-wikipedia-org-2350 130 94 4 4 CD en-wikipedia-org-2350 130 95 4 4 CD en-wikipedia-org-2350 130 96 π π NN en-wikipedia-org-2350 130 97 ε ε NN en-wikipedia-org-2350 130 98 0 0 CD en-wikipedia-org-2350 130 99 L l NN en-wikipedia-org-2350 130 100 2 2 CD en-wikipedia-org-2350 130 101 2 2 CD en-wikipedia-org-2350 130 102 ) ) -RRB- en-wikipedia-org-2350 130 103 = = NFP en-wikipedia-org-2350 130 104 m m NNP en-wikipedia-org-2350 130 105 g g NNP en-wikipedia-org-2350 130 106 tan tan NNP en-wikipedia-org-2350 130 107 ⁡ ⁡ NNP en-wikipedia-org-2350 130 108 θ θ NNP en-wikipedia-org-2350 130 109 1 1 CD en-wikipedia-org-2350 130 110 m m NNP en-wikipedia-org-2350 130 111 g g NNP en-wikipedia-org-2350 130 112 tan tan NNP en-wikipedia-org-2350 130 113 ⁡ ⁡ NNP en-wikipedia-org-2350 130 114 θ θ NNP en-wikipedia-org-2350 130 115 2 2 CD en-wikipedia-org-2350 130 116 ⇒ ⇒ CD en-wikipedia-org-2350 130 117 4 4 CD en-wikipedia-org-2350 130 118 ( ( -LRB- en-wikipedia-org-2350 130 119 L l NN en-wikipedia-org-2350 130 120 2 2 CD en-wikipedia-org-2350 130 121 L l NN en-wikipedia-org-2350 130 122 1 1 CD en-wikipedia-org-2350 130 123 ) ) -RRB- en-wikipedia-org-2350 130 124 2 2 CD en-wikipedia-org-2350 130 125 = = SYM en-wikipedia-org-2350 130 126 tan tan NNP en-wikipedia-org-2350 130 127 ⁡ ⁡ NNP en-wikipedia-org-2350 130 128 θ θ NNP en-wikipedia-org-2350 130 129 1 1 CD en-wikipedia-org-2350 130 130 tan tan NNP en-wikipedia-org-2350 130 131 ⁡ ⁡ NNP en-wikipedia-org-2350 130 132 θ θ NNP en-wikipedia-org-2350 130 133 2 2 CD en-wikipedia-org-2350 130 134 { { -LRB- en-wikipedia-org-2350 130 135 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 136 { { -LRB- en-wikipedia-org-2350 130 137 \frac \frac CD en-wikipedia-org-2350 130 138 { { -LRB- en-wikipedia-org-2350 130 139 \left({\cfrac \left({\cfrac CD en-wikipedia-org-2350 130 140 { { -LRB- en-wikipedia-org-2350 130 141 q^{2}}{4\pi q^{2}}{4\pi NNP en-wikipedia-org-2350 130 142 \varepsilon \varepsilon NNP en-wikipedia-org-2350 130 143 _ _ NNP en-wikipedia-org-2350 130 144 { { -LRB- en-wikipedia-org-2350 130 145 0}L_{1}^{2}}}\right)}{\left({\cfrac 0}L_{1}^{2}}}\right)}{\left({\cfrac NNP en-wikipedia-org-2350 130 146 { { -LRB- en-wikipedia-org-2350 130 147 \frac \frac NNP en-wikipedia-org-2350 130 148 { { -LRB- en-wikipedia-org-2350 130 149 q^{2}}{4}}{4\pi q^{2}}{4}}{4\pi NNP en-wikipedia-org-2350 130 150 \varepsilon \varepsilon CD en-wikipedia-org-2350 130 151 _ _ NNP en-wikipedia-org-2350 130 152 { { -LRB- en-wikipedia-org-2350 130 153 0}L_{2}^{2}}}\right)}}={\frac 0}l_{2}^{2}}}\right)}}={\frac CD en-wikipedia-org-2350 130 154 { { -LRB- en-wikipedia-org-2350 130 155 mg\tan mg\tan NNP en-wikipedia-org-2350 130 156 \theta \theta XX en-wikipedia-org-2350 130 157 _ _ NNP en-wikipedia-org-2350 130 158 { { -LRB- en-wikipedia-org-2350 130 159 1}}{mg\tan 1}}{mg\tan CD en-wikipedia-org-2350 130 160 \theta \theta CD en-wikipedia-org-2350 130 161 _ _ IN en-wikipedia-org-2350 130 162 { { -LRB- en-wikipedia-org-2350 130 163 2}}}\Rightarrow 2}}}\rightarrow CD en-wikipedia-org-2350 130 164 4{\left({\frac 4{\left({\frac NN en-wikipedia-org-2350 130 165 { { -LRB- en-wikipedia-org-2350 130 166 L_{2}}{L_{1}}}\right)}^{2}={\frac l_{2}}{l_{1}}}\right)}^{2}={\frac NN en-wikipedia-org-2350 130 167 { { -LRB- en-wikipedia-org-2350 130 168 \tan \tan CD en-wikipedia-org-2350 130 169 \theta \theta NNP en-wikipedia-org-2350 130 170 _ _ NNP en-wikipedia-org-2350 130 171 { { -LRB- en-wikipedia-org-2350 130 172 1}}{\tan 1}}{\tan CD en-wikipedia-org-2350 130 173 \theta \theta CD en-wikipedia-org-2350 130 174 _ _ IN en-wikipedia-org-2350 130 175 { { -LRB- en-wikipedia-org-2350 130 176 2 2 CD en-wikipedia-org-2350 130 177 } } -RRB- en-wikipedia-org-2350 130 178 } } -RRB- en-wikipedia-org-2350 130 179 } } -RRB- en-wikipedia-org-2350 130 180 } } -RRB- en-wikipedia-org-2350 130 181                 _SP en-wikipedia-org-2350 130 182 ( ( -LRB- en-wikipedia-org-2350 130 183 6 6 CD en-wikipedia-org-2350 130 184 ) ) -RRB- en-wikipedia-org-2350 130 185 Measuring measure VBG en-wikipedia-org-2350 130 186 the the DT en-wikipedia-org-2350 130 187 angles angle NNS en-wikipedia-org-2350 130 188 θ θ NN en-wikipedia-org-2350 130 189 1 1 CD en-wikipedia-org-2350 130 190 { { -LRB- en-wikipedia-org-2350 130 191 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 192 \theta \theta CD en-wikipedia-org-2350 130 193 _ _ NNP en-wikipedia-org-2350 130 194 { { -LRB- en-wikipedia-org-2350 130 195 1 1 CD en-wikipedia-org-2350 130 196 } } -RRB- en-wikipedia-org-2350 130 197 } } -RRB- en-wikipedia-org-2350 130 198 and and CC en-wikipedia-org-2350 130 199 θ θ NNP en-wikipedia-org-2350 130 200 2 2 CD en-wikipedia-org-2350 130 201 { { -LRB- en-wikipedia-org-2350 130 202 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 203 \theta \theta CD en-wikipedia-org-2350 130 204 _ _ NNP en-wikipedia-org-2350 130 205 { { -LRB- en-wikipedia-org-2350 130 206 2 2 CD en-wikipedia-org-2350 130 207 } } -RRB- en-wikipedia-org-2350 130 208 } } -RRB- en-wikipedia-org-2350 130 209 and and CC en-wikipedia-org-2350 130 210 the the DT en-wikipedia-org-2350 130 211 distance distance NN en-wikipedia-org-2350 130 212 between between IN en-wikipedia-org-2350 130 213 the the DT en-wikipedia-org-2350 130 214 charges charge NNS en-wikipedia-org-2350 130 215 L L NNP en-wikipedia-org-2350 130 216 1 1 CD en-wikipedia-org-2350 130 217 { { -LRB- en-wikipedia-org-2350 130 218 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 219 \mathbf \mathbf CD en-wikipedia-org-2350 130 220 { { -LRB- en-wikipedia-org-2350 130 221 L L NNP en-wikipedia-org-2350 130 222 } } -RRB- en-wikipedia-org-2350 130 223 _ _ NNP en-wikipedia-org-2350 130 224 { { -LRB- en-wikipedia-org-2350 130 225 1 1 CD en-wikipedia-org-2350 130 226 } } -RRB- en-wikipedia-org-2350 130 227 } } -RRB- en-wikipedia-org-2350 130 228 and and CC en-wikipedia-org-2350 130 229 L l NN en-wikipedia-org-2350 130 230 2 2 CD en-wikipedia-org-2350 130 231 { { -LRB- en-wikipedia-org-2350 130 232 \displaystyle \displaystyle CD en-wikipedia-org-2350 130 233 \mathbf \mathbf CD en-wikipedia-org-2350 130 234 { { -LRB- en-wikipedia-org-2350 130 235 L L NNP en-wikipedia-org-2350 130 236 } } -RRB- en-wikipedia-org-2350 130 237 _ _ NNP en-wikipedia-org-2350 130 238 { { -LRB- en-wikipedia-org-2350 130 239 2 2 CD en-wikipedia-org-2350 130 240 } } -RRB- en-wikipedia-org-2350 130 241 } } -RRB- en-wikipedia-org-2350 130 242 is be VBZ en-wikipedia-org-2350 130 243 sufficient sufficient JJ en-wikipedia-org-2350 130 244 to to TO en-wikipedia-org-2350 130 245 verify verify VB en-wikipedia-org-2350 130 246 that that IN en-wikipedia-org-2350 130 247 the the DT en-wikipedia-org-2350 130 248 equality equality NN en-wikipedia-org-2350 130 249 is be VBZ en-wikipedia-org-2350 130 250 true true JJ en-wikipedia-org-2350 130 251 taking take VBG en-wikipedia-org-2350 130 252 into into IN en-wikipedia-org-2350 130 253 account account NN en-wikipedia-org-2350 130 254 the the DT en-wikipedia-org-2350 130 255 experimental experimental JJ en-wikipedia-org-2350 130 256 error error NN en-wikipedia-org-2350 130 257 . . . en-wikipedia-org-2350 131 1 In in IN en-wikipedia-org-2350 131 2 practice practice NN en-wikipedia-org-2350 131 3 , , , en-wikipedia-org-2350 131 4 angles angle NNS en-wikipedia-org-2350 131 5 can can MD en-wikipedia-org-2350 131 6 be be VB en-wikipedia-org-2350 131 7 difficult difficult JJ en-wikipedia-org-2350 131 8 to to TO en-wikipedia-org-2350 131 9 measure measure VB en-wikipedia-org-2350 131 10 , , , en-wikipedia-org-2350 131 11 so so CC en-wikipedia-org-2350 131 12 if if IN en-wikipedia-org-2350 131 13 the the DT en-wikipedia-org-2350 131 14 length length NN en-wikipedia-org-2350 131 15 of of IN en-wikipedia-org-2350 131 16 the the DT en-wikipedia-org-2350 131 17 ropes rope NNS en-wikipedia-org-2350 131 18 is be VBZ en-wikipedia-org-2350 131 19 sufficiently sufficiently RB en-wikipedia-org-2350 131 20 great great JJ en-wikipedia-org-2350 131 21 , , , en-wikipedia-org-2350 131 22 the the DT en-wikipedia-org-2350 131 23 angles angle NNS en-wikipedia-org-2350 131 24 will will MD en-wikipedia-org-2350 131 25 be be VB en-wikipedia-org-2350 131 26 small small JJ en-wikipedia-org-2350 131 27 enough enough RB en-wikipedia-org-2350 131 28 to to TO en-wikipedia-org-2350 131 29 make make VB en-wikipedia-org-2350 131 30 the the DT en-wikipedia-org-2350 131 31 following follow VBG en-wikipedia-org-2350 131 32 approximation approximation NN en-wikipedia-org-2350 131 33 : : : en-wikipedia-org-2350 131 34 tan tan NNP en-wikipedia-org-2350 131 35 ⁡ ⁡ NNP en-wikipedia-org-2350 131 36 θ θ NNP en-wikipedia-org-2350 131 37 ≈ ≈ NNP en-wikipedia-org-2350 131 38 sin sin NN en-wikipedia-org-2350 131 39 ⁡ ⁡ NNP en-wikipedia-org-2350 131 40 θ θ NNP en-wikipedia-org-2350 131 41 = = SYM en-wikipedia-org-2350 131 42 L l NN en-wikipedia-org-2350 131 43 2 2 CD en-wikipedia-org-2350 131 44 ℓ ℓ NN en-wikipedia-org-2350 131 45 = = SYM en-wikipedia-org-2350 131 46 L l NN en-wikipedia-org-2350 131 47 2 2 CD en-wikipedia-org-2350 131 48 ℓ ℓ CD en-wikipedia-org-2350 131 49 ⇒ ⇒ CD en-wikipedia-org-2350 131 50 tan tan NNP en-wikipedia-org-2350 131 51 ⁡ ⁡ NNP en-wikipedia-org-2350 131 52 θ θ NNP en-wikipedia-org-2350 131 53 1 1 CD en-wikipedia-org-2350 131 54 tan tan NNP en-wikipedia-org-2350 131 55 ⁡ ⁡ NNP en-wikipedia-org-2350 131 56 θ θ NNP en-wikipedia-org-2350 131 57 2 2 CD en-wikipedia-org-2350 131 58 ≈ ≈ NNP en-wikipedia-org-2350 131 59 L l NN en-wikipedia-org-2350 131 60 1 1 CD en-wikipedia-org-2350 131 61 2 2 CD en-wikipedia-org-2350 131 62 ℓ ℓ NN en-wikipedia-org-2350 131 63 L l NN en-wikipedia-org-2350 131 64 2 2 CD en-wikipedia-org-2350 131 65 2 2 CD en-wikipedia-org-2350 131 66 ℓ ℓ NN en-wikipedia-org-2350 131 67 { { -LRB- en-wikipedia-org-2350 131 68 \displaystyle \displaystyle CD en-wikipedia-org-2350 131 69 \tan \tan CD en-wikipedia-org-2350 131 70 \theta \theta XX en-wikipedia-org-2350 131 71 \approx \approx CD en-wikipedia-org-2350 131 72 \sin \sin CD en-wikipedia-org-2350 131 73 \theta \theta XX en-wikipedia-org-2350 131 74 = = FW en-wikipedia-org-2350 131 75 { { -LRB- en-wikipedia-org-2350 131 76 \frac \frac CD en-wikipedia-org-2350 131 77 { { -LRB- en-wikipedia-org-2350 131 78 \frac \frac NNP en-wikipedia-org-2350 131 79 { { -LRB- en-wikipedia-org-2350 131 80 L}{2}}{\ell L}{2}}{\ell NNP en-wikipedia-org-2350 131 81 } } -RRB- en-wikipedia-org-2350 131 82 } } -RRB- en-wikipedia-org-2350 131 83 = = NFP en-wikipedia-org-2350 131 84 { { -LRB- en-wikipedia-org-2350 131 85 \frac \frac UH en-wikipedia-org-2350 131 86 { { -LRB- en-wikipedia-org-2350 131 87 L}{2\ell L}{2\ell NNP en-wikipedia-org-2350 131 88 } } -RRB- en-wikipedia-org-2350 131 89 } } -RRB- en-wikipedia-org-2350 131 90 \Rightarrow \Rightarrow NNP en-wikipedia-org-2350 131 91 { { -LRB- en-wikipedia-org-2350 131 92 \frac \frac CD en-wikipedia-org-2350 131 93 { { -LRB- en-wikipedia-org-2350 131 94 \tan \tan CD en-wikipedia-org-2350 131 95 \theta \theta NNP en-wikipedia-org-2350 131 96 _ _ NNP en-wikipedia-org-2350 131 97 { { -LRB- en-wikipedia-org-2350 131 98 1}}{\tan 1}}{\tan CD en-wikipedia-org-2350 131 99 \theta \theta CD en-wikipedia-org-2350 131 100 _ _ IN en-wikipedia-org-2350 131 101 { { -LRB- en-wikipedia-org-2350 131 102 2}}}\approx 2}}}\approx CD en-wikipedia-org-2350 131 103 { { -LRB- en-wikipedia-org-2350 131 104 \frac \frac CD en-wikipedia-org-2350 131 105 { { -LRB- en-wikipedia-org-2350 131 106 \frac \frac NNP en-wikipedia-org-2350 131 107 { { -LRB- en-wikipedia-org-2350 131 108 L_{1}}{2\ell l_{1}}{2\ell NN en-wikipedia-org-2350 131 109 } } -RRB- en-wikipedia-org-2350 131 110 } } -RRB- en-wikipedia-org-2350 131 111 { { -LRB- en-wikipedia-org-2350 131 112 \frac \frac CD en-wikipedia-org-2350 131 113 { { -LRB- en-wikipedia-org-2350 131 114 L_{2}}{2\ell L_{2}}{2\ell NNP en-wikipedia-org-2350 131 115 } } -RRB- en-wikipedia-org-2350 131 116 } } -RRB- en-wikipedia-org-2350 131 117 } } -RRB- en-wikipedia-org-2350 131 118 } } -RRB- en-wikipedia-org-2350 131 119                 _SP en-wikipedia-org-2350 131 120 ( ( -LRB- en-wikipedia-org-2350 131 121 7 7 LS en-wikipedia-org-2350 131 122 ) ) -RRB- en-wikipedia-org-2350 131 123 Using use VBG en-wikipedia-org-2350 131 124 this this DT en-wikipedia-org-2350 131 125 approximation approximation NN en-wikipedia-org-2350 131 126 , , , en-wikipedia-org-2350 131 127 the the DT en-wikipedia-org-2350 131 128 relationship relationship NN en-wikipedia-org-2350 131 129 ( ( -LRB- en-wikipedia-org-2350 131 130 6 6 CD en-wikipedia-org-2350 131 131 ) ) -RRB- en-wikipedia-org-2350 131 132 becomes become VBZ en-wikipedia-org-2350 131 133 the the DT en-wikipedia-org-2350 131 134 much much RB en-wikipedia-org-2350 131 135 simpler simple JJR en-wikipedia-org-2350 131 136 expression expression NN en-wikipedia-org-2350 131 137 : : : en-wikipedia-org-2350 131 138 L l NN en-wikipedia-org-2350 131 139 1 1 CD en-wikipedia-org-2350 131 140 2 2 CD en-wikipedia-org-2350 131 141 ℓ ℓ NN en-wikipedia-org-2350 131 142 L l NN en-wikipedia-org-2350 131 143 2 2 CD en-wikipedia-org-2350 131 144 2 2 CD en-wikipedia-org-2350 131 145 ℓ ℓ NN en-wikipedia-org-2350 131 146 ≈ ≈ NN en-wikipedia-org-2350 131 147 4 4 CD en-wikipedia-org-2350 131 148 ( ( -LRB- en-wikipedia-org-2350 131 149 L l NN en-wikipedia-org-2350 131 150 2 2 CD en-wikipedia-org-2350 131 151 L l NN en-wikipedia-org-2350 131 152 1 1 CD en-wikipedia-org-2350 131 153 ) ) -RRB- en-wikipedia-org-2350 131 154 2 2 CD en-wikipedia-org-2350 131 155 ⇒ ⇒ CD en-wikipedia-org-2350 131 156 { { -LRB- en-wikipedia-org-2350 131 157 \displaystyle \displaystyle CD en-wikipedia-org-2350 131 158 { { -LRB- en-wikipedia-org-2350 131 159 \frac \frac CD en-wikipedia-org-2350 131 160 { { -LRB- en-wikipedia-org-2350 131 161 \frac \frac NNP en-wikipedia-org-2350 131 162 { { -LRB- en-wikipedia-org-2350 131 163 L_{1}}{2\ell l_{1}}{2\ell NN en-wikipedia-org-2350 131 164 } } -RRB- en-wikipedia-org-2350 131 165 } } -RRB- en-wikipedia-org-2350 131 166 { { -LRB- en-wikipedia-org-2350 131 167 \frac \frac CD en-wikipedia-org-2350 131 168 { { -LRB- en-wikipedia-org-2350 131 169 L_{2}}{2\ell L_{2}}{2\ell NNP en-wikipedia-org-2350 131 170 } } -RRB- en-wikipedia-org-2350 131 171 } } -RRB- en-wikipedia-org-2350 131 172 } } -RRB- en-wikipedia-org-2350 131 173 \approx \approx CD en-wikipedia-org-2350 131 174 4{\left({\frac 4{\left({\frac NN en-wikipedia-org-2350 131 175 { { -LRB- en-wikipedia-org-2350 131 176 L_{2}}{L_{1}}}\right)}^{2}\Rightarrow l_{2}}{l_{1}}}\right)}^{2}\rightarrow NN en-wikipedia-org-2350 131 177 \,\ \,\ NNP en-wikipedia-org-2350 131 178 ! ! . en-wikipedia-org-2350 131 179 } } -RRB- en-wikipedia-org-2350 132 1 L l NN en-wikipedia-org-2350 132 2 1 1 CD en-wikipedia-org-2350 132 3 L l NN en-wikipedia-org-2350 132 4 2 2 CD en-wikipedia-org-2350 132 5 ≈ ≈ NNP en-wikipedia-org-2350 132 6 4 4 CD en-wikipedia-org-2350 132 7 ( ( -LRB- en-wikipedia-org-2350 132 8 L l NN en-wikipedia-org-2350 132 9 2 2 CD en-wikipedia-org-2350 132 10 L l NN en-wikipedia-org-2350 132 11 1 1 CD en-wikipedia-org-2350 132 12 ) ) -RRB- en-wikipedia-org-2350 132 13 2 2 CD en-wikipedia-org-2350 132 14 ⇒ ⇒ CD en-wikipedia-org-2350 132 15 L l NN en-wikipedia-org-2350 132 16 1 1 CD en-wikipedia-org-2350 132 17 L l NN en-wikipedia-org-2350 132 18 2 2 CD en-wikipedia-org-2350 132 19 ≈ ≈ NNP en-wikipedia-org-2350 132 20 4 4 CD en-wikipedia-org-2350 132 21 3 3 CD en-wikipedia-org-2350 132 22 { { -LRB- en-wikipedia-org-2350 132 23 \displaystyle \displaystyle CD en-wikipedia-org-2350 132 24 { { -LRB- en-wikipedia-org-2350 132 25 \frac \frac CD en-wikipedia-org-2350 132 26 { { -LRB- en-wikipedia-org-2350 132 27 L_{1}}{L_{2}}}\approx L_{1}}{L_{2}}}\approx NNP en-wikipedia-org-2350 132 28 4{\left({\frac 4{\left({\frac NNP en-wikipedia-org-2350 132 29 { { -LRB- en-wikipedia-org-2350 132 30 L_{2}}{L_{1}}}\right)}^{2}\Rightarrow l_{2}}{l_{1}}}\right)}^{2}\rightarrow NN en-wikipedia-org-2350 132 31 { { -LRB- en-wikipedia-org-2350 132 32 \frac \frac NNP en-wikipedia-org-2350 132 33 { { -LRB- en-wikipedia-org-2350 132 34 L_{1}}{L_{2}}}\approx l_{1}}{l_{2}}}\approx NN en-wikipedia-org-2350 132 35 { { -LRB- en-wikipedia-org-2350 132 36 \sqrt[{3}]{4}}\,\ \sqrt[{3}]{4}}\,\ NNP en-wikipedia-org-2350 132 37 ! ! . en-wikipedia-org-2350 132 38 } } -RRB- en-wikipedia-org-2350 133 1 ( ( -LRB- en-wikipedia-org-2350 133 2 8) 8) CD en-wikipedia-org-2350 133 3 In in IN en-wikipedia-org-2350 133 4 this this DT en-wikipedia-org-2350 133 5 way way NN en-wikipedia-org-2350 133 6 , , , en-wikipedia-org-2350 133 7 the the DT en-wikipedia-org-2350 133 8 verification verification NN en-wikipedia-org-2350 133 9 is be VBZ en-wikipedia-org-2350 133 10 limited limit VBN en-wikipedia-org-2350 133 11 to to IN en-wikipedia-org-2350 133 12 measuring measure VBG en-wikipedia-org-2350 133 13 the the DT en-wikipedia-org-2350 133 14 distance distance NN en-wikipedia-org-2350 133 15 between between IN en-wikipedia-org-2350 133 16 the the DT en-wikipedia-org-2350 133 17 charges charge NNS en-wikipedia-org-2350 133 18 and and CC en-wikipedia-org-2350 133 19 check check VB en-wikipedia-org-2350 133 20 that that IN en-wikipedia-org-2350 133 21 the the DT en-wikipedia-org-2350 133 22 division division NN en-wikipedia-org-2350 133 23 approximates approximate VBZ en-wikipedia-org-2350 133 24 the the DT en-wikipedia-org-2350 133 25 theoretical theoretical JJ en-wikipedia-org-2350 133 26 value value NN en-wikipedia-org-2350 133 27 . . . en-wikipedia-org-2350 134 1 See see VB en-wikipedia-org-2350 134 2 also[edit also[edit LS en-wikipedia-org-2350 134 3 ] ] -RRB- en-wikipedia-org-2350 134 4 Articles article NNS en-wikipedia-org-2350 134 5 about about IN en-wikipedia-org-2350 134 6 Electromagnetism Electromagnetism NNP en-wikipedia-org-2350 134 7 Electricity Electricity NNP en-wikipedia-org-2350 134 8 Magnetism Magnetism NNP en-wikipedia-org-2350 134 9 History History NNP en-wikipedia-org-2350 134 10 Textbooks Textbooks NNP en-wikipedia-org-2350 134 11 Electrostatics Electrostatics NNPS en-wikipedia-org-2350 134 12 Electric Electric NNP en-wikipedia-org-2350 134 13 charge charge NN en-wikipedia-org-2350 134 14 Coulomb Coulomb NNP en-wikipedia-org-2350 134 15 's 's POS en-wikipedia-org-2350 134 16 law law NN en-wikipedia-org-2350 134 17 Conductor Conductor NNP en-wikipedia-org-2350 134 18 Charge Charge NNP en-wikipedia-org-2350 134 19 density density NN en-wikipedia-org-2350 134 20 Permittivity Permittivity NNP en-wikipedia-org-2350 134 21 Electric Electric NNP en-wikipedia-org-2350 134 22 dipole dipole JJ en-wikipedia-org-2350 134 23 moment moment NN en-wikipedia-org-2350 134 24 Electric electric JJ en-wikipedia-org-2350 134 25 field field NN en-wikipedia-org-2350 134 26 Electric Electric NNP en-wikipedia-org-2350 134 27 potential potential JJ en-wikipedia-org-2350 134 28 Electric Electric NNP en-wikipedia-org-2350 134 29 flux flux NN en-wikipedia-org-2350 134 30   _SP en-wikipedia-org-2350 134 31 / / SYM en-wikipedia-org-2350 134 32 potential potential JJ en-wikipedia-org-2350 134 33 energy energy NN en-wikipedia-org-2350 134 34 Electrostatic electrostatic JJ en-wikipedia-org-2350 134 35 discharge discharge NN en-wikipedia-org-2350 134 36 Gauss Gauss NNP en-wikipedia-org-2350 134 37 's 's POS en-wikipedia-org-2350 134 38 law law NN en-wikipedia-org-2350 134 39 Induction Induction NNP en-wikipedia-org-2350 134 40 Insulator Insulator NNP en-wikipedia-org-2350 134 41 Polarization Polarization NNP en-wikipedia-org-2350 134 42 density density NN en-wikipedia-org-2350 134 43 Static static JJ en-wikipedia-org-2350 134 44 electricity electricity NN en-wikipedia-org-2350 134 45 Triboelectricity Triboelectricity NNP en-wikipedia-org-2350 134 46 Magnetostatics Magnetostatics NNP en-wikipedia-org-2350 134 47 Ampère Ampère NNP en-wikipedia-org-2350 134 48 's 's POS en-wikipedia-org-2350 134 49 law law NN en-wikipedia-org-2350 134 50 Biot Biot NNP en-wikipedia-org-2350 134 51 – – : en-wikipedia-org-2350 134 52 Savart Savart NNP en-wikipedia-org-2350 134 53 law law NN en-wikipedia-org-2350 134 54 Gauss Gauss NNP en-wikipedia-org-2350 134 55 's 's POS en-wikipedia-org-2350 134 56 law law NN en-wikipedia-org-2350 134 57 for for IN en-wikipedia-org-2350 134 58 magnetism magnetism NN en-wikipedia-org-2350 134 59 Magnetic magnetic JJ en-wikipedia-org-2350 134 60 field field NN en-wikipedia-org-2350 134 61 Magnetic magnetic JJ en-wikipedia-org-2350 134 62 flux flux NN en-wikipedia-org-2350 134 63 Magnetic magnetic JJ en-wikipedia-org-2350 134 64 dipole dipole JJ en-wikipedia-org-2350 134 65 moment moment NN en-wikipedia-org-2350 134 66 Magnetic magnetic JJ en-wikipedia-org-2350 134 67 permeability permeability NN en-wikipedia-org-2350 134 68 Magnetic magnetic JJ en-wikipedia-org-2350 134 69 scalar scalar JJ en-wikipedia-org-2350 134 70 potential potential NN en-wikipedia-org-2350 134 71 Magnetization Magnetization NNP en-wikipedia-org-2350 134 72 Magnetomotive Magnetomotive NNP en-wikipedia-org-2350 134 73 force force NN en-wikipedia-org-2350 134 74 Right right JJ en-wikipedia-org-2350 134 75 - - HYPH en-wikipedia-org-2350 134 76 hand hand NN en-wikipedia-org-2350 134 77 rule rule NN en-wikipedia-org-2350 134 78 Electrodynamics Electrodynamics NNP en-wikipedia-org-2350 134 79 Lorentz Lorentz NNP en-wikipedia-org-2350 134 80 force force NN en-wikipedia-org-2350 134 81 law law NN en-wikipedia-org-2350 134 82 Electromagnetic Electromagnetic NNP en-wikipedia-org-2350 134 83 induction induction NN en-wikipedia-org-2350 134 84 Faraday Faraday NNP en-wikipedia-org-2350 134 85 's 's POS en-wikipedia-org-2350 134 86 law law NN en-wikipedia-org-2350 134 87 Lenz Lenz NNP en-wikipedia-org-2350 134 88 's 's POS en-wikipedia-org-2350 134 89 law law NN en-wikipedia-org-2350 134 90 Displacement Displacement NNP en-wikipedia-org-2350 134 91 current current JJ en-wikipedia-org-2350 134 92 Magnetic magnetic JJ en-wikipedia-org-2350 134 93 vector vector NN en-wikipedia-org-2350 134 94 potential potential NN en-wikipedia-org-2350 134 95 Maxwell Maxwell NNP en-wikipedia-org-2350 134 96 's 's POS en-wikipedia-org-2350 134 97 equations equation NNS en-wikipedia-org-2350 134 98 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 99 field field NN en-wikipedia-org-2350 134 100 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 101 pulse pulse NN en-wikipedia-org-2350 134 102 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 103 radiation radiation NN en-wikipedia-org-2350 134 104 Maxwell Maxwell NNP en-wikipedia-org-2350 134 105 tensor tensor NN en-wikipedia-org-2350 134 106 Poynting Poynting NNP en-wikipedia-org-2350 134 107 vector vector NN en-wikipedia-org-2350 134 108 Liénard Liénard NNP en-wikipedia-org-2350 134 109 – – : en-wikipedia-org-2350 134 110 Wiechert Wiechert NNP en-wikipedia-org-2350 134 111 potential potential JJ en-wikipedia-org-2350 134 112 Jefimenko Jefimenko NNP en-wikipedia-org-2350 134 113 's 's POS en-wikipedia-org-2350 134 114 equations equation NNS en-wikipedia-org-2350 134 115 Eddy Eddy NNP en-wikipedia-org-2350 134 116 current current JJ en-wikipedia-org-2350 134 117 London London NNP en-wikipedia-org-2350 134 118 equations equation NNS en-wikipedia-org-2350 134 119 Mathematical mathematical JJ en-wikipedia-org-2350 134 120 descriptions description NNS en-wikipedia-org-2350 134 121 of of IN en-wikipedia-org-2350 134 122 the the DT en-wikipedia-org-2350 134 123 electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 124 field field NN en-wikipedia-org-2350 134 125 Electrical electrical JJ en-wikipedia-org-2350 134 126 network network NN en-wikipedia-org-2350 134 127 Alternating alternate VBG en-wikipedia-org-2350 134 128 current current JJ en-wikipedia-org-2350 134 129 Capacitance Capacitance NNP en-wikipedia-org-2350 134 130 Direct Direct NNP en-wikipedia-org-2350 134 131 current current JJ en-wikipedia-org-2350 134 132 Electric electric JJ en-wikipedia-org-2350 134 133 current current JJ en-wikipedia-org-2350 134 134 Electrolysis Electrolysis NNP en-wikipedia-org-2350 134 135 Current current JJ en-wikipedia-org-2350 134 136 density density NN en-wikipedia-org-2350 134 137 Joule Joule NNP en-wikipedia-org-2350 134 138 heating heating NN en-wikipedia-org-2350 134 139 Electromotive electromotive JJ en-wikipedia-org-2350 134 140 force force NN en-wikipedia-org-2350 134 141 Impedance Impedance NNP en-wikipedia-org-2350 134 142 Inductance Inductance NNP en-wikipedia-org-2350 134 143 Ohm Ohm NNP en-wikipedia-org-2350 134 144 's 's POS en-wikipedia-org-2350 134 145 law law NN en-wikipedia-org-2350 134 146 Parallel Parallel NNP en-wikipedia-org-2350 134 147 circuit circuit NN en-wikipedia-org-2350 134 148 Resistance Resistance NNP en-wikipedia-org-2350 134 149 Resonant Resonant NNP en-wikipedia-org-2350 134 150 cavities cavitie VBZ en-wikipedia-org-2350 134 151 Series Series NNP en-wikipedia-org-2350 134 152 circuit circuit NN en-wikipedia-org-2350 134 153 Voltage Voltage NNP en-wikipedia-org-2350 134 154 Waveguides Waveguides NNP en-wikipedia-org-2350 134 155 Covariant Covariant NNP en-wikipedia-org-2350 134 156 formulation formulation NN en-wikipedia-org-2350 134 157 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 158 tensor tensor NN en-wikipedia-org-2350 134 159 ( ( -LRB- en-wikipedia-org-2350 134 160 stress stress NN en-wikipedia-org-2350 134 161 – – : en-wikipedia-org-2350 134 162 energy energy NN en-wikipedia-org-2350 134 163 tensor tensor NN en-wikipedia-org-2350 134 164 ) ) -RRB- en-wikipedia-org-2350 134 165 Four four CD en-wikipedia-org-2350 134 166 - - HYPH en-wikipedia-org-2350 134 167 current current JJ en-wikipedia-org-2350 134 168 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 134 169 four four CD en-wikipedia-org-2350 134 170 - - HYPH en-wikipedia-org-2350 134 171 potential potential JJ en-wikipedia-org-2350 134 172 Scientists Scientists NNPS en-wikipedia-org-2350 134 173 Ampère Ampère NNP en-wikipedia-org-2350 134 174 Biot Biot NNP en-wikipedia-org-2350 134 175 Coulomb Coulomb NNP en-wikipedia-org-2350 134 176 Davy Davy NNP en-wikipedia-org-2350 134 177 Einstein Einstein NNP en-wikipedia-org-2350 134 178 Faraday Faraday NNP en-wikipedia-org-2350 134 179 Fizeau Fizeau NNP en-wikipedia-org-2350 134 180 Gauss Gauss NNP en-wikipedia-org-2350 134 181 Heaviside Heaviside NNP en-wikipedia-org-2350 134 182 Henry Henry NNP en-wikipedia-org-2350 134 183 Hertz Hertz NNP en-wikipedia-org-2350 134 184 Joule Joule NNP en-wikipedia-org-2350 134 185 Lenz Lenz NNP en-wikipedia-org-2350 134 186 Lorentz Lorentz NNP en-wikipedia-org-2350 134 187 Maxwell Maxwell NNP en-wikipedia-org-2350 134 188 Ørsted Ørsted NNP en-wikipedia-org-2350 134 189 Ohm Ohm NNP en-wikipedia-org-2350 134 190 Ritchie Ritchie NNP en-wikipedia-org-2350 134 191 Savart Savart NNP en-wikipedia-org-2350 134 192 Singer Singer NNP en-wikipedia-org-2350 134 193 Tesla Tesla NNP en-wikipedia-org-2350 134 194 Volta Volta NNP en-wikipedia-org-2350 134 195 Weber Weber NNP en-wikipedia-org-2350 134 196 v v NN en-wikipedia-org-2350 134 197 t t NN en-wikipedia-org-2350 134 198 e e NN en-wikipedia-org-2350 134 199 Wikimedia Wikimedia NNP en-wikipedia-org-2350 134 200 Commons Commons NNPS en-wikipedia-org-2350 134 201 has have VBZ en-wikipedia-org-2350 134 202 media medium NNS en-wikipedia-org-2350 134 203 related relate VBN en-wikipedia-org-2350 134 204 to to IN en-wikipedia-org-2350 134 205 Coulomb Coulomb NNP en-wikipedia-org-2350 134 206 's 's POS en-wikipedia-org-2350 134 207 law law NN en-wikipedia-org-2350 134 208 . . . en-wikipedia-org-2350 135 1 Electronics electronic NNS en-wikipedia-org-2350 135 2 portal portal JJ en-wikipedia-org-2350 135 3 Biot Biot NNP en-wikipedia-org-2350 135 4 – – : en-wikipedia-org-2350 135 5 Savart Savart NNP en-wikipedia-org-2350 135 6 law law NN en-wikipedia-org-2350 135 7 Darwin Darwin NNP en-wikipedia-org-2350 135 8 Lagrangian Lagrangian NNP en-wikipedia-org-2350 135 9 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 135 10 force force NN en-wikipedia-org-2350 135 11 Gauss Gauss NNP en-wikipedia-org-2350 135 12 's 's POS en-wikipedia-org-2350 135 13 law law NN en-wikipedia-org-2350 135 14 Method method NN en-wikipedia-org-2350 135 15 of of IN en-wikipedia-org-2350 135 16 image image NN en-wikipedia-org-2350 135 17 charges charge VBZ en-wikipedia-org-2350 135 18 Molecular Molecular NNP en-wikipedia-org-2350 135 19 modelling model VBG en-wikipedia-org-2350 135 20 Newton Newton NNP en-wikipedia-org-2350 135 21 's 's POS en-wikipedia-org-2350 135 22 law law NN en-wikipedia-org-2350 135 23 of of IN en-wikipedia-org-2350 135 24 universal universal NNP en-wikipedia-org-2350 135 25 gravitation gravitation NNP en-wikipedia-org-2350 135 26 , , , en-wikipedia-org-2350 135 27 which which WDT en-wikipedia-org-2350 135 28 uses use VBZ en-wikipedia-org-2350 135 29 a a DT en-wikipedia-org-2350 135 30 similar similar JJ en-wikipedia-org-2350 135 31 structure structure NN en-wikipedia-org-2350 135 32 , , , en-wikipedia-org-2350 135 33 but but CC en-wikipedia-org-2350 135 34 for for IN en-wikipedia-org-2350 135 35 mass mass NN en-wikipedia-org-2350 135 36 instead instead RB en-wikipedia-org-2350 135 37 of of IN en-wikipedia-org-2350 135 38 charge charge NN en-wikipedia-org-2350 135 39 Static static JJ en-wikipedia-org-2350 135 40 forces force NNS en-wikipedia-org-2350 135 41 and and CC en-wikipedia-org-2350 135 42 virtual virtual JJ en-wikipedia-org-2350 135 43 - - HYPH en-wikipedia-org-2350 135 44 particle particle NN en-wikipedia-org-2350 135 45 exchange exchange NN en-wikipedia-org-2350 135 46 References[edit references[edit NN en-wikipedia-org-2350 135 47 ] ] -RRB- en-wikipedia-org-2350 135 48 ^ ^ FW en-wikipedia-org-2350 135 49 a a DT en-wikipedia-org-2350 135 50 b b NN en-wikipedia-org-2350 135 51 c c NN en-wikipedia-org-2350 135 52 Huray Huray NNP en-wikipedia-org-2350 135 53 , , , en-wikipedia-org-2350 135 54 Paul Paul NNP en-wikipedia-org-2350 135 55 G. G. NNP en-wikipedia-org-2350 135 56 , , , en-wikipedia-org-2350 135 57 1941- 1941- NNP en-wikipedia-org-2350 135 58 ( ( -LRB- en-wikipedia-org-2350 135 59 2010 2010 CD en-wikipedia-org-2350 135 60 ) ) -RRB- en-wikipedia-org-2350 135 61 . . . en-wikipedia-org-2350 136 1 Maxwell Maxwell NNP en-wikipedia-org-2350 136 2 's 's POS en-wikipedia-org-2350 136 3 equations equation NNS en-wikipedia-org-2350 136 4 . . . en-wikipedia-org-2350 137 1 Hoboken Hoboken NNP en-wikipedia-org-2350 137 2 , , , en-wikipedia-org-2350 137 3 N.J. New Jersey NNP en-wikipedia-org-2350 137 4 : : : en-wikipedia-org-2350 137 5 Wiley Wiley NNP en-wikipedia-org-2350 137 6 . . . en-wikipedia-org-2350 138 1 pp pp NNP en-wikipedia-org-2350 138 2 . . . en-wikipedia-org-2350 139 1 8 8 CD en-wikipedia-org-2350 139 2 , , , en-wikipedia-org-2350 139 3 57 57 CD en-wikipedia-org-2350 139 4 . . . en-wikipedia-org-2350 140 1 ISBN ISBN NNP en-wikipedia-org-2350 140 2   _SP en-wikipedia-org-2350 140 3 978 978 CD en-wikipedia-org-2350 140 4 - - HYPH en-wikipedia-org-2350 140 5 0 0 CD en-wikipedia-org-2350 140 6 - - HYPH en-wikipedia-org-2350 140 7 470 470 CD en-wikipedia-org-2350 140 8 - - HYPH en-wikipedia-org-2350 140 9 54991 54991 CD en-wikipedia-org-2350 140 10 - - SYM en-wikipedia-org-2350 140 11 9 9 CD en-wikipedia-org-2350 140 12 . . . en-wikipedia-org-2350 141 1 OCLC oclc NN en-wikipedia-org-2350 141 2   _SP en-wikipedia-org-2350 141 3 739118459.CS1 739118459.cs1 CD en-wikipedia-org-2350 141 4 maint maint NN en-wikipedia-org-2350 141 5 : : : en-wikipedia-org-2350 141 6 multiple multiple JJ en-wikipedia-org-2350 141 7 names name NNS en-wikipedia-org-2350 141 8 : : : en-wikipedia-org-2350 141 9 authors author NNS en-wikipedia-org-2350 141 10 list list NNP en-wikipedia-org-2350 141 11 ( ( -LRB- en-wikipedia-org-2350 141 12 link link NNP en-wikipedia-org-2350 141 13 ) ) -RRB- en-wikipedia-org-2350 141 14 ^ ^ FW en-wikipedia-org-2350 141 15 a a DT en-wikipedia-org-2350 141 16 b b NN en-wikipedia-org-2350 141 17 Halliday Halliday NNP en-wikipedia-org-2350 141 18 , , , en-wikipedia-org-2350 141 19 David David NNP en-wikipedia-org-2350 141 20 ; ; : en-wikipedia-org-2350 141 21 Resnick Resnick NNP en-wikipedia-org-2350 141 22 , , , en-wikipedia-org-2350 141 23 Robert Robert NNP en-wikipedia-org-2350 141 24 ; ; : en-wikipedia-org-2350 141 25 Walker Walker NNP en-wikipedia-org-2350 141 26 , , , en-wikipedia-org-2350 141 27 Jearl Jearl NNP en-wikipedia-org-2350 141 28 ( ( -LRB- en-wikipedia-org-2350 141 29 2013 2013 CD en-wikipedia-org-2350 141 30 ) ) -RRB- en-wikipedia-org-2350 141 31 . . . en-wikipedia-org-2350 142 1 Fundamentals fundamental NNS en-wikipedia-org-2350 142 2 of of IN en-wikipedia-org-2350 142 3 Physics Physics NNP en-wikipedia-org-2350 142 4 . . . en-wikipedia-org-2350 143 1 John John NNP en-wikipedia-org-2350 143 2 Wiley Wiley NNP en-wikipedia-org-2350 143 3 & & CC en-wikipedia-org-2350 143 4 Sons Sons NNP en-wikipedia-org-2350 143 5 . . . en-wikipedia-org-2350 144 1 pp pp NNP en-wikipedia-org-2350 144 2 . . . en-wikipedia-org-2350 145 1 609 609 CD en-wikipedia-org-2350 145 2 , , , en-wikipedia-org-2350 145 3 611 611 CD en-wikipedia-org-2350 145 4 . . . en-wikipedia-org-2350 146 1 ISBN ISBN NNP en-wikipedia-org-2350 146 2   _SP en-wikipedia-org-2350 146 3 9781118230718 9781118230718 CD en-wikipedia-org-2350 146 4 . . . en-wikipedia-org-2350 147 1 ^ ^ NNP en-wikipedia-org-2350 147 2 Roller Roller NNP en-wikipedia-org-2350 147 3 , , , en-wikipedia-org-2350 147 4 Duane Duane NNP en-wikipedia-org-2350 147 5 ; ; : en-wikipedia-org-2350 147 6 Roller Roller NNP en-wikipedia-org-2350 147 7 , , , en-wikipedia-org-2350 147 8 D.H.D. D.H.D. NNP en-wikipedia-org-2350 148 1 ( ( -LRB- en-wikipedia-org-2350 148 2 1954 1954 CD en-wikipedia-org-2350 148 3 ) ) -RRB- en-wikipedia-org-2350 148 4 . . . en-wikipedia-org-2350 149 1 The the DT en-wikipedia-org-2350 149 2 development development NN en-wikipedia-org-2350 149 3 of of IN en-wikipedia-org-2350 149 4 the the DT en-wikipedia-org-2350 149 5 concept concept NN en-wikipedia-org-2350 149 6 of of IN en-wikipedia-org-2350 149 7 electric electric JJ en-wikipedia-org-2350 149 8 charge charge NN en-wikipedia-org-2350 149 9 : : : en-wikipedia-org-2350 149 10 Electricity electricity NN en-wikipedia-org-2350 149 11 from from IN en-wikipedia-org-2350 149 12 the the DT en-wikipedia-org-2350 149 13 Greeks Greeks NNPS en-wikipedia-org-2350 149 14 to to IN en-wikipedia-org-2350 149 15 Coulomb Coulomb NNP en-wikipedia-org-2350 149 16 . . . en-wikipedia-org-2350 150 1 Cambridge Cambridge NNP en-wikipedia-org-2350 150 2 , , , en-wikipedia-org-2350 150 3 MA MA NNP en-wikipedia-org-2350 150 4 : : : en-wikipedia-org-2350 150 5 Harvard Harvard NNP en-wikipedia-org-2350 150 6 University University NNP en-wikipedia-org-2350 150 7 Press Press NNP en-wikipedia-org-2350 150 8 . . . en-wikipedia-org-2350 151 1 p. p. NN en-wikipedia-org-2350 151 2   _SP en-wikipedia-org-2350 151 3 79 79 CD en-wikipedia-org-2350 151 4 . . . en-wikipedia-org-2350 152 1 ^ ^ NNP en-wikipedia-org-2350 152 2 a a DT en-wikipedia-org-2350 152 3 b b NNP en-wikipedia-org-2350 152 4 Coulomb Coulomb NNP en-wikipedia-org-2350 152 5 ( ( -LRB- en-wikipedia-org-2350 152 6 1785 1785 CD en-wikipedia-org-2350 152 7 ) ) -RRB- en-wikipedia-org-2350 152 8 " " `` en-wikipedia-org-2350 152 9 Premier premier NN en-wikipedia-org-2350 152 10 mémoire mémoire VBP en-wikipedia-org-2350 152 11 sur sur FW en-wikipedia-org-2350 152 12 l’électricité l’électricité NNP en-wikipedia-org-2350 152 13 et et NNP en-wikipedia-org-2350 152 14 le le NNP en-wikipedia-org-2350 152 15 magnétisme magnétisme NNP en-wikipedia-org-2350 152 16 , , , en-wikipedia-org-2350 152 17 " " `` en-wikipedia-org-2350 152 18 Histoire Histoire NNP en-wikipedia-org-2350 152 19 de de NNP en-wikipedia-org-2350 152 20 l’Académie l’Académie NNP en-wikipedia-org-2350 152 21 Royale Royale NNP en-wikipedia-org-2350 152 22 des des NNP en-wikipedia-org-2350 152 23 Sciences Sciences NNPS en-wikipedia-org-2350 152 24 , , , en-wikipedia-org-2350 152 25 pp pp NNP en-wikipedia-org-2350 152 26 . . . en-wikipedia-org-2350 153 1 569–577 569–577 CD en-wikipedia-org-2350 153 2 — — : en-wikipedia-org-2350 153 3 Coulomb Coulomb NNP en-wikipedia-org-2350 153 4 studied study VBD en-wikipedia-org-2350 153 5 the the DT en-wikipedia-org-2350 153 6 repulsive repulsive JJ en-wikipedia-org-2350 153 7 force force NN en-wikipedia-org-2350 153 8 between between IN en-wikipedia-org-2350 153 9 bodies body NNS en-wikipedia-org-2350 153 10 having have VBG en-wikipedia-org-2350 153 11 electrical electrical JJ en-wikipedia-org-2350 153 12 charges charge NNS en-wikipedia-org-2350 153 13 of of IN en-wikipedia-org-2350 153 14 the the DT en-wikipedia-org-2350 153 15 same same JJ en-wikipedia-org-2350 153 16 sign sign NN en-wikipedia-org-2350 153 17 : : : en-wikipedia-org-2350 153 18 Il il IN en-wikipedia-org-2350 153 19 résulte résulte JJ en-wikipedia-org-2350 153 20 donc donc NNS en-wikipedia-org-2350 153 21 de de IN en-wikipedia-org-2350 153 22 ces ces NNP en-wikipedia-org-2350 153 23 trois trois NNP en-wikipedia-org-2350 153 24 essais essais NNP en-wikipedia-org-2350 153 25 , , , en-wikipedia-org-2350 153 26 que que NNP en-wikipedia-org-2350 153 27 l'action l'action NNP en-wikipedia-org-2350 153 28 répulsive répulsive JJ en-wikipedia-org-2350 153 29 que que NNP en-wikipedia-org-2350 153 30 les les FW en-wikipedia-org-2350 153 31 deux deux FW en-wikipedia-org-2350 153 32 balles balles NNP en-wikipedia-org-2350 153 33 électrifées électrifées NNP en-wikipedia-org-2350 153 34 de de FW en-wikipedia-org-2350 153 35 la la NNP en-wikipedia-org-2350 153 36 même même NNP en-wikipedia-org-2350 153 37 nature nature NNP en-wikipedia-org-2350 153 38 d'électricité d'électricité NNP en-wikipedia-org-2350 153 39 exercent exercent NNP en-wikipedia-org-2350 153 40 l'une l'une UH en-wikipedia-org-2350 153 41 sur sur NNP en-wikipedia-org-2350 153 42 l'autre l'autre NNP en-wikipedia-org-2350 153 43 , , , en-wikipedia-org-2350 153 44 suit suit NN en-wikipedia-org-2350 153 45 la la NNP en-wikipedia-org-2350 153 46 raison raison NNP en-wikipedia-org-2350 153 47 inverse inverse NNP en-wikipedia-org-2350 153 48 du du NNP en-wikipedia-org-2350 153 49 carré carré NNP en-wikipedia-org-2350 153 50 des des NNP en-wikipedia-org-2350 153 51 distances distance NNS en-wikipedia-org-2350 153 52 . . . en-wikipedia-org-2350 154 1 Translation translation NN en-wikipedia-org-2350 154 2 : : : en-wikipedia-org-2350 154 3 It -PRON- PRP en-wikipedia-org-2350 154 4 follows follow VBZ en-wikipedia-org-2350 154 5 therefore therefore RB en-wikipedia-org-2350 154 6 from from IN en-wikipedia-org-2350 154 7 these these DT en-wikipedia-org-2350 154 8 three three CD en-wikipedia-org-2350 154 9 tests test NNS en-wikipedia-org-2350 154 10 , , , en-wikipedia-org-2350 154 11 that that IN en-wikipedia-org-2350 154 12 the the DT en-wikipedia-org-2350 154 13 repulsive repulsive JJ en-wikipedia-org-2350 154 14 force force NN en-wikipedia-org-2350 154 15 that that IN en-wikipedia-org-2350 154 16 the the DT en-wikipedia-org-2350 154 17 two two CD en-wikipedia-org-2350 154 18 balls ball NNS en-wikipedia-org-2350 154 19 — — : en-wikipedia-org-2350 154 20 [ [ -LRB- en-wikipedia-org-2350 154 21 that that WDT en-wikipedia-org-2350 154 22 were be VBD en-wikipedia-org-2350 154 23 ] ] -RRB- en-wikipedia-org-2350 154 24 electrified electrify VBN en-wikipedia-org-2350 154 25 with with IN en-wikipedia-org-2350 154 26 the the DT en-wikipedia-org-2350 154 27 same same JJ en-wikipedia-org-2350 154 28 kind kind NN en-wikipedia-org-2350 154 29 of of IN en-wikipedia-org-2350 154 30 electricity electricity NN en-wikipedia-org-2350 154 31 — — : en-wikipedia-org-2350 154 32 exert exert VB en-wikipedia-org-2350 154 33 on on IN en-wikipedia-org-2350 154 34 each each DT en-wikipedia-org-2350 154 35 other other JJ en-wikipedia-org-2350 154 36 , , , en-wikipedia-org-2350 154 37 follows follow VBZ en-wikipedia-org-2350 154 38 the the DT en-wikipedia-org-2350 154 39 inverse inverse JJ en-wikipedia-org-2350 154 40 proportion proportion NN en-wikipedia-org-2350 154 41 of of IN en-wikipedia-org-2350 154 42 the the DT en-wikipedia-org-2350 154 43 square square NN en-wikipedia-org-2350 154 44 of of IN en-wikipedia-org-2350 154 45 the the DT en-wikipedia-org-2350 154 46 distance distance NN en-wikipedia-org-2350 154 47 . . . en-wikipedia-org-2350 155 1 — — : en-wikipedia-org-2350 155 2     _SP en-wikipedia-org-2350 155 3 Coulomb Coulomb NNP en-wikipedia-org-2350 155 4 ( ( -LRB- en-wikipedia-org-2350 155 5 1785b 1785b CD en-wikipedia-org-2350 155 6 ) ) -RRB- en-wikipedia-org-2350 155 7 " " `` en-wikipedia-org-2350 155 8 Second second JJ en-wikipedia-org-2350 155 9 mémoire mémoire NN en-wikipedia-org-2350 155 10 sur sur NN en-wikipedia-org-2350 155 11 l’électricité l’électricité NNP en-wikipedia-org-2350 155 12 et et FW en-wikipedia-org-2350 155 13 le le NNP en-wikipedia-org-2350 155 14 magnétisme magnétisme NNP en-wikipedia-org-2350 155 15 , , , en-wikipedia-org-2350 155 16 " " `` en-wikipedia-org-2350 155 17 Histoire Histoire NNP en-wikipedia-org-2350 155 18 de de NNP en-wikipedia-org-2350 155 19 l’Académie l’Académie NNP en-wikipedia-org-2350 155 20 Royale Royale NNP en-wikipedia-org-2350 155 21 des des NNP en-wikipedia-org-2350 155 22 Sciences Sciences NNPS en-wikipedia-org-2350 155 23 , , , en-wikipedia-org-2350 155 24 pages page VBZ en-wikipedia-org-2350 155 25 578–611 578–611 CD en-wikipedia-org-2350 155 26 Coulomb Coulomb NNP en-wikipedia-org-2350 155 27 also also RB en-wikipedia-org-2350 155 28 showed show VBD en-wikipedia-org-2350 155 29 that that IN en-wikipedia-org-2350 155 30 oppositely oppositely RB en-wikipedia-org-2350 155 31 charged charge VBN en-wikipedia-org-2350 155 32 bodies body NNS en-wikipedia-org-2350 155 33 obey obey VBP en-wikipedia-org-2350 155 34 an an DT en-wikipedia-org-2350 155 35 inverse inverse NN en-wikipedia-org-2350 155 36 - - HYPH en-wikipedia-org-2350 155 37 square square JJ en-wikipedia-org-2350 155 38 law law NN en-wikipedia-org-2350 155 39 of of IN en-wikipedia-org-2350 155 40 attraction attraction NN en-wikipedia-org-2350 155 41 . . . en-wikipedia-org-2350 156 1 ^ ^ NNP en-wikipedia-org-2350 156 2 a a DT en-wikipedia-org-2350 156 3 b b NNP en-wikipedia-org-2350 156 4 Purcell Purcell NNP en-wikipedia-org-2350 156 5 , , , en-wikipedia-org-2350 156 6 Edward Edward NNP en-wikipedia-org-2350 156 7 M. M. NNP en-wikipedia-org-2350 156 8 ( ( -LRB- en-wikipedia-org-2350 156 9 21 21 CD en-wikipedia-org-2350 156 10 January January NNP en-wikipedia-org-2350 156 11 2013 2013 CD en-wikipedia-org-2350 156 12 ) ) -RRB- en-wikipedia-org-2350 156 13 . . . en-wikipedia-org-2350 157 1 Electricity electricity NN en-wikipedia-org-2350 157 2 and and CC en-wikipedia-org-2350 157 3 magnetism magnetism NN en-wikipedia-org-2350 157 4 ( ( -LRB- en-wikipedia-org-2350 157 5 Third Third NNP en-wikipedia-org-2350 157 6 ed ed NNP en-wikipedia-org-2350 157 7 . . . en-wikipedia-org-2350 157 8 ) ) -RRB- en-wikipedia-org-2350 157 9 . . . en-wikipedia-org-2350 158 1 Cambridge Cambridge NNP en-wikipedia-org-2350 158 2 . . . en-wikipedia-org-2350 159 1 ISBN ISBN NNP en-wikipedia-org-2350 159 2   _SP en-wikipedia-org-2350 159 3 9781107014022 9781107014022 CD en-wikipedia-org-2350 159 4 . . . en-wikipedia-org-2350 160 1 ^ ^ NFP en-wikipedia-org-2350 160 2 Cork Cork NNP en-wikipedia-org-2350 160 3 , , , en-wikipedia-org-2350 160 4 C.R. C.R. NNP en-wikipedia-org-2350 161 1 ( ( -LRB- en-wikipedia-org-2350 161 2 2015 2015 CD en-wikipedia-org-2350 161 3 ) ) -RRB- en-wikipedia-org-2350 161 4 . . . en-wikipedia-org-2350 162 1 " " `` en-wikipedia-org-2350 162 2 Conductive conductive JJ en-wikipedia-org-2350 162 3 fibres fibre NNS en-wikipedia-org-2350 162 4 for for IN en-wikipedia-org-2350 162 5 electronic electronic JJ en-wikipedia-org-2350 162 6 textiles textile NNS en-wikipedia-org-2350 162 7 " " '' en-wikipedia-org-2350 162 8 . . . en-wikipedia-org-2350 163 1 Electronic Electronic NNP en-wikipedia-org-2350 163 2 Textiles Textiles NNPS en-wikipedia-org-2350 163 3 : : : en-wikipedia-org-2350 163 4 3–20 3–20 LS en-wikipedia-org-2350 163 5 . . . en-wikipedia-org-2350 164 1 doi:10.1016 doi:10.1016 LS en-wikipedia-org-2350 164 2 / / SYM en-wikipedia-org-2350 164 3 B978 B978 NNP en-wikipedia-org-2350 164 4 - - HYPH en-wikipedia-org-2350 164 5 0 0 CD en-wikipedia-org-2350 164 6 - - HYPH en-wikipedia-org-2350 164 7 08 08 CD en-wikipedia-org-2350 164 8 - - HYPH en-wikipedia-org-2350 164 9 100201 100201 CD en-wikipedia-org-2350 164 10 - - HYPH en-wikipedia-org-2350 164 11 8.00002 8.00002 CD en-wikipedia-org-2350 164 12 - - HYPH en-wikipedia-org-2350 164 13 3 3 CD en-wikipedia-org-2350 164 14 . . . en-wikipedia-org-2350 165 1 ISBN ISBN NNP en-wikipedia-org-2350 165 2   _SP en-wikipedia-org-2350 165 3 9780081002018 9780081002018 CD en-wikipedia-org-2350 165 4 . . . en-wikipedia-org-2350 166 1 ^ ^ NNP en-wikipedia-org-2350 166 2 a a DT en-wikipedia-org-2350 166 3 b b NNP en-wikipedia-org-2350 166 4 Stewart Stewart NNP en-wikipedia-org-2350 166 5 , , , en-wikipedia-org-2350 166 6 Joseph Joseph NNP en-wikipedia-org-2350 166 7 ( ( -LRB- en-wikipedia-org-2350 166 8 2001 2001 CD en-wikipedia-org-2350 166 9 ) ) -RRB- en-wikipedia-org-2350 166 10 . . . en-wikipedia-org-2350 167 1 Intermediate intermediate JJ en-wikipedia-org-2350 167 2 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 167 3 Theory theory NN en-wikipedia-org-2350 167 4 . . . en-wikipedia-org-2350 168 1 World World NNP en-wikipedia-org-2350 168 2 Scientific Scientific NNP en-wikipedia-org-2350 168 3 . . . en-wikipedia-org-2350 169 1 p. p. NN en-wikipedia-org-2350 169 2   _SP en-wikipedia-org-2350 169 3 50 50 CD en-wikipedia-org-2350 169 4 . . . en-wikipedia-org-2350 170 1 ISBN ISBN NNP en-wikipedia-org-2350 170 2   _SP en-wikipedia-org-2350 170 3 978 978 CD en-wikipedia-org-2350 170 4 - - CD en-wikipedia-org-2350 170 5 981 981 CD en-wikipedia-org-2350 170 6 - - HYPH en-wikipedia-org-2350 170 7 02 02 CD en-wikipedia-org-2350 170 8 - - HYPH en-wikipedia-org-2350 170 9 4471 4471 CD en-wikipedia-org-2350 170 10 - - HYPH en-wikipedia-org-2350 170 11 2 2 CD en-wikipedia-org-2350 170 12 . . . en-wikipedia-org-2350 171 1 ^ ^ NNP en-wikipedia-org-2350 171 2 Simpson Simpson NNP en-wikipedia-org-2350 171 3 , , , en-wikipedia-org-2350 171 4 Brian Brian NNP en-wikipedia-org-2350 171 5 ( ( -LRB- en-wikipedia-org-2350 171 6 2003 2003 CD en-wikipedia-org-2350 171 7 ) ) -RRB- en-wikipedia-org-2350 171 8 . . . en-wikipedia-org-2350 172 1 Electrical electrical JJ en-wikipedia-org-2350 172 2 Stimulation Stimulation NNP en-wikipedia-org-2350 172 3 and and CC en-wikipedia-org-2350 172 4 the the DT en-wikipedia-org-2350 172 5 Relief Relief NNP en-wikipedia-org-2350 172 6 of of IN en-wikipedia-org-2350 172 7 Pain Pain NNP en-wikipedia-org-2350 172 8 . . . en-wikipedia-org-2350 173 1 Elsevier Elsevier NNP en-wikipedia-org-2350 173 2 Health Health NNP en-wikipedia-org-2350 173 3 Sciences Sciences NNPS en-wikipedia-org-2350 173 4 . . . en-wikipedia-org-2350 174 1 pp pp NNP en-wikipedia-org-2350 174 2 . . . en-wikipedia-org-2350 175 1 6–7 6–7 XX en-wikipedia-org-2350 175 2 . . . en-wikipedia-org-2350 176 1 ISBN ISBN NNP en-wikipedia-org-2350 176 2   _SP en-wikipedia-org-2350 176 3 978 978 CD en-wikipedia-org-2350 176 4 - - HYPH en-wikipedia-org-2350 176 5 0 0 CD en-wikipedia-org-2350 176 6 - - HYPH en-wikipedia-org-2350 176 7 444 444 CD en-wikipedia-org-2350 176 8 - - HYPH en-wikipedia-org-2350 176 9 51258 51258 CD en-wikipedia-org-2350 176 10 - - HYPH en-wikipedia-org-2350 176 11 1 1 CD en-wikipedia-org-2350 176 12 . . . en-wikipedia-org-2350 177 1 ^ ^ NNP en-wikipedia-org-2350 177 2 Baigrie Baigrie NNP en-wikipedia-org-2350 177 3 , , , en-wikipedia-org-2350 177 4 Brian Brian NNP en-wikipedia-org-2350 177 5 ( ( -LRB- en-wikipedia-org-2350 177 6 2007 2007 CD en-wikipedia-org-2350 177 7 ) ) -RRB- en-wikipedia-org-2350 177 8 . . . en-wikipedia-org-2350 178 1 Electricity Electricity NNP en-wikipedia-org-2350 178 2 and and CC en-wikipedia-org-2350 178 3 Magnetism magnetism NN en-wikipedia-org-2350 178 4 : : : en-wikipedia-org-2350 178 5 A a DT en-wikipedia-org-2350 178 6 Historical Historical NNP en-wikipedia-org-2350 178 7 Perspective Perspective NNP en-wikipedia-org-2350 178 8 . . . en-wikipedia-org-2350 179 1 Greenwood Greenwood NNP en-wikipedia-org-2350 179 2 Press Press NNP en-wikipedia-org-2350 179 3 . . . en-wikipedia-org-2350 180 1 pp pp NNP en-wikipedia-org-2350 180 2 . . . en-wikipedia-org-2350 181 1 7–8 7–8 LS en-wikipedia-org-2350 181 2 . . . en-wikipedia-org-2350 182 1 ISBN ISBN NNP en-wikipedia-org-2350 182 2   _SP en-wikipedia-org-2350 182 3 978 978 CD en-wikipedia-org-2350 182 4 - - HYPH en-wikipedia-org-2350 182 5 0 0 CD en-wikipedia-org-2350 182 6 - - HYPH en-wikipedia-org-2350 182 7 313 313 CD en-wikipedia-org-2350 182 8 - - HYPH en-wikipedia-org-2350 182 9 33358 33358 CD en-wikipedia-org-2350 182 10 - - HYPH en-wikipedia-org-2350 182 11 3 3 CD en-wikipedia-org-2350 182 12 . . . en-wikipedia-org-2350 183 1 ^ ^ NNP en-wikipedia-org-2350 183 2 Chalmers Chalmers NNP en-wikipedia-org-2350 183 3 , , , en-wikipedia-org-2350 183 4 Gordon Gordon NNP en-wikipedia-org-2350 183 5 ( ( -LRB- en-wikipedia-org-2350 183 6 1937 1937 CD en-wikipedia-org-2350 183 7 ) ) -RRB- en-wikipedia-org-2350 183 8 . . . en-wikipedia-org-2350 184 1 " " `` en-wikipedia-org-2350 184 2 The the DT en-wikipedia-org-2350 184 3 Lodestone Lodestone NNP en-wikipedia-org-2350 184 4 and and CC en-wikipedia-org-2350 184 5 the the DT en-wikipedia-org-2350 184 6 Understanding understanding NN en-wikipedia-org-2350 184 7 of of IN en-wikipedia-org-2350 184 8 Matter Matter NNP en-wikipedia-org-2350 184 9 in in IN en-wikipedia-org-2350 184 10 Seventeenth Seventeenth NNP en-wikipedia-org-2350 184 11 Century Century NNP en-wikipedia-org-2350 184 12 England England NNP en-wikipedia-org-2350 184 13 " " '' en-wikipedia-org-2350 184 14 . . . en-wikipedia-org-2350 185 1 Philosophy Philosophy NNP en-wikipedia-org-2350 185 2 of of IN en-wikipedia-org-2350 185 3 Science Science NNP en-wikipedia-org-2350 185 4 . . . en-wikipedia-org-2350 186 1 4 4 CD en-wikipedia-org-2350 186 2 ( ( -LRB- en-wikipedia-org-2350 186 3 1 1 CD en-wikipedia-org-2350 186 4 ) ) -RRB- en-wikipedia-org-2350 186 5 : : : en-wikipedia-org-2350 186 6 75–95 75–95 CD en-wikipedia-org-2350 186 7 . . . en-wikipedia-org-2350 187 1 doi:10.1086/286445 doi:10.1086/286445 FW en-wikipedia-org-2350 187 2 . . . en-wikipedia-org-2350 188 1 S2CID S2CID NNS en-wikipedia-org-2350 188 2   _SP en-wikipedia-org-2350 188 3 121067746 121067746 CD en-wikipedia-org-2350 188 4 . . . en-wikipedia-org-2350 189 1 ^ ^ FW en-wikipedia-org-2350 189 2 Socin Socin NNP en-wikipedia-org-2350 189 3 , , , en-wikipedia-org-2350 189 4 Abel Abel NNP en-wikipedia-org-2350 189 5 ( ( -LRB- en-wikipedia-org-2350 189 6 1760 1760 CD en-wikipedia-org-2350 189 7 ) ) -RRB- en-wikipedia-org-2350 189 8 . . . en-wikipedia-org-2350 190 1 Acta Acta NNP en-wikipedia-org-2350 190 2 Helvetica Helvetica NNP en-wikipedia-org-2350 190 3 Physico Physico NNP en-wikipedia-org-2350 190 4 - - HYPH en-wikipedia-org-2350 190 5 Mathematico Mathematico NNP en-wikipedia-org-2350 190 6 - - HYPH en-wikipedia-org-2350 190 7 Anatomico Anatomico NNP en-wikipedia-org-2350 190 8 - - HYPH en-wikipedia-org-2350 190 9 Botanico Botanico NNP en-wikipedia-org-2350 190 10 - - HYPH en-wikipedia-org-2350 190 11 Medica Medica NNP en-wikipedia-org-2350 190 12 ( ( -LRB- en-wikipedia-org-2350 190 13 in in IN en-wikipedia-org-2350 190 14 Latin Latin NNP en-wikipedia-org-2350 190 15 ) ) -RRB- en-wikipedia-org-2350 190 16 . . . en-wikipedia-org-2350 191 1 4 4 LS en-wikipedia-org-2350 191 2 . . . en-wikipedia-org-2350 192 1 Basileae Basileae NNP en-wikipedia-org-2350 192 2 . . . en-wikipedia-org-2350 193 1 pp pp NNP en-wikipedia-org-2350 193 2 . . . en-wikipedia-org-2350 194 1 224–25 224–25 CD en-wikipedia-org-2350 194 2 . . . en-wikipedia-org-2350 195 1 ^ ^ NNP en-wikipedia-org-2350 195 2 Heilbron Heilbron NNP en-wikipedia-org-2350 195 3 , , , en-wikipedia-org-2350 195 4 J.L. J.L. NNP en-wikipedia-org-2350 196 1 ( ( -LRB- en-wikipedia-org-2350 196 2 1979 1979 CD en-wikipedia-org-2350 196 3 ) ) -RRB- en-wikipedia-org-2350 196 4 . . . en-wikipedia-org-2350 197 1 Electricity electricity NN en-wikipedia-org-2350 197 2 in in IN en-wikipedia-org-2350 197 3 the the DT en-wikipedia-org-2350 197 4 17th 17th JJ en-wikipedia-org-2350 197 5 and and CC en-wikipedia-org-2350 197 6 18th 18th JJ en-wikipedia-org-2350 197 7 Centuries century NNS en-wikipedia-org-2350 197 8 : : : en-wikipedia-org-2350 197 9 A a DT en-wikipedia-org-2350 197 10 Study Study NNP en-wikipedia-org-2350 197 11 of of IN en-wikipedia-org-2350 197 12 Early early JJ en-wikipedia-org-2350 197 13 Modern Modern NNP en-wikipedia-org-2350 197 14 Physics Physics NNP en-wikipedia-org-2350 197 15 . . . en-wikipedia-org-2350 198 1 Los Los NNP en-wikipedia-org-2350 198 2 Angeles Angeles NNP en-wikipedia-org-2350 198 3 , , , en-wikipedia-org-2350 198 4 California California NNP en-wikipedia-org-2350 198 5 : : : en-wikipedia-org-2350 198 6 University University NNP en-wikipedia-org-2350 198 7 of of IN en-wikipedia-org-2350 198 8 California California NNP en-wikipedia-org-2350 198 9 Press Press NNP en-wikipedia-org-2350 198 10 . . . en-wikipedia-org-2350 199 1 pp pp NNP en-wikipedia-org-2350 199 2 . . . en-wikipedia-org-2350 200 1 460–462 460–462 CD en-wikipedia-org-2350 200 2 and and CC en-wikipedia-org-2350 200 3 464 464 CD en-wikipedia-org-2350 200 4 ( ( -LRB- en-wikipedia-org-2350 200 5 including include VBG en-wikipedia-org-2350 200 6 footnote footnote NNP en-wikipedia-org-2350 200 7 44 44 CD en-wikipedia-org-2350 200 8 ) ) -RRB- en-wikipedia-org-2350 200 9 . . . en-wikipedia-org-2350 201 1 ISBN ISBN NNP en-wikipedia-org-2350 201 2   _SP en-wikipedia-org-2350 201 3 978 978 CD en-wikipedia-org-2350 201 4 - - HYPH en-wikipedia-org-2350 201 5 0486406886 0486406886 CD en-wikipedia-org-2350 201 6 . . . en-wikipedia-org-2350 202 1 ^ ^ NNP en-wikipedia-org-2350 202 2 Schofield Schofield NNP en-wikipedia-org-2350 202 3 , , , en-wikipedia-org-2350 202 4 Robert Robert NNP en-wikipedia-org-2350 202 5 E. E. NNP en-wikipedia-org-2350 202 6 ( ( -LRB- en-wikipedia-org-2350 202 7 1997 1997 CD en-wikipedia-org-2350 202 8 ) ) -RRB- en-wikipedia-org-2350 202 9 . . . en-wikipedia-org-2350 203 1 The the DT en-wikipedia-org-2350 203 2 Enlightenment Enlightenment NNP en-wikipedia-org-2350 203 3 of of IN en-wikipedia-org-2350 203 4 Joseph Joseph NNP en-wikipedia-org-2350 203 5 Priestley Priestley NNP en-wikipedia-org-2350 203 6 : : : en-wikipedia-org-2350 203 7 A A NNP en-wikipedia-org-2350 203 8 Study Study NNP en-wikipedia-org-2350 203 9 of of IN en-wikipedia-org-2350 203 10 his -PRON- PRP$ en-wikipedia-org-2350 203 11 Life Life NNP en-wikipedia-org-2350 203 12 and and CC en-wikipedia-org-2350 203 13 Work Work NNP en-wikipedia-org-2350 203 14 from from IN en-wikipedia-org-2350 203 15 1733 1733 CD en-wikipedia-org-2350 203 16 to to IN en-wikipedia-org-2350 203 17 1773 1773 CD en-wikipedia-org-2350 203 18 . . . en-wikipedia-org-2350 204 1 University University NNP en-wikipedia-org-2350 204 2 Park Park NNP en-wikipedia-org-2350 204 3 : : : en-wikipedia-org-2350 204 4 Pennsylvania Pennsylvania NNP en-wikipedia-org-2350 204 5 State State NNP en-wikipedia-org-2350 204 6 University University NNP en-wikipedia-org-2350 204 7 Press Press NNP en-wikipedia-org-2350 204 8 . . . en-wikipedia-org-2350 205 1 pp pp NNP en-wikipedia-org-2350 205 2 . . . en-wikipedia-org-2350 206 1 144–56 144–56 CD en-wikipedia-org-2350 206 2 . . . en-wikipedia-org-2350 207 1 ISBN ISBN NNP en-wikipedia-org-2350 207 2   _SP en-wikipedia-org-2350 207 3 978 978 CD en-wikipedia-org-2350 207 4 - - HYPH en-wikipedia-org-2350 207 5 0 0 CD en-wikipedia-org-2350 207 6 - - HYPH en-wikipedia-org-2350 207 7 271 271 CD en-wikipedia-org-2350 207 8 - - HYPH en-wikipedia-org-2350 207 9 01662 01662 CD en-wikipedia-org-2350 207 10 - - HYPH en-wikipedia-org-2350 207 11 7 7 CD en-wikipedia-org-2350 207 12 . . . en-wikipedia-org-2350 208 1 ^ ^ NNP en-wikipedia-org-2350 208 2 Priestley Priestley NNP en-wikipedia-org-2350 208 3 , , , en-wikipedia-org-2350 208 4 Joseph Joseph NNP en-wikipedia-org-2350 208 5 ( ( -LRB- en-wikipedia-org-2350 208 6 1767 1767 CD en-wikipedia-org-2350 208 7 ) ) -RRB- en-wikipedia-org-2350 208 8 . . . en-wikipedia-org-2350 209 1 The the DT en-wikipedia-org-2350 209 2 History History NNP en-wikipedia-org-2350 209 3 and and CC en-wikipedia-org-2350 209 4 Present Present NNP en-wikipedia-org-2350 209 5 State State NNP en-wikipedia-org-2350 209 6 of of IN en-wikipedia-org-2350 209 7 Electricity Electricity NNP en-wikipedia-org-2350 209 8 , , , en-wikipedia-org-2350 209 9 with with IN en-wikipedia-org-2350 209 10 Original original JJ en-wikipedia-org-2350 209 11 Experiments Experiments NNPS en-wikipedia-org-2350 209 12 . . . en-wikipedia-org-2350 210 1 London London NNP en-wikipedia-org-2350 210 2 , , , en-wikipedia-org-2350 210 3 England England NNP en-wikipedia-org-2350 210 4 . . . en-wikipedia-org-2350 211 1 p. p. NN en-wikipedia-org-2350 211 2   _SP en-wikipedia-org-2350 211 3 732 732 CD en-wikipedia-org-2350 211 4 . . . en-wikipedia-org-2350 212 1 ^ ^ NNP en-wikipedia-org-2350 212 2 Elliott Elliott NNP en-wikipedia-org-2350 212 3 , , , en-wikipedia-org-2350 212 4 Robert Robert NNP en-wikipedia-org-2350 212 5 S. S. NNP en-wikipedia-org-2350 212 6 ( ( -LRB- en-wikipedia-org-2350 212 7 1999 1999 CD en-wikipedia-org-2350 212 8 ) ) -RRB- en-wikipedia-org-2350 212 9 . . . en-wikipedia-org-2350 213 1 Electromagnetics electromagnetic NNS en-wikipedia-org-2350 213 2 : : : en-wikipedia-org-2350 213 3 History history NN en-wikipedia-org-2350 213 4 , , , en-wikipedia-org-2350 213 5 Theory theory NN en-wikipedia-org-2350 213 6 , , , en-wikipedia-org-2350 213 7 and and CC en-wikipedia-org-2350 213 8 Applications application NNS en-wikipedia-org-2350 213 9 . . . en-wikipedia-org-2350 214 1 ISBN ISBN NNP en-wikipedia-org-2350 214 2   _SP en-wikipedia-org-2350 214 3 978 978 CD en-wikipedia-org-2350 214 4 - - HYPH en-wikipedia-org-2350 214 5 0 0 CD en-wikipedia-org-2350 214 6 - - HYPH en-wikipedia-org-2350 214 7 7803 7803 CD en-wikipedia-org-2350 214 8 - - HYPH en-wikipedia-org-2350 214 9 5384 5384 CD en-wikipedia-org-2350 214 10 - - HYPH en-wikipedia-org-2350 214 11 8 8 CD en-wikipedia-org-2350 214 12 . . . en-wikipedia-org-2350 215 1 ^ ^ NNP en-wikipedia-org-2350 215 2 Robison Robison NNP en-wikipedia-org-2350 215 3 , , , en-wikipedia-org-2350 215 4 John John NNP en-wikipedia-org-2350 215 5 ( ( -LRB- en-wikipedia-org-2350 215 6 1822 1822 CD en-wikipedia-org-2350 215 7 ) ) -RRB- en-wikipedia-org-2350 215 8 . . . en-wikipedia-org-2350 216 1 Murray Murray NNP en-wikipedia-org-2350 216 2 , , , en-wikipedia-org-2350 216 3 John John NNP en-wikipedia-org-2350 216 4 ( ( -LRB- en-wikipedia-org-2350 216 5 ed ed NNP en-wikipedia-org-2350 216 6 . . . en-wikipedia-org-2350 216 7 ) ) -RRB- en-wikipedia-org-2350 216 8 . . . en-wikipedia-org-2350 217 1 A a DT en-wikipedia-org-2350 217 2 System system NN en-wikipedia-org-2350 217 3 of of IN en-wikipedia-org-2350 217 4 Mechanical Mechanical NNP en-wikipedia-org-2350 217 5 Philosophy Philosophy NNP en-wikipedia-org-2350 217 6 . . . en-wikipedia-org-2350 218 1 4 4 LS en-wikipedia-org-2350 218 2 . . . en-wikipedia-org-2350 219 1 London London NNP en-wikipedia-org-2350 219 2 , , , en-wikipedia-org-2350 219 3 England England NNP en-wikipedia-org-2350 219 4 . . . en-wikipedia-org-2350 220 1 ^ ^ NNP en-wikipedia-org-2350 220 2 Maxwell Maxwell NNP en-wikipedia-org-2350 220 3 , , , en-wikipedia-org-2350 220 4 James James NNP en-wikipedia-org-2350 220 5 Clerk Clerk NNP en-wikipedia-org-2350 220 6 , , , en-wikipedia-org-2350 220 7 ed ed NN en-wikipedia-org-2350 220 8 . . . en-wikipedia-org-2350 221 1 ( ( -LRB- en-wikipedia-org-2350 221 2 1967 1967 CD en-wikipedia-org-2350 221 3 ) ) -RRB- en-wikipedia-org-2350 221 4 [ [ -LRB- en-wikipedia-org-2350 221 5 1879 1879 CD en-wikipedia-org-2350 221 6 ] ] -RRB- en-wikipedia-org-2350 221 7 . . . en-wikipedia-org-2350 222 1 " " `` en-wikipedia-org-2350 222 2 Experiments experiment NNS en-wikipedia-org-2350 222 3 on on IN en-wikipedia-org-2350 222 4 Electricity electricity NN en-wikipedia-org-2350 222 5 : : : en-wikipedia-org-2350 222 6 Experimental experimental JJ en-wikipedia-org-2350 222 7 determination determination NN en-wikipedia-org-2350 222 8 of of IN en-wikipedia-org-2350 222 9 the the DT en-wikipedia-org-2350 222 10 law law NN en-wikipedia-org-2350 222 11 of of IN en-wikipedia-org-2350 222 12 electric electric JJ en-wikipedia-org-2350 222 13 force force NN en-wikipedia-org-2350 222 14 . . . en-wikipedia-org-2350 222 15 " " '' en-wikipedia-org-2350 222 16 . . . en-wikipedia-org-2350 223 1 The the DT en-wikipedia-org-2350 223 2 Electrical electrical JJ en-wikipedia-org-2350 223 3 Researches Researches NNPS en-wikipedia-org-2350 223 4 of of IN en-wikipedia-org-2350 223 5 the the DT en-wikipedia-org-2350 223 6 Honourable honourable JJ en-wikipedia-org-2350 223 7 Henry Henry NNP en-wikipedia-org-2350 223 8 Cavendish Cavendish NNP en-wikipedia-org-2350 223 9 ... ... NFP en-wikipedia-org-2350 223 10 ( ( -LRB- en-wikipedia-org-2350 223 11 1st 1st NNP en-wikipedia-org-2350 223 12 ed ed NNP en-wikipedia-org-2350 223 13 . . . en-wikipedia-org-2350 223 14 ) ) -RRB- en-wikipedia-org-2350 223 15 . . . en-wikipedia-org-2350 224 1 Cambridge Cambridge NNP en-wikipedia-org-2350 224 2 , , , en-wikipedia-org-2350 224 3 England England NNP en-wikipedia-org-2350 224 4 : : : en-wikipedia-org-2350 224 5 Cambridge Cambridge NNP en-wikipedia-org-2350 224 6 University University NNP en-wikipedia-org-2350 224 7 Press Press NNP en-wikipedia-org-2350 224 8 . . . en-wikipedia-org-2350 225 1 pp pp NNP en-wikipedia-org-2350 225 2 . . . en-wikipedia-org-2350 226 1 104–113 104–113 CD en-wikipedia-org-2350 226 2 . . . en-wikipedia-org-2350 227 1 On on IN en-wikipedia-org-2350 227 2 pages page NNS en-wikipedia-org-2350 227 3 111 111 CD en-wikipedia-org-2350 227 4 and and CC en-wikipedia-org-2350 227 5 112 112 CD en-wikipedia-org-2350 227 6 the the DT en-wikipedia-org-2350 227 7 author author NN en-wikipedia-org-2350 227 8 states state VBZ en-wikipedia-org-2350 227 9 : : : en-wikipedia-org-2350 227 10 " " `` en-wikipedia-org-2350 227 11 We -PRON- PRP en-wikipedia-org-2350 227 12 may may MD en-wikipedia-org-2350 227 13 therefore therefore RB en-wikipedia-org-2350 227 14 conclude conclude VB en-wikipedia-org-2350 227 15 that that IN en-wikipedia-org-2350 227 16 the the DT en-wikipedia-org-2350 227 17 electric electric JJ en-wikipedia-org-2350 227 18 attraction attraction NN en-wikipedia-org-2350 227 19 and and CC en-wikipedia-org-2350 227 20 repulsion repulsion NN en-wikipedia-org-2350 227 21 must must MD en-wikipedia-org-2350 227 22 be be VB en-wikipedia-org-2350 227 23 inversely inversely RB en-wikipedia-org-2350 227 24 as as IN en-wikipedia-org-2350 227 25 some some DT en-wikipedia-org-2350 227 26 power power NN en-wikipedia-org-2350 227 27 of of IN en-wikipedia-org-2350 227 28 the the DT en-wikipedia-org-2350 227 29 distance distance NN en-wikipedia-org-2350 227 30 between between IN en-wikipedia-org-2350 227 31 that that DT en-wikipedia-org-2350 227 32 of of IN en-wikipedia-org-2350 227 33 the the DT en-wikipedia-org-2350 227 34 2 2 CD en-wikipedia-org-2350 227 35 + + SYM en-wikipedia-org-2350 227 36 ​1⁄50 ​1⁄50 UH en-wikipedia-org-2350 227 37 th th XX en-wikipedia-org-2350 227 38 and and CC en-wikipedia-org-2350 227 39 that that DT en-wikipedia-org-2350 227 40 of of IN en-wikipedia-org-2350 227 41 the the DT en-wikipedia-org-2350 227 42 2 2 CD en-wikipedia-org-2350 227 43 − − NNP en-wikipedia-org-2350 227 44 ​1⁄50 ​1⁄50 NNP en-wikipedia-org-2350 227 45 th th XX en-wikipedia-org-2350 227 46 , , , en-wikipedia-org-2350 227 47 and and CC en-wikipedia-org-2350 227 48 there there EX en-wikipedia-org-2350 227 49 is be VBZ en-wikipedia-org-2350 227 50 no no DT en-wikipedia-org-2350 227 51 reason reason NN en-wikipedia-org-2350 227 52 to to TO en-wikipedia-org-2350 227 53 think think VB en-wikipedia-org-2350 227 54 that that IN en-wikipedia-org-2350 227 55 it -PRON- PRP en-wikipedia-org-2350 227 56 differs differ VBZ en-wikipedia-org-2350 227 57 at at RB en-wikipedia-org-2350 227 58 all all RB en-wikipedia-org-2350 227 59 from from IN en-wikipedia-org-2350 227 60 the the DT en-wikipedia-org-2350 227 61 inverse inverse NN en-wikipedia-org-2350 227 62 duplicate duplicate VBP en-wikipedia-org-2350 227 63 ratio ratio NN en-wikipedia-org-2350 227 64 " " '' en-wikipedia-org-2350 227 65 . . . en-wikipedia-org-2350 228 1 ^ ^ NFP en-wikipedia-org-2350 228 2 Coulomb Coulomb NNP en-wikipedia-org-2350 228 3 's 's POS en-wikipedia-org-2350 228 4 law law NN en-wikipedia-org-2350 228 5 , , , en-wikipedia-org-2350 228 6 Hyperphysics Hyperphysics NNP en-wikipedia-org-2350 228 7 ^ ^ NN en-wikipedia-org-2350 228 8 a a DT en-wikipedia-org-2350 228 9 b b NN en-wikipedia-org-2350 228 10 c c NN en-wikipedia-org-2350 228 11 Feynman Feynman NNP en-wikipedia-org-2350 228 12 , , , en-wikipedia-org-2350 228 13 Richard Richard NNP en-wikipedia-org-2350 228 14 P. P. NNP en-wikipedia-org-2350 228 15 ( ( -LRB- en-wikipedia-org-2350 228 16 1970 1970 CD en-wikipedia-org-2350 228 17 ) ) -RRB- en-wikipedia-org-2350 228 18 . . . en-wikipedia-org-2350 229 1 The the DT en-wikipedia-org-2350 229 2 Feynman Feynman NNP en-wikipedia-org-2350 229 3 Lectures Lectures NNP en-wikipedia-org-2350 229 4 on on IN en-wikipedia-org-2350 229 5 Physics Physics NNP en-wikipedia-org-2350 229 6 Vol Vol NNP en-wikipedia-org-2350 229 7 II II NNP en-wikipedia-org-2350 229 8 . . . en-wikipedia-org-2350 230 1 ISBN ISBN NNP en-wikipedia-org-2350 230 2   _SP en-wikipedia-org-2350 230 3 9780201021158 9780201021158 CD en-wikipedia-org-2350 230 4 . . . en-wikipedia-org-2350 231 1 ^ ^ NNP en-wikipedia-org-2350 231 2 a a DT en-wikipedia-org-2350 231 3 b b NN en-wikipedia-org-2350 231 4 c c NN en-wikipedia-org-2350 231 5 Coulomb Coulomb NNP en-wikipedia-org-2350 231 6 's 's POS en-wikipedia-org-2350 231 7 law law NN en-wikipedia-org-2350 231 8 , , , en-wikipedia-org-2350 231 9 University University NNP en-wikipedia-org-2350 231 10 of of IN en-wikipedia-org-2350 231 11 Texas Texas NNP en-wikipedia-org-2350 231 12 ^ ^ NN en-wikipedia-org-2350 231 13 Charged charge VBN en-wikipedia-org-2350 231 14 rods rod NNS en-wikipedia-org-2350 231 15 , , , en-wikipedia-org-2350 231 16 PhysicsLab.org physicslab.org NN en-wikipedia-org-2350 231 17 ^ ^ NN en-wikipedia-org-2350 231 18 Walker Walker NNP en-wikipedia-org-2350 231 19 , , , en-wikipedia-org-2350 231 20 Jearl Jearl NNP en-wikipedia-org-2350 231 21 ; ; : en-wikipedia-org-2350 231 22 Halliday Halliday NNP en-wikipedia-org-2350 231 23 , , , en-wikipedia-org-2350 231 24 David David NNP en-wikipedia-org-2350 231 25 ; ; : en-wikipedia-org-2350 231 26 Resnick Resnick NNP en-wikipedia-org-2350 231 27 , , , en-wikipedia-org-2350 231 28 Robert Robert NNP en-wikipedia-org-2350 231 29 ( ( -LRB- en-wikipedia-org-2350 231 30 2014 2014 CD en-wikipedia-org-2350 231 31 ) ) -RRB- en-wikipedia-org-2350 231 32 . . . en-wikipedia-org-2350 232 1 Fundamentals fundamental NNS en-wikipedia-org-2350 232 2 of of IN en-wikipedia-org-2350 232 3 physics physics NN en-wikipedia-org-2350 232 4 ( ( -LRB- en-wikipedia-org-2350 232 5 10th 10th JJ en-wikipedia-org-2350 232 6 ed ed NNP en-wikipedia-org-2350 232 7 . . . en-wikipedia-org-2350 232 8 ) ) -RRB- en-wikipedia-org-2350 232 9 . . . en-wikipedia-org-2350 233 1 Hoboken Hoboken NNP en-wikipedia-org-2350 233 2 , , , en-wikipedia-org-2350 233 3 NJ NJ NNP en-wikipedia-org-2350 233 4 : : : en-wikipedia-org-2350 233 5 Wiley Wiley NNP en-wikipedia-org-2350 233 6 . . . en-wikipedia-org-2350 234 1 p. p. NN en-wikipedia-org-2350 234 2   _SP en-wikipedia-org-2350 234 3 614 614 CD en-wikipedia-org-2350 234 4 . . . en-wikipedia-org-2350 235 1 ISBN ISBN NNP en-wikipedia-org-2350 235 2   _SP en-wikipedia-org-2350 235 3 9781118230732 9781118230732 CD en-wikipedia-org-2350 235 4 . . . en-wikipedia-org-2350 236 1 OCLC oclc NN en-wikipedia-org-2350 236 2   _SP en-wikipedia-org-2350 236 3 950235056 950235056 CD en-wikipedia-org-2350 236 4 . . . en-wikipedia-org-2350 237 1 ^ ^ NNP en-wikipedia-org-2350 237 2 International International NNP en-wikipedia-org-2350 237 3 Bureau Bureau NNP en-wikipedia-org-2350 237 4 of of IN en-wikipedia-org-2350 237 5 Weights Weights NNPS en-wikipedia-org-2350 237 6 and and CC en-wikipedia-org-2350 237 7 Measures Measures NNPS en-wikipedia-org-2350 237 8 ( ( -LRB- en-wikipedia-org-2350 237 9 2019 2019 CD en-wikipedia-org-2350 237 10 - - SYM en-wikipedia-org-2350 237 11 05 05 CD en-wikipedia-org-2350 237 12 - - SYM en-wikipedia-org-2350 237 13 20 20 CD en-wikipedia-org-2350 237 14 ) ) -RRB- en-wikipedia-org-2350 237 15 , , , en-wikipedia-org-2350 237 16 SI SI NNP en-wikipedia-org-2350 237 17 Brochure Brochure NNP en-wikipedia-org-2350 237 18 : : : en-wikipedia-org-2350 237 19 The the DT en-wikipedia-org-2350 237 20 International International NNP en-wikipedia-org-2350 237 21 System System NNP en-wikipedia-org-2350 237 22 of of IN en-wikipedia-org-2350 237 23 Units Units NNP en-wikipedia-org-2350 237 24 ( ( -LRB- en-wikipedia-org-2350 237 25 SI SI NNP en-wikipedia-org-2350 237 26 ) ) -RRB- en-wikipedia-org-2350 237 27 ( ( -LRB- en-wikipedia-org-2350 237 28 PDF PDF NNP en-wikipedia-org-2350 237 29 ) ) -RRB- en-wikipedia-org-2350 237 30 ( ( -LRB- en-wikipedia-org-2350 237 31 9th 9th JJ en-wikipedia-org-2350 237 32 ed ed NN en-wikipedia-org-2350 237 33 . . . en-wikipedia-org-2350 238 1 ) ) -RRB- en-wikipedia-org-2350 238 2 , , , en-wikipedia-org-2350 238 3 ISBN ISBN NNP en-wikipedia-org-2350 238 4   _SP en-wikipedia-org-2350 238 5 978 978 CD en-wikipedia-org-2350 238 6 - - HYPH en-wikipedia-org-2350 238 7 92 92 CD en-wikipedia-org-2350 238 8 - - HYPH en-wikipedia-org-2350 238 9 822 822 CD en-wikipedia-org-2350 238 10 - - HYPH en-wikipedia-org-2350 238 11 2272 2272 CD en-wikipedia-org-2350 238 12 - - HYPH en-wikipedia-org-2350 238 13 0 0 CD en-wikipedia-org-2350 238 14 , , , en-wikipedia-org-2350 238 15 p. p. NN en-wikipedia-org-2350 238 16 15 15 CD en-wikipedia-org-2350 238 17 ^ ^ NNP en-wikipedia-org-2350 238 18 BIPM BIPM NNP en-wikipedia-org-2350 238 19 statement statement NN en-wikipedia-org-2350 238 20 : : : en-wikipedia-org-2350 238 21 Information information NN en-wikipedia-org-2350 238 22 for for IN en-wikipedia-org-2350 238 23 users user NNS en-wikipedia-org-2350 238 24 about about IN en-wikipedia-org-2350 238 25 the the DT en-wikipedia-org-2350 238 26 proposed propose VBN en-wikipedia-org-2350 238 27 revision revision NN en-wikipedia-org-2350 238 28 of of IN en-wikipedia-org-2350 238 29 the the DT en-wikipedia-org-2350 238 30 SI SI NNP en-wikipedia-org-2350 238 31 ( ( -LRB- en-wikipedia-org-2350 238 32 PDF PDF NNP en-wikipedia-org-2350 238 33 ) ) -RRB- en-wikipedia-org-2350 238 34 ^ ^ NN en-wikipedia-org-2350 238 35 " " `` en-wikipedia-org-2350 238 36 Decision Decision NNP en-wikipedia-org-2350 238 37 CIPM/105 CIPM/105 NNP en-wikipedia-org-2350 238 38 - - HYPH en-wikipedia-org-2350 238 39 13 13 CD en-wikipedia-org-2350 238 40 ( ( -LRB- en-wikipedia-org-2350 238 41 October October NNP en-wikipedia-org-2350 238 42 2016 2016 CD en-wikipedia-org-2350 238 43 ) ) -RRB- en-wikipedia-org-2350 238 44 " " '' en-wikipedia-org-2350 238 45 . . . en-wikipedia-org-2350 239 1 The the DT en-wikipedia-org-2350 239 2 day day NN en-wikipedia-org-2350 239 3 is be VBZ en-wikipedia-org-2350 239 4 the the DT en-wikipedia-org-2350 239 5 144th 144th JJ en-wikipedia-org-2350 239 6 anniversary anniversary NN en-wikipedia-org-2350 239 7 of of IN en-wikipedia-org-2350 239 8 the the DT en-wikipedia-org-2350 239 9 Metre Metre NNP en-wikipedia-org-2350 239 10 Convention Convention NNP en-wikipedia-org-2350 239 11 . . . en-wikipedia-org-2350 240 1 ^ ^ NNP en-wikipedia-org-2350 240 2 Derived derive VBN en-wikipedia-org-2350 240 3 from from IN en-wikipedia-org-2350 240 4 ke ke NNP en-wikipedia-org-2350 240 5 = = SYM en-wikipedia-org-2350 240 6 1 1 CD en-wikipedia-org-2350 240 7 / / SYM en-wikipedia-org-2350 240 8 ( ( -LRB- en-wikipedia-org-2350 240 9 4π 4π NNP en-wikipedia-org-2350 240 10 ε0 ε0 NNP en-wikipedia-org-2350 240 11 ) ) -RRB- en-wikipedia-org-2350 240 12 – – : en-wikipedia-org-2350 240 13 " " `` en-wikipedia-org-2350 240 14 2018 2018 CD en-wikipedia-org-2350 240 15 CODATA CODATA NNP en-wikipedia-org-2350 240 16 Value value NN en-wikipedia-org-2350 240 17 : : : en-wikipedia-org-2350 240 18 vacuum vacuum NN en-wikipedia-org-2350 240 19 electric electric JJ en-wikipedia-org-2350 240 20 permittivity permittivity NN en-wikipedia-org-2350 240 21 " " '' en-wikipedia-org-2350 240 22 . . . en-wikipedia-org-2350 241 1 The the DT en-wikipedia-org-2350 241 2 NIST NIST NNP en-wikipedia-org-2350 241 3 Reference Reference NNP en-wikipedia-org-2350 241 4 on on IN en-wikipedia-org-2350 241 5 Constants Constants NNPS en-wikipedia-org-2350 241 6 , , , en-wikipedia-org-2350 241 7 Units Units NNPS en-wikipedia-org-2350 241 8 , , , en-wikipedia-org-2350 241 9 and and CC en-wikipedia-org-2350 241 10 Uncertainty uncertainty NN en-wikipedia-org-2350 241 11 . . . en-wikipedia-org-2350 242 1 NIST NIST NNP en-wikipedia-org-2350 242 2 . . . en-wikipedia-org-2350 243 1 20 20 CD en-wikipedia-org-2350 243 2 May May NNP en-wikipedia-org-2350 243 3 2019 2019 CD en-wikipedia-org-2350 243 4 . . . en-wikipedia-org-2350 244 1 Retrieved Retrieved NNP en-wikipedia-org-2350 244 2 2019 2019 CD en-wikipedia-org-2350 244 3 - - SYM en-wikipedia-org-2350 244 4 05 05 CD en-wikipedia-org-2350 244 5 - - SYM en-wikipedia-org-2350 244 6 20 20 CD en-wikipedia-org-2350 244 7 . . . en-wikipedia-org-2350 245 1 ^ ^ NNP en-wikipedia-org-2350 245 2 a a DT en-wikipedia-org-2350 245 3 b b NNP en-wikipedia-org-2350 245 4 Jackson Jackson NNP en-wikipedia-org-2350 245 5 , , , en-wikipedia-org-2350 245 6 John John NNP en-wikipedia-org-2350 245 7 D. D. NNP en-wikipedia-org-2350 245 8 Classical Classical NNP en-wikipedia-org-2350 245 9 Electrodynamics Electrodynamics NNP en-wikipedia-org-2350 245 10 ( ( -LRB- en-wikipedia-org-2350 245 11 1999 1999 CD en-wikipedia-org-2350 245 12 ) ) -RRB- en-wikipedia-org-2350 245 13 pp pp NNP en-wikipedia-org-2350 245 14 . . . en-wikipedia-org-2350 246 1 784 784 CD en-wikipedia-org-2350 246 2 ISBN ISBN NNP en-wikipedia-org-2350 246 3   _SP en-wikipedia-org-2350 246 4 9788126510948 9788126510948 CD en-wikipedia-org-2350 246 5 ^ ^ NN en-wikipedia-org-2350 246 6 " " `` en-wikipedia-org-2350 246 7 Discussion discussion NN en-wikipedia-org-2350 246 8 on on IN en-wikipedia-org-2350 246 9 physics physics NN en-wikipedia-org-2350 246 10 teaching teaching NN en-wikipedia-org-2350 246 11 innovation innovation NN en-wikipedia-org-2350 246 12 : : : en-wikipedia-org-2350 246 13 Taking take VBG en-wikipedia-org-2350 246 14 Coulomb Coulomb NNP en-wikipedia-org-2350 246 15 's 's POS en-wikipedia-org-2350 246 16 law law NN en-wikipedia-org-2350 246 17 as as IN en-wikipedia-org-2350 246 18 an an DT en-wikipedia-org-2350 246 19 example example NN en-wikipedia-org-2350 246 20 " " '' en-wikipedia-org-2350 246 21 , , , en-wikipedia-org-2350 246 22 Education Education NNP en-wikipedia-org-2350 246 23 Management Management NNP en-wikipedia-org-2350 246 24 and and CC en-wikipedia-org-2350 246 25 Management Management NNP en-wikipedia-org-2350 246 26 Science Science NNP en-wikipedia-org-2350 246 27 , , , en-wikipedia-org-2350 246 28 CRC CRC NNP en-wikipedia-org-2350 246 29 Press Press NNP en-wikipedia-org-2350 246 30 , , , en-wikipedia-org-2350 246 31 pp pp NNP en-wikipedia-org-2350 246 32 . . . en-wikipedia-org-2350 247 1 465–468 465–468 CD en-wikipedia-org-2350 247 2 , , , en-wikipedia-org-2350 247 3 2015 2015 CD en-wikipedia-org-2350 247 4 - - SYM en-wikipedia-org-2350 247 5 07 07 CD en-wikipedia-org-2350 247 6 - - HYPH en-wikipedia-org-2350 247 7 28 28 CD en-wikipedia-org-2350 247 8 , , , en-wikipedia-org-2350 247 9 doi:10.1201 doi:10.1201 NNP en-wikipedia-org-2350 247 10 / / SYM en-wikipedia-org-2350 247 11 b18636 b18636 NNP en-wikipedia-org-2350 247 12 - - HYPH en-wikipedia-org-2350 247 13 105 105 CD en-wikipedia-org-2350 247 14 , , , en-wikipedia-org-2350 247 15 ISBN ISBN NNP en-wikipedia-org-2350 247 16   _SP en-wikipedia-org-2350 247 17 978 978 CD en-wikipedia-org-2350 247 18 - - HYPH en-wikipedia-org-2350 247 19 0 0 CD en-wikipedia-org-2350 247 20 - - HYPH en-wikipedia-org-2350 247 21 429 429 CD en-wikipedia-org-2350 247 22 - - HYPH en-wikipedia-org-2350 247 23 22704 22704 CD en-wikipedia-org-2350 247 24 - - HYPH en-wikipedia-org-2350 247 25 2 2 CD en-wikipedia-org-2350 247 26 , , , en-wikipedia-org-2350 247 27 retrieved retrieve VBD en-wikipedia-org-2350 247 28 2020 2020 CD en-wikipedia-org-2350 247 29 - - SYM en-wikipedia-org-2350 247 30 09 09 CD en-wikipedia-org-2350 247 31 - - HYPH en-wikipedia-org-2350 247 32 24 24 CD en-wikipedia-org-2350 247 33 ^ ^ . en-wikipedia-org-2350 247 34 See see VB en-wikipedia-org-2350 247 35 , , , en-wikipedia-org-2350 247 36 for for IN en-wikipedia-org-2350 247 37 example example NN en-wikipedia-org-2350 247 38 , , , en-wikipedia-org-2350 247 39 Griffiths Griffiths NNP en-wikipedia-org-2350 247 40 , , , en-wikipedia-org-2350 247 41 David David NNP en-wikipedia-org-2350 247 42 J. J. NNP en-wikipedia-org-2350 248 1 ( ( -LRB- en-wikipedia-org-2350 248 2 2013 2013 CD en-wikipedia-org-2350 248 3 ) ) -RRB- en-wikipedia-org-2350 248 4 . . . en-wikipedia-org-2350 249 1 Introduction introduction NN en-wikipedia-org-2350 249 2 to to IN en-wikipedia-org-2350 249 3 Electrodynamics Electrodynamics NNP en-wikipedia-org-2350 249 4 ( ( -LRB- en-wikipedia-org-2350 249 5 4th 4th NNP en-wikipedia-org-2350 249 6 ed ed NNP en-wikipedia-org-2350 249 7 . . . en-wikipedia-org-2350 249 8 ) ) -RRB- en-wikipedia-org-2350 249 9 . . . en-wikipedia-org-2350 250 1 Prentice Prentice NNP en-wikipedia-org-2350 250 2 Hall Hall NNP en-wikipedia-org-2350 250 3 . . . en-wikipedia-org-2350 251 1 p. p. NN en-wikipedia-org-2350 251 2   _SP en-wikipedia-org-2350 251 3 50 50 CD en-wikipedia-org-2350 251 4 . . . en-wikipedia-org-2350 252 1 ^ ^ NNP en-wikipedia-org-2350 252 2 a a DT en-wikipedia-org-2350 252 3 b b NNP en-wikipedia-org-2350 252 4 Griffiths Griffiths NNP en-wikipedia-org-2350 252 5 , , , en-wikipedia-org-2350 252 6 David David NNP en-wikipedia-org-2350 252 7 J. J. NNP en-wikipedia-org-2350 253 1 ( ( -LRB- en-wikipedia-org-2350 253 2 16 16 CD en-wikipedia-org-2350 253 3 August August NNP en-wikipedia-org-2350 253 4 2018 2018 CD en-wikipedia-org-2350 253 5 ) ) -RRB- en-wikipedia-org-2350 253 6 . . . en-wikipedia-org-2350 254 1 Introduction introduction NN en-wikipedia-org-2350 254 2 to to IN en-wikipedia-org-2350 254 3 quantum quantum VB en-wikipedia-org-2350 254 4 mechanics mechanic NNS en-wikipedia-org-2350 254 5 ( ( -LRB- en-wikipedia-org-2350 254 6 Third Third NNP en-wikipedia-org-2350 254 7 ed ed NNP en-wikipedia-org-2350 254 8 . . . en-wikipedia-org-2350 254 9 ) ) -RRB- en-wikipedia-org-2350 254 10 . . . en-wikipedia-org-2350 255 1 Cambridge Cambridge NNP en-wikipedia-org-2350 255 2 , , , en-wikipedia-org-2350 255 3 United United NNP en-wikipedia-org-2350 255 4 Kingdom Kingdom NNP en-wikipedia-org-2350 255 5 . . . en-wikipedia-org-2350 256 1 ISBN ISBN NNP en-wikipedia-org-2350 256 2   _SP en-wikipedia-org-2350 256 3 978 978 CD en-wikipedia-org-2350 256 4 - - HYPH en-wikipedia-org-2350 256 5 1 1 CD en-wikipedia-org-2350 256 6 - - HYPH en-wikipedia-org-2350 256 7 107 107 CD en-wikipedia-org-2350 256 8 - - HYPH en-wikipedia-org-2350 256 9 18963 18963 CD en-wikipedia-org-2350 256 10 - - SYM en-wikipedia-org-2350 256 11 8 8 CD en-wikipedia-org-2350 256 12 . . . en-wikipedia-org-2350 257 1 ^ ^ FW en-wikipedia-org-2350 257 2 " " `` en-wikipedia-org-2350 257 3 Quantum Quantum NNP en-wikipedia-org-2350 257 4 Field Field NNP en-wikipedia-org-2350 257 5 Theory theory NN en-wikipedia-org-2350 257 6 I i NN en-wikipedia-org-2350 257 7 + + CC en-wikipedia-org-2350 257 8 II ii NN en-wikipedia-org-2350 257 9 " " '' en-wikipedia-org-2350 257 10 ( ( -LRB- en-wikipedia-org-2350 257 11 PDF PDF NNP en-wikipedia-org-2350 257 12 ) ) -RRB- en-wikipedia-org-2350 257 13 . . . en-wikipedia-org-2350 258 1 Institute Institute NNP en-wikipedia-org-2350 258 2 for for IN en-wikipedia-org-2350 258 3 Theoretical Theoretical NNP en-wikipedia-org-2350 258 4 Physics Physics NNP en-wikipedia-org-2350 258 5 , , , en-wikipedia-org-2350 258 6 Heidelberg Heidelberg NNP en-wikipedia-org-2350 258 7 University University NNP en-wikipedia-org-2350 258 8 . . . en-wikipedia-org-2350 259 1 ^ ^ NNP en-wikipedia-org-2350 259 2 Baym Baym NNP en-wikipedia-org-2350 259 3 , , , en-wikipedia-org-2350 259 4 Gordon Gordon NNP en-wikipedia-org-2350 259 5 . . . en-wikipedia-org-2350 260 1 Lectures lecture NNS en-wikipedia-org-2350 260 2 on on IN en-wikipedia-org-2350 260 3 quantum quantum JJ en-wikipedia-org-2350 260 4 mechanics mechanic NNS en-wikipedia-org-2350 260 5 . . . en-wikipedia-org-2350 261 1 Boca Boca NNP en-wikipedia-org-2350 261 2 Raton Raton NNP en-wikipedia-org-2350 261 3 . . . en-wikipedia-org-2350 262 1 ISBN ISBN NNP en-wikipedia-org-2350 262 2   _SP en-wikipedia-org-2350 262 3 978 978 CD en-wikipedia-org-2350 262 4 - - HYPH en-wikipedia-org-2350 262 5 0 0 CD en-wikipedia-org-2350 262 6 - - HYPH en-wikipedia-org-2350 262 7 429 429 CD en-wikipedia-org-2350 262 8 - - HYPH en-wikipedia-org-2350 262 9 49926 49926 CD en-wikipedia-org-2350 262 10 - - SYM en-wikipedia-org-2350 262 11 5 5 CD en-wikipedia-org-2350 262 12 . . . en-wikipedia-org-2350 263 1 OCLC oclc NN en-wikipedia-org-2350 263 2   _SP en-wikipedia-org-2350 263 3 1028553174 1028553174 CD en-wikipedia-org-2350 263 4 . . . en-wikipedia-org-2350 264 1 ^ ^ NNP en-wikipedia-org-2350 264 2 Gould Gould NNP en-wikipedia-org-2350 264 3 , , , en-wikipedia-org-2350 264 4 Robert Robert NNP en-wikipedia-org-2350 264 5 J. J. NNP en-wikipedia-org-2350 265 1 ( ( -LRB- en-wikipedia-org-2350 265 2 Robert Robert NNP en-wikipedia-org-2350 265 3 Joseph Joseph NNP en-wikipedia-org-2350 265 4 ) ) -RRB- en-wikipedia-org-2350 265 5 , , , en-wikipedia-org-2350 265 6 1935- 1935- CD en-wikipedia-org-2350 265 7 ( ( -LRB- en-wikipedia-org-2350 265 8 21 21 CD en-wikipedia-org-2350 265 9 July July NNP en-wikipedia-org-2350 265 10 2020 2020 CD en-wikipedia-org-2350 265 11 ) ) -RRB- en-wikipedia-org-2350 265 12 . . . en-wikipedia-org-2350 266 1 Electromagnetic electromagnetic JJ en-wikipedia-org-2350 266 2 processes process NNS en-wikipedia-org-2350 266 3 . . . en-wikipedia-org-2350 267 1 Princeton Princeton NNP en-wikipedia-org-2350 267 2 , , , en-wikipedia-org-2350 267 3 N.J. New Jersey NNP en-wikipedia-org-2350 267 4 ISBN ISBN NNP en-wikipedia-org-2350 267 5   _SP en-wikipedia-org-2350 267 6 978 978 CD en-wikipedia-org-2350 267 7 - - HYPH en-wikipedia-org-2350 267 8 0 0 CD en-wikipedia-org-2350 267 9 - - HYPH en-wikipedia-org-2350 267 10 691 691 CD en-wikipedia-org-2350 267 11 - - HYPH en-wikipedia-org-2350 267 12 21584 21584 CD en-wikipedia-org-2350 267 13 - - SYM en-wikipedia-org-2350 267 14 6 6 CD en-wikipedia-org-2350 267 15 . . . en-wikipedia-org-2350 268 1 OCLC oclc NN en-wikipedia-org-2350 268 2   _SP en-wikipedia-org-2350 268 3 1176566442.CS1 1176566442.cs1 CD en-wikipedia-org-2350 268 4 maint maint NN en-wikipedia-org-2350 268 5 : : : en-wikipedia-org-2350 268 6 multiple multiple JJ en-wikipedia-org-2350 268 7 names name NNS en-wikipedia-org-2350 268 8 : : : en-wikipedia-org-2350 268 9 authors author NNS en-wikipedia-org-2350 268 10 list list NN en-wikipedia-org-2350 268 11 ( ( -LRB- en-wikipedia-org-2350 268 12 link link VB en-wikipedia-org-2350 268 13 ) ) -RRB- en-wikipedia-org-2350 268 14 Related Related NNP en-wikipedia-org-2350 268 15 reading[edit reading[edit LS en-wikipedia-org-2350 268 16 ] ] -RRB- en-wikipedia-org-2350 268 17 Coulomb Coulomb NNP en-wikipedia-org-2350 268 18 , , , en-wikipedia-org-2350 268 19 Charles Charles NNP en-wikipedia-org-2350 268 20 Augustin Augustin NNP en-wikipedia-org-2350 268 21 ( ( -LRB- en-wikipedia-org-2350 268 22 1788 1788 CD en-wikipedia-org-2350 268 23 ) ) -RRB- en-wikipedia-org-2350 268 24 [ [ -LRB- en-wikipedia-org-2350 268 25 1785 1785 CD en-wikipedia-org-2350 268 26 ] ] -RRB- en-wikipedia-org-2350 268 27 . . . en-wikipedia-org-2350 269 1 " " `` en-wikipedia-org-2350 269 2 Premier premier NN en-wikipedia-org-2350 269 3 mémoire mémoire VBP en-wikipedia-org-2350 269 4 sur sur FW en-wikipedia-org-2350 269 5 l'électricité l'électricité NNP en-wikipedia-org-2350 269 6 et et NNP en-wikipedia-org-2350 269 7 le le NNP en-wikipedia-org-2350 269 8 magnétisme magnétisme NNP en-wikipedia-org-2350 269 9 " " '' en-wikipedia-org-2350 269 10 . . . en-wikipedia-org-2350 270 1 Histoire Histoire NNP en-wikipedia-org-2350 270 2 de de NNP en-wikipedia-org-2350 270 3 l'Académie l'Académie NNP en-wikipedia-org-2350 270 4 Royale Royale NNP en-wikipedia-org-2350 270 5 des des NNP en-wikipedia-org-2350 270 6 Sciences Sciences NNPS en-wikipedia-org-2350 270 7 . . . en-wikipedia-org-2350 271 1 Imprimerie Imprimerie NNP en-wikipedia-org-2350 271 2 Royale Royale NNP en-wikipedia-org-2350 271 3 . . . en-wikipedia-org-2350 272 1 pp pp NNP en-wikipedia-org-2350 272 2 . . . en-wikipedia-org-2350 273 1 569–577 569–577 CD en-wikipedia-org-2350 273 2 . . . en-wikipedia-org-2350 274 1 Coulomb Coulomb NNP en-wikipedia-org-2350 274 2 , , , en-wikipedia-org-2350 274 3 Charles Charles NNP en-wikipedia-org-2350 274 4 Augustin Augustin NNP en-wikipedia-org-2350 274 5 ( ( -LRB- en-wikipedia-org-2350 274 6 1788 1788 CD en-wikipedia-org-2350 274 7 ) ) -RRB- en-wikipedia-org-2350 274 8 [ [ -LRB- en-wikipedia-org-2350 274 9 1785 1785 CD en-wikipedia-org-2350 274 10 ] ] -RRB- en-wikipedia-org-2350 274 11 . . . en-wikipedia-org-2350 275 1 " " `` en-wikipedia-org-2350 275 2 Second second JJ en-wikipedia-org-2350 275 3 mémoire mémoire NN en-wikipedia-org-2350 275 4 sur sur FW en-wikipedia-org-2350 275 5 l'électricité l'électricité NNP en-wikipedia-org-2350 275 6 et et NNP en-wikipedia-org-2350 275 7 le le NNP en-wikipedia-org-2350 275 8 magnétisme magnétisme NNP en-wikipedia-org-2350 275 9 " " '' en-wikipedia-org-2350 275 10 . . . en-wikipedia-org-2350 276 1 Histoire Histoire NNP en-wikipedia-org-2350 276 2 de de NNP en-wikipedia-org-2350 276 3 l'Académie l'Académie NNP en-wikipedia-org-2350 276 4 Royale Royale NNP en-wikipedia-org-2350 276 5 des des NNP en-wikipedia-org-2350 276 6 Sciences Sciences NNPS en-wikipedia-org-2350 276 7 . . . en-wikipedia-org-2350 277 1 Imprimerie Imprimerie NNP en-wikipedia-org-2350 277 2 Royale Royale NNP en-wikipedia-org-2350 277 3 . . . en-wikipedia-org-2350 278 1 pp pp NNP en-wikipedia-org-2350 278 2 . . . en-wikipedia-org-2350 279 1 578–611 578–611 CD en-wikipedia-org-2350 279 2 . . . en-wikipedia-org-2350 280 1 Coulomb Coulomb NNP en-wikipedia-org-2350 280 2 , , , en-wikipedia-org-2350 280 3 Charles Charles NNP en-wikipedia-org-2350 280 4 Augustin Augustin NNP en-wikipedia-org-2350 280 5 ( ( -LRB- en-wikipedia-org-2350 280 6 1788 1788 CD en-wikipedia-org-2350 280 7 ) ) -RRB- en-wikipedia-org-2350 280 8 [ [ -LRB- en-wikipedia-org-2350 280 9 1785 1785 CD en-wikipedia-org-2350 280 10 ] ] -RRB- en-wikipedia-org-2350 280 11 . . . en-wikipedia-org-2350 281 1 " " `` en-wikipedia-org-2350 281 2 Troisième Troisième NNP en-wikipedia-org-2350 281 3 mémoire mémoire VBP en-wikipedia-org-2350 281 4 sur sur FW en-wikipedia-org-2350 281 5 l'électricité l'électricité NNP en-wikipedia-org-2350 281 6 et et NNP en-wikipedia-org-2350 281 7 le le NNP en-wikipedia-org-2350 281 8 magnétisme magnétisme NNP en-wikipedia-org-2350 281 9 " " '' en-wikipedia-org-2350 281 10 . . . en-wikipedia-org-2350 282 1 Histoire Histoire NNP en-wikipedia-org-2350 282 2 de de NNP en-wikipedia-org-2350 282 3 l'Académie l'Académie NNP en-wikipedia-org-2350 282 4 Royale Royale NNP en-wikipedia-org-2350 282 5 des des NNP en-wikipedia-org-2350 282 6 Sciences Sciences NNPS en-wikipedia-org-2350 282 7 . . . en-wikipedia-org-2350 283 1 Imprimerie Imprimerie NNP en-wikipedia-org-2350 283 2 Royale Royale NNP en-wikipedia-org-2350 283 3 . . . en-wikipedia-org-2350 284 1 pp pp NNP en-wikipedia-org-2350 284 2 . . . en-wikipedia-org-2350 285 1 612–638 612–638 CD en-wikipedia-org-2350 285 2 . . . en-wikipedia-org-2350 286 1 Griffiths Griffiths NNP en-wikipedia-org-2350 286 2 , , , en-wikipedia-org-2350 286 3 David David NNP en-wikipedia-org-2350 286 4 J. J. NNP en-wikipedia-org-2350 287 1 ( ( -LRB- en-wikipedia-org-2350 287 2 1999 1999 CD en-wikipedia-org-2350 287 3 ) ) -RRB- en-wikipedia-org-2350 287 4 . . . en-wikipedia-org-2350 288 1 Introduction introduction NN en-wikipedia-org-2350 288 2 to to IN en-wikipedia-org-2350 288 3 Electrodynamics Electrodynamics NNP en-wikipedia-org-2350 288 4 ( ( -LRB- en-wikipedia-org-2350 288 5 3rd 3rd NNP en-wikipedia-org-2350 288 6 ed ed NNP en-wikipedia-org-2350 288 7 . . . en-wikipedia-org-2350 288 8 ) ) -RRB- en-wikipedia-org-2350 288 9 . . . en-wikipedia-org-2350 289 1 Prentice Prentice NNP en-wikipedia-org-2350 289 2 Hall Hall NNP en-wikipedia-org-2350 289 3 . . . en-wikipedia-org-2350 290 1 ISBN ISBN NNP en-wikipedia-org-2350 290 2   _SP en-wikipedia-org-2350 290 3 978 978 CD en-wikipedia-org-2350 290 4 - - HYPH en-wikipedia-org-2350 290 5 0 0 CD en-wikipedia-org-2350 290 6 - - HYPH en-wikipedia-org-2350 290 7 13 13 CD en-wikipedia-org-2350 290 8 - - HYPH en-wikipedia-org-2350 290 9 805326 805326 CD en-wikipedia-org-2350 290 10 - - HYPH en-wikipedia-org-2350 290 11 0 0 CD en-wikipedia-org-2350 290 12 . . . en-wikipedia-org-2350 291 1 Tamm Tamm NNP en-wikipedia-org-2350 291 2 , , , en-wikipedia-org-2350 291 3 Igor Igor NNP en-wikipedia-org-2350 291 4 E. E. NNP en-wikipedia-org-2350 291 5 ( ( -LRB- en-wikipedia-org-2350 291 6 1979 1979 CD en-wikipedia-org-2350 291 7 ) ) -RRB- en-wikipedia-org-2350 291 8 [ [ -LRB- en-wikipedia-org-2350 291 9 1976 1976 CD en-wikipedia-org-2350 291 10 ] ] -RRB- en-wikipedia-org-2350 291 11 . . . en-wikipedia-org-2350 292 1 Fundamentals fundamental NNS en-wikipedia-org-2350 292 2 of of IN en-wikipedia-org-2350 292 3 the the DT en-wikipedia-org-2350 292 4 Theory Theory NNP en-wikipedia-org-2350 292 5 of of IN en-wikipedia-org-2350 292 6 Electricity Electricity NNP en-wikipedia-org-2350 292 7 ( ( -LRB- en-wikipedia-org-2350 292 8 9th 9th NNP en-wikipedia-org-2350 292 9 ed ed NNP en-wikipedia-org-2350 292 10 . . . en-wikipedia-org-2350 292 11 ) ) -RRB- en-wikipedia-org-2350 292 12 . . . en-wikipedia-org-2350 293 1 Moscow Moscow NNP en-wikipedia-org-2350 293 2 : : : en-wikipedia-org-2350 293 3 Mir Mir NNP en-wikipedia-org-2350 293 4 . . . en-wikipedia-org-2350 294 1 pp pp NNP en-wikipedia-org-2350 294 2 . . . en-wikipedia-org-2350 295 1 23–27 23–27 LS en-wikipedia-org-2350 295 2 . . . en-wikipedia-org-2350 296 1 Tipler Tipler NNP en-wikipedia-org-2350 296 2 , , , en-wikipedia-org-2350 296 3 Paul Paul NNP en-wikipedia-org-2350 296 4 A. a. NN en-wikipedia-org-2350 296 5 ; ; : en-wikipedia-org-2350 296 6 Mosca Mosca NNP en-wikipedia-org-2350 296 7 , , , en-wikipedia-org-2350 296 8 Gene Gene NNP en-wikipedia-org-2350 296 9 ( ( -LRB- en-wikipedia-org-2350 296 10 2008 2008 CD en-wikipedia-org-2350 296 11 ) ) -RRB- en-wikipedia-org-2350 296 12 . . . en-wikipedia-org-2350 297 1 Physics Physics NNP en-wikipedia-org-2350 297 2 for for IN en-wikipedia-org-2350 297 3 Scientists Scientists NNPS en-wikipedia-org-2350 297 4 and and CC en-wikipedia-org-2350 297 5 Engineers Engineers NNPS en-wikipedia-org-2350 297 6 ( ( -LRB- en-wikipedia-org-2350 297 7 6th 6th NNP en-wikipedia-org-2350 297 8 ed ed NNP en-wikipedia-org-2350 297 9 . . . en-wikipedia-org-2350 297 10 ) ) -RRB- en-wikipedia-org-2350 297 11 . . . en-wikipedia-org-2350 298 1 New New NNP en-wikipedia-org-2350 298 2 York York NNP en-wikipedia-org-2350 298 3 : : : en-wikipedia-org-2350 298 4 W. W. NNP en-wikipedia-org-2350 298 5 H. H. NNP en-wikipedia-org-2350 298 6 Freeman Freeman NNP en-wikipedia-org-2350 298 7 and and CC en-wikipedia-org-2350 298 8 Company Company NNP en-wikipedia-org-2350 298 9 . . . en-wikipedia-org-2350 299 1 ISBN ISBN NNP en-wikipedia-org-2350 299 2   _SP en-wikipedia-org-2350 299 3 978 978 CD en-wikipedia-org-2350 299 4 - - HYPH en-wikipedia-org-2350 299 5 0 0 CD en-wikipedia-org-2350 299 6 - - HYPH en-wikipedia-org-2350 299 7 7167 7167 CD en-wikipedia-org-2350 299 8 - - HYPH en-wikipedia-org-2350 299 9 8964 8964 CD en-wikipedia-org-2350 299 10 - - HYPH en-wikipedia-org-2350 299 11 2 2 CD en-wikipedia-org-2350 299 12 . . . en-wikipedia-org-2350 300 1 LCCN LCCN NNP en-wikipedia-org-2350 300 2   _SP en-wikipedia-org-2350 300 3 2007010418 2007010418 CD en-wikipedia-org-2350 300 4 . . . en-wikipedia-org-2350 301 1 Young Young NNP en-wikipedia-org-2350 301 2 , , , en-wikipedia-org-2350 301 3 Hugh Hugh NNP en-wikipedia-org-2350 301 4 D. D. NNP en-wikipedia-org-2350 301 5 ; ; : en-wikipedia-org-2350 301 6 Freedman Freedman NNP en-wikipedia-org-2350 301 7 , , , en-wikipedia-org-2350 301 8 Roger Roger NNP en-wikipedia-org-2350 301 9 A. A. NNP en-wikipedia-org-2350 302 1 ( ( -LRB- en-wikipedia-org-2350 302 2 2010 2010 CD en-wikipedia-org-2350 302 3 ) ) -RRB- en-wikipedia-org-2350 302 4 . . . en-wikipedia-org-2350 303 1 Sears Sears NNP en-wikipedia-org-2350 303 2 and and CC en-wikipedia-org-2350 303 3 Zemansky Zemansky NNP en-wikipedia-org-2350 303 4 's 's POS en-wikipedia-org-2350 303 5 University University NNP en-wikipedia-org-2350 303 6 Physics Physics NNP en-wikipedia-org-2350 303 7   _SP en-wikipedia-org-2350 303 8 : : : en-wikipedia-org-2350 303 9 With with IN en-wikipedia-org-2350 303 10 Modern Modern NNP en-wikipedia-org-2350 303 11 Physics Physics NNP en-wikipedia-org-2350 303 12 ( ( -LRB- en-wikipedia-org-2350 303 13 13th 13th NNP en-wikipedia-org-2350 303 14 ed ed NNP en-wikipedia-org-2350 303 15 . . . en-wikipedia-org-2350 303 16 ) ) -RRB- en-wikipedia-org-2350 303 17 . . . en-wikipedia-org-2350 304 1 Addison Addison NNP en-wikipedia-org-2350 304 2 - - HYPH en-wikipedia-org-2350 304 3 Wesley Wesley NNP en-wikipedia-org-2350 304 4 ( ( -LRB- en-wikipedia-org-2350 304 5 Pearson Pearson NNP en-wikipedia-org-2350 304 6 ) ) -RRB- en-wikipedia-org-2350 304 7 . . . en-wikipedia-org-2350 305 1 ISBN ISBN NNP en-wikipedia-org-2350 305 2   _SP en-wikipedia-org-2350 305 3 978 978 CD en-wikipedia-org-2350 305 4 - - HYPH en-wikipedia-org-2350 305 5 0 0 CD en-wikipedia-org-2350 305 6 - - HYPH en-wikipedia-org-2350 305 7 321 321 CD en-wikipedia-org-2350 305 8 - - HYPH en-wikipedia-org-2350 305 9 69686 69686 CD en-wikipedia-org-2350 305 10 - - HYPH en-wikipedia-org-2350 305 11 1 1 CD en-wikipedia-org-2350 305 12 . . . en-wikipedia-org-2350 306 1 External external JJ en-wikipedia-org-2350 306 2 links[edit links[edit NFP en-wikipedia-org-2350 306 3 ] ] -RRB- en-wikipedia-org-2350 306 4 Coulomb Coulomb NNP en-wikipedia-org-2350 306 5 's 's POS en-wikipedia-org-2350 306 6 Law Law NNP en-wikipedia-org-2350 306 7 on on IN en-wikipedia-org-2350 306 8 Project Project NNP en-wikipedia-org-2350 306 9 PHYSNET PHYSNET NNP en-wikipedia-org-2350 306 10 Electricity Electricity NNP en-wikipedia-org-2350 306 11 and and CC en-wikipedia-org-2350 306 12 the the DT en-wikipedia-org-2350 306 13 Atom atom NN en-wikipedia-org-2350 306 14 — — : en-wikipedia-org-2350 306 15 a a DT en-wikipedia-org-2350 306 16 chapter chapter NN en-wikipedia-org-2350 306 17 from from IN en-wikipedia-org-2350 306 18 an an DT en-wikipedia-org-2350 306 19 online online JJ en-wikipedia-org-2350 306 20 textbook textbook NN en-wikipedia-org-2350 306 21 A a DT en-wikipedia-org-2350 306 22 maze maze NN en-wikipedia-org-2350 306 23 game game NN en-wikipedia-org-2350 306 24 for for IN en-wikipedia-org-2350 306 25 teaching teach VBG en-wikipedia-org-2350 306 26 Coulomb Coulomb NNP en-wikipedia-org-2350 306 27 's 's POS en-wikipedia-org-2350 306 28 Law Law NNP en-wikipedia-org-2350 306 29 — — : en-wikipedia-org-2350 306 30 a a DT en-wikipedia-org-2350 306 31 game game NN en-wikipedia-org-2350 306 32 created create VBN en-wikipedia-org-2350 306 33 by by IN en-wikipedia-org-2350 306 34 the the DT en-wikipedia-org-2350 306 35 Molecular Molecular NNP en-wikipedia-org-2350 306 36 Workbench Workbench NNP en-wikipedia-org-2350 306 37 software software NN en-wikipedia-org-2350 306 38 Electric Electric NNP en-wikipedia-org-2350 306 39 Charges Charges NNPS en-wikipedia-org-2350 306 40 , , , en-wikipedia-org-2350 306 41 Polarization Polarization NNP en-wikipedia-org-2350 306 42 , , , en-wikipedia-org-2350 306 43 Electric Electric NNP en-wikipedia-org-2350 306 44 Force Force NNP en-wikipedia-org-2350 306 45 , , , en-wikipedia-org-2350 306 46 Coulomb Coulomb NNP en-wikipedia-org-2350 306 47 's 's POS en-wikipedia-org-2350 306 48 Law Law NNP en-wikipedia-org-2350 306 49 Walter Walter NNP en-wikipedia-org-2350 306 50 Lewin Lewin NNP en-wikipedia-org-2350 306 51 , , , en-wikipedia-org-2350 306 52 8.02 8.02 CD en-wikipedia-org-2350 306 53 Electricity Electricity NNP en-wikipedia-org-2350 306 54 and and CC en-wikipedia-org-2350 306 55 Magnetism Magnetism NNP en-wikipedia-org-2350 306 56 , , , en-wikipedia-org-2350 306 57 Spring Spring NNP en-wikipedia-org-2350 306 58 2002 2002 CD en-wikipedia-org-2350 306 59 : : : en-wikipedia-org-2350 306 60 Lecture lecture NN en-wikipedia-org-2350 306 61 1 1 CD en-wikipedia-org-2350 306 62 ( ( -LRB- en-wikipedia-org-2350 306 63 video video NN en-wikipedia-org-2350 306 64 ) ) -RRB- en-wikipedia-org-2350 306 65 . . . en-wikipedia-org-2350 307 1 MIT MIT NNP en-wikipedia-org-2350 307 2 OpenCourseWare OpenCourseWare NNP en-wikipedia-org-2350 307 3 . . . en-wikipedia-org-2350 308 1 License license NN en-wikipedia-org-2350 308 2 : : : en-wikipedia-org-2350 308 3 Creative Creative NNP en-wikipedia-org-2350 308 4 Commons Commons NNP en-wikipedia-org-2350 308 5 Attribution Attribution NNP en-wikipedia-org-2350 308 6 - - HYPH en-wikipedia-org-2350 308 7 Noncommercial Noncommercial NNP en-wikipedia-org-2350 308 8 - - HYPH en-wikipedia-org-2350 308 9 Share share NN en-wikipedia-org-2350 308 10 Alike alike RB en-wikipedia-org-2350 308 11 . . . en-wikipedia-org-2350 309 1 Retrieved retrieve VBN en-wikipedia-org-2350 309 2 from from IN en-wikipedia-org-2350 309 3 " " `` en-wikipedia-org-2350 309 4 https://en.wikipedia.org/w/index.php?title=Coulomb%27s_law&oldid=993259141 https://en.wikipedia.org/w/index.php?title=coulomb%27s_law&oldid=993259141 JJ en-wikipedia-org-2350 309 5 " " '' en-wikipedia-org-2350 309 6 Categories category NNS en-wikipedia-org-2350 309 7 : : : en-wikipedia-org-2350 309 8 Electromagnetism Electromagnetism NNP en-wikipedia-org-2350 309 9 Electrostatics Electrostatics NNP en-wikipedia-org-2350 309 10 Force Force NNP en-wikipedia-org-2350 309 11 Scientific Scientific NNP en-wikipedia-org-2350 309 12 laws law NNS en-wikipedia-org-2350 309 13 Hidden hide VBN en-wikipedia-org-2350 309 14 categories category NNS en-wikipedia-org-2350 309 15 : : : en-wikipedia-org-2350 309 16 CS1 cs1 NN en-wikipedia-org-2350 309 17 maint maint NN en-wikipedia-org-2350 309 18 : : : en-wikipedia-org-2350 309 19 multiple multiple JJ en-wikipedia-org-2350 309 20 names name NNS en-wikipedia-org-2350 309 21 : : : en-wikipedia-org-2350 309 22 authors author NNS en-wikipedia-org-2350 309 23 list list VBP en-wikipedia-org-2350 309 24 CS1 CS1 NNP en-wikipedia-org-2350 309 25 Latin Latin NNP en-wikipedia-org-2350 309 26 - - HYPH en-wikipedia-org-2350 309 27 language language NN en-wikipedia-org-2350 309 28 sources source NNS en-wikipedia-org-2350 309 29 ( ( -LRB- en-wikipedia-org-2350 309 30 la la NNP en-wikipedia-org-2350 309 31 ) ) -RRB- en-wikipedia-org-2350 309 32 Articles article NNS en-wikipedia-org-2350 309 33 needing need VBG en-wikipedia-org-2350 309 34 cleanup cleanup NN en-wikipedia-org-2350 309 35 from from IN en-wikipedia-org-2350 309 36 March March NNP en-wikipedia-org-2350 309 37 2020 2020 CD en-wikipedia-org-2350 309 38 All all DT en-wikipedia-org-2350 309 39 pages page NNS en-wikipedia-org-2350 309 40 needing need VBG en-wikipedia-org-2350 309 41 cleanup cleanup NN en-wikipedia-org-2350 309 42 Cleanup Cleanup NNP en-wikipedia-org-2350 309 43 tagged tag VBD en-wikipedia-org-2350 309 44 articles article NNS en-wikipedia-org-2350 309 45 with with IN en-wikipedia-org-2350 309 46 a a DT en-wikipedia-org-2350 309 47 reason reason NN en-wikipedia-org-2350 309 48 field field NN en-wikipedia-org-2350 309 49 from from IN en-wikipedia-org-2350 309 50 March March NNP en-wikipedia-org-2350 309 51 2020 2020 CD en-wikipedia-org-2350 309 52 Wikipedia Wikipedia NNP en-wikipedia-org-2350 309 53 pages page NNS en-wikipedia-org-2350 309 54 needing need VBG en-wikipedia-org-2350 309 55 cleanup cleanup NN en-wikipedia-org-2350 309 56 from from IN en-wikipedia-org-2350 309 57 March March NNP en-wikipedia-org-2350 309 58 2020 2020 CD en-wikipedia-org-2350 309 59 Use Use NNP en-wikipedia-org-2350 309 60 American American NNP en-wikipedia-org-2350 309 61 English English NNP en-wikipedia-org-2350 309 62 from from IN en-wikipedia-org-2350 309 63 August August NNP en-wikipedia-org-2350 309 64 2019 2019 CD en-wikipedia-org-2350 309 65 All all DT en-wikipedia-org-2350 309 66 Wikipedia Wikipedia NNP en-wikipedia-org-2350 309 67 articles article NNS en-wikipedia-org-2350 309 68 written write VBN en-wikipedia-org-2350 309 69 in in IN en-wikipedia-org-2350 309 70 American American NNP en-wikipedia-org-2350 309 71 English English NNP en-wikipedia-org-2350 309 72 Articles Articles NNPS en-wikipedia-org-2350 309 73 with with IN en-wikipedia-org-2350 309 74 short short JJ en-wikipedia-org-2350 309 75 description description NN en-wikipedia-org-2350 309 76 Short short JJ en-wikipedia-org-2350 309 77 description description NN en-wikipedia-org-2350 309 78 is be VBZ en-wikipedia-org-2350 309 79 different different JJ en-wikipedia-org-2350 309 80 from from IN en-wikipedia-org-2350 309 81 Wikidata Wikidata NNP en-wikipedia-org-2350 309 82 Articles Articles NNPS en-wikipedia-org-2350 309 83 containing contain VBG en-wikipedia-org-2350 309 84 Ancient Ancient NNP en-wikipedia-org-2350 309 85 Greek Greek NNP en-wikipedia-org-2350 309 86 ( ( -LRB- en-wikipedia-org-2350 309 87 to to TO en-wikipedia-org-2350 309 88 1453)-language 1453)-language VB en-wikipedia-org-2350 309 89 text text NN en-wikipedia-org-2350 309 90 Wikipedia wikipedia NN en-wikipedia-org-2350 309 91 articles article NNS en-wikipedia-org-2350 309 92 that that WDT en-wikipedia-org-2350 309 93 are be VBP en-wikipedia-org-2350 309 94 too too RB en-wikipedia-org-2350 309 95 technical technical JJ en-wikipedia-org-2350 309 96 from from IN en-wikipedia-org-2350 309 97 October October NNP en-wikipedia-org-2350 309 98 2020 2020 CD en-wikipedia-org-2350 309 99 All all DT en-wikipedia-org-2350 309 100 articles article NNS en-wikipedia-org-2350 309 101 that that WDT en-wikipedia-org-2350 309 102 are be VBP en-wikipedia-org-2350 309 103 too too RB en-wikipedia-org-2350 309 104 technical technical JJ en-wikipedia-org-2350 309 105 Wikipedia Wikipedia NNP en-wikipedia-org-2350 309 106 articles article NNS en-wikipedia-org-2350 309 107 that that WDT en-wikipedia-org-2350 309 108 are be VBP en-wikipedia-org-2350 309 109 excessively excessively RB en-wikipedia-org-2350 309 110 detailed detail VBN en-wikipedia-org-2350 309 111 from from IN en-wikipedia-org-2350 309 112 October October NNP en-wikipedia-org-2350 309 113 2020 2020 CD en-wikipedia-org-2350 309 114 All all DT en-wikipedia-org-2350 309 115 articles article NNS en-wikipedia-org-2350 309 116 that that WDT en-wikipedia-org-2350 309 117 are be VBP en-wikipedia-org-2350 309 118 excessively excessively RB en-wikipedia-org-2350 309 119 detailed detailed JJ en-wikipedia-org-2350 309 120 Wikipedia Wikipedia NNP en-wikipedia-org-2350 309 121 articles article NNS en-wikipedia-org-2350 309 122 with with IN en-wikipedia-org-2350 309 123 style style NN en-wikipedia-org-2350 309 124 issues issue NNS en-wikipedia-org-2350 309 125 from from IN en-wikipedia-org-2350 309 126 October October NNP en-wikipedia-org-2350 309 127 2020 2020 CD en-wikipedia-org-2350 309 128 All all DT en-wikipedia-org-2350 309 129 articles article NNS en-wikipedia-org-2350 309 130 with with IN en-wikipedia-org-2350 309 131 style style NN en-wikipedia-org-2350 309 132 issues issue NNS en-wikipedia-org-2350 309 133 Commons Commons NNP en-wikipedia-org-2350 309 134 category category NN en-wikipedia-org-2350 309 135 link link NN en-wikipedia-org-2350 309 136 is be VBZ en-wikipedia-org-2350 309 137 on on IN en-wikipedia-org-2350 309 138 Wikidata Wikidata NNP en-wikipedia-org-2350 309 139 Navigation Navigation NNP en-wikipedia-org-2350 309 140 menu menu NN en-wikipedia-org-2350 309 141 Personal personal JJ en-wikipedia-org-2350 309 142 tools tool NNS en-wikipedia-org-2350 309 143 Not not RB en-wikipedia-org-2350 309 144 logged log VBN en-wikipedia-org-2350 309 145 in in IN en-wikipedia-org-2350 309 146 Talk Talk NNP en-wikipedia-org-2350 309 147 Contributions Contributions NNP en-wikipedia-org-2350 309 148 Create Create NNP en-wikipedia-org-2350 309 149 account account NN en-wikipedia-org-2350 309 150 Log Log NNP en-wikipedia-org-2350 309 151 in in IN en-wikipedia-org-2350 309 152 Namespaces Namespaces NNP en-wikipedia-org-2350 309 153 Article Article NNP en-wikipedia-org-2350 309 154 Talk talk NN en-wikipedia-org-2350 309 155 Variants variant VBZ en-wikipedia-org-2350 309 156 Views view NNS en-wikipedia-org-2350 309 157 Read read VBP en-wikipedia-org-2350 309 158 Edit edit NN en-wikipedia-org-2350 309 159 View View NNP en-wikipedia-org-2350 309 160 history history NN en-wikipedia-org-2350 309 161 More More JJR en-wikipedia-org-2350 309 162 Search Search NNP en-wikipedia-org-2350 309 163 Navigation Navigation NNP en-wikipedia-org-2350 309 164 Main Main NNP en-wikipedia-org-2350 309 165 page page NN en-wikipedia-org-2350 309 166 Contents content VBZ en-wikipedia-org-2350 309 167 Current current JJ en-wikipedia-org-2350 309 168 events event NNS en-wikipedia-org-2350 309 169 Random random JJ en-wikipedia-org-2350 309 170 article article NN en-wikipedia-org-2350 309 171 About about IN en-wikipedia-org-2350 309 172 Wikipedia Wikipedia NNP en-wikipedia-org-2350 309 173 Contact Contact NNP en-wikipedia-org-2350 309 174 us -PRON- PRP en-wikipedia-org-2350 309 175 Donate Donate NNP en-wikipedia-org-2350 309 176 Contribute contribute NN en-wikipedia-org-2350 309 177 Help help NN en-wikipedia-org-2350 309 178 Learn learn VB en-wikipedia-org-2350 309 179 to to TO en-wikipedia-org-2350 309 180 edit edit VB en-wikipedia-org-2350 309 181 Community community NN en-wikipedia-org-2350 309 182 portal portal JJ en-wikipedia-org-2350 309 183 Recent recent JJ en-wikipedia-org-2350 309 184 changes change NNS en-wikipedia-org-2350 309 185 Upload upload JJ en-wikipedia-org-2350 309 186 file file NN en-wikipedia-org-2350 309 187 Tools tool NNS en-wikipedia-org-2350 309 188 What what WP en-wikipedia-org-2350 309 189 links link NNS en-wikipedia-org-2350 309 190 here here RB en-wikipedia-org-2350 309 191 Related relate VBN en-wikipedia-org-2350 309 192 changes change VBZ en-wikipedia-org-2350 309 193 Upload upload JJ en-wikipedia-org-2350 309 194 file file VBP en-wikipedia-org-2350 309 195 Special special JJ en-wikipedia-org-2350 309 196 pages page NNS en-wikipedia-org-2350 309 197 Permanent permanent JJ en-wikipedia-org-2350 309 198 link link NN en-wikipedia-org-2350 309 199 Page Page NNP en-wikipedia-org-2350 309 200 information information NN en-wikipedia-org-2350 309 201 Cite cite VB en-wikipedia-org-2350 309 202 this this DT en-wikipedia-org-2350 309 203 page page NN en-wikipedia-org-2350 309 204 Wikidata wikidata NN en-wikipedia-org-2350 309 205 item item NN en-wikipedia-org-2350 309 206 Print print NN en-wikipedia-org-2350 309 207 / / SYM en-wikipedia-org-2350 309 208 export export NN en-wikipedia-org-2350 309 209 Download Download NNP en-wikipedia-org-2350 309 210 as as IN en-wikipedia-org-2350 309 211 PDF PDF NNP en-wikipedia-org-2350 309 212 Printable Printable NNP en-wikipedia-org-2350 309 213 version version NN en-wikipedia-org-2350 309 214 In in IN en-wikipedia-org-2350 309 215 other other JJ en-wikipedia-org-2350 309 216 projects project NNS en-wikipedia-org-2350 309 217 Wikimedia Wikimedia NNP en-wikipedia-org-2350 309 218 Commons Commons NNPS en-wikipedia-org-2350 309 219 Languages Languages NNPS en-wikipedia-org-2350 309 220 Afrikaans Afrikaans NNPS en-wikipedia-org-2350 309 221 Alemannisch Alemannisch NNP en-wikipedia-org-2350 309 222 አማርኛ አማርኛ NNP en-wikipedia-org-2350 309 223 العربية العربية NN en-wikipedia-org-2350 309 224 Asturianu Asturianu NNP en-wikipedia-org-2350 309 225 Azərbaycanca Azərbaycanca NNP en-wikipedia-org-2350 309 226 বাংলা বাংলা NNP en-wikipedia-org-2350 309 227 Беларуская Беларуская NNP en-wikipedia-org-2350 309 228 Беларуская Беларуская NNP en-wikipedia-org-2350 309 229 ( ( -LRB- en-wikipedia-org-2350 309 230 тарашкевіца)‎ тарашкевіца)‎ NNP en-wikipedia-org-2350 309 231 Български Български NNP en-wikipedia-org-2350 309 232 Català Català NNP en-wikipedia-org-2350 309 233 Чӑвашла Чӑвашла NNP en-wikipedia-org-2350 309 234 Čeština Čeština NNP en-wikipedia-org-2350 309 235 Dansk Dansk NNP en-wikipedia-org-2350 309 236 Deutsch Deutsch NNP en-wikipedia-org-2350 309 237 Eesti Eesti NNP en-wikipedia-org-2350 309 238 Ελληνικά Ελληνικά NNP en-wikipedia-org-2350 309 239 Español Español NNP en-wikipedia-org-2350 309 240 Esperanto Esperanto NNP en-wikipedia-org-2350 309 241 Euskara Euskara NNP en-wikipedia-org-2350 309 242 فارسی فارسی JJ en-wikipedia-org-2350 309 243 Français Français NNP en-wikipedia-org-2350 309 244 Galego Galego NNP en-wikipedia-org-2350 309 245 한국어 한국어 NN en-wikipedia-org-2350 309 246 Հայերեն Հայերեն NNP en-wikipedia-org-2350 309 247 हिन्दी हिन्दी CD en-wikipedia-org-2350 309 248 Hrvatski Hrvatski NNP en-wikipedia-org-2350 309 249 Bahasa Bahasa NNP en-wikipedia-org-2350 309 250 Indonesia Indonesia NNP en-wikipedia-org-2350 309 251 Íslenska Íslenska NNP en-wikipedia-org-2350 309 252 Italiano Italiano NNP en-wikipedia-org-2350 309 253 עברית עברית NN en-wikipedia-org-2350 309 254 ქართული ქართული NN en-wikipedia-org-2350 309 255 Қазақша Қазақша NNP en-wikipedia-org-2350 309 256 Kreyòl Kreyòl NNP en-wikipedia-org-2350 309 257 ayisyen ayisyen NN en-wikipedia-org-2350 309 258 Kurdî Kurdî NNP en-wikipedia-org-2350 309 259 Latviešu Latviešu NNP en-wikipedia-org-2350 309 260 Lietuvių Lietuvių NNP en-wikipedia-org-2350 309 261 Magyar Magyar NNP en-wikipedia-org-2350 309 262 Македонски Македонски NNP en-wikipedia-org-2350 309 263 മലയാളം മലയാളം . en-wikipedia-org-2350 309 264 Монгол Монгол NNP en-wikipedia-org-2350 309 265 မြန်မာဘာသာ မြန်မာဘာသာ CD en-wikipedia-org-2350 309 266 Nederlands Nederlands NNP en-wikipedia-org-2350 309 267 नेपाली नेपाली NNP en-wikipedia-org-2350 309 268 日本語 日本語 . en-wikipedia-org-2350 309 269 Norsk Norsk NNP en-wikipedia-org-2350 309 270 bokmål bokmål NN en-wikipedia-org-2350 309 271 Norsk Norsk NNP en-wikipedia-org-2350 309 272 nynorsk nynorsk NNP en-wikipedia-org-2350 309 273 ਪੰਜਾਬੀ ਪੰਜਾਬੀ NNP en-wikipedia-org-2350 309 274 پنجابی پنجابی JJ en-wikipedia-org-2350 309 275 ភាសាខ្មែរ ភាសាខ្មែរ NNP en-wikipedia-org-2350 309 276 Piemontèis Piemontèis NNP en-wikipedia-org-2350 309 277 Polski Polski NNP en-wikipedia-org-2350 309 278 Português Português NNP en-wikipedia-org-2350 309 279 Română Română NNP en-wikipedia-org-2350 309 280 Русский Русский NNP en-wikipedia-org-2350 309 281 Scots scot NNS en-wikipedia-org-2350 309 282 Shqip Shqip NNP en-wikipedia-org-2350 309 283 Simple simple JJ en-wikipedia-org-2350 309 284 English English NNP en-wikipedia-org-2350 309 285 Slovenčina Slovenčina NNP en-wikipedia-org-2350 309 286 Slovenščina Slovenščina NNP en-wikipedia-org-2350 309 287 Српски Српски NNP en-wikipedia-org-2350 309 288 / / SYM en-wikipedia-org-2350 309 289 srpski srpski JJ en-wikipedia-org-2350 309 290 Srpskohrvatski Srpskohrvatski NNP en-wikipedia-org-2350 309 291 / / SYM en-wikipedia-org-2350 309 292 српскохрватски српскохрватски NN en-wikipedia-org-2350 309 293 Suomi Suomi NNP en-wikipedia-org-2350 309 294 Svenska Svenska NNP en-wikipedia-org-2350 309 295 Tagalog Tagalog NNP en-wikipedia-org-2350 309 296 தமிழ் தமிழ் , en-wikipedia-org-2350 309 297 Татарча Татарча NNP en-wikipedia-org-2350 309 298 / / SYM en-wikipedia-org-2350 309 299 tatarça tatarça NNS en-wikipedia-org-2350 309 300 Türkçe Türkçe NNP en-wikipedia-org-2350 309 301 Українська Українська NNP en-wikipedia-org-2350 309 302 اردو اردو NN en-wikipedia-org-2350 309 303 Tiếng Tiếng NNP en-wikipedia-org-2350 309 304 Việt Việt NNP en-wikipedia-org-2350 309 305 吴语 吴语 NNP en-wikipedia-org-2350 309 306 粵語 粵語 NNP en-wikipedia-org-2350 309 307 中文 中文 NNP en-wikipedia-org-2350 309 308 Edit Edit NNP en-wikipedia-org-2350 309 309 links link NNS en-wikipedia-org-2350 309 310 This this DT en-wikipedia-org-2350 309 311 page page NN en-wikipedia-org-2350 309 312 was be VBD en-wikipedia-org-2350 309 313 last last RB en-wikipedia-org-2350 309 314 edited edit VBN en-wikipedia-org-2350 309 315 on on IN en-wikipedia-org-2350 309 316 9 9 CD en-wikipedia-org-2350 309 317 December December NNP en-wikipedia-org-2350 309 318 2020 2020 CD en-wikipedia-org-2350 309 319 , , , en-wikipedia-org-2350 309 320 at at IN en-wikipedia-org-2350 309 321 17:25 17:25 CD en-wikipedia-org-2350 309 322   _SP en-wikipedia-org-2350 309 323 ( ( -LRB- en-wikipedia-org-2350 309 324 UTC UTC NNP en-wikipedia-org-2350 309 325 ) ) -RRB- en-wikipedia-org-2350 309 326 . . . en-wikipedia-org-2350 310 1 Text text NN en-wikipedia-org-2350 310 2 is be VBZ en-wikipedia-org-2350 310 3 available available JJ en-wikipedia-org-2350 310 4 under under IN en-wikipedia-org-2350 310 5 the the DT en-wikipedia-org-2350 310 6 Creative Creative NNP en-wikipedia-org-2350 310 7 Commons Commons NNP en-wikipedia-org-2350 310 8 Attribution Attribution NNP en-wikipedia-org-2350 310 9 - - HYPH en-wikipedia-org-2350 310 10 ShareAlike ShareAlike NNP en-wikipedia-org-2350 310 11 License License NNP en-wikipedia-org-2350 310 12 ; ; , en-wikipedia-org-2350 310 13 additional additional JJ en-wikipedia-org-2350 310 14 terms term NNS en-wikipedia-org-2350 310 15 may may MD en-wikipedia-org-2350 310 16 apply apply VB en-wikipedia-org-2350 310 17 . . . en-wikipedia-org-2350 311 1 By by IN en-wikipedia-org-2350 311 2 using use VBG en-wikipedia-org-2350 311 3 this this DT en-wikipedia-org-2350 311 4 site site NN en-wikipedia-org-2350 311 5 , , , en-wikipedia-org-2350 311 6 you -PRON- PRP en-wikipedia-org-2350 311 7 agree agree VBP en-wikipedia-org-2350 311 8 to to IN en-wikipedia-org-2350 311 9 the the DT en-wikipedia-org-2350 311 10 Terms term NNS en-wikipedia-org-2350 311 11 of of IN en-wikipedia-org-2350 311 12 Use Use NNP en-wikipedia-org-2350 311 13 and and CC en-wikipedia-org-2350 311 14 Privacy Privacy NNP en-wikipedia-org-2350 311 15 Policy Policy NNP en-wikipedia-org-2350 311 16 . . . en-wikipedia-org-2350 312 1 Wikipedia Wikipedia NNP en-wikipedia-org-2350 312 2 ® ® NNPS en-wikipedia-org-2350 312 3 is be VBZ en-wikipedia-org-2350 312 4 a a DT en-wikipedia-org-2350 312 5 registered registered JJ en-wikipedia-org-2350 312 6 trademark trademark NN en-wikipedia-org-2350 312 7 of of IN en-wikipedia-org-2350 312 8 the the DT en-wikipedia-org-2350 312 9 Wikimedia Wikimedia NNP en-wikipedia-org-2350 312 10 Foundation Foundation NNP en-wikipedia-org-2350 312 11 , , , en-wikipedia-org-2350 312 12 Inc. Inc. NNP en-wikipedia-org-2350 312 13 , , , en-wikipedia-org-2350 312 14 a a DT en-wikipedia-org-2350 312 15 non non JJ en-wikipedia-org-2350 312 16 - - JJ en-wikipedia-org-2350 312 17 profit profit JJ en-wikipedia-org-2350 312 18 organization organization NN en-wikipedia-org-2350 312 19 . . . en-wikipedia-org-2350 313 1 Privacy privacy NN en-wikipedia-org-2350 313 2 policy policy NN en-wikipedia-org-2350 313 3 About about IN en-wikipedia-org-2350 313 4 Wikipedia Wikipedia NNP en-wikipedia-org-2350 313 5 Disclaimers Disclaimers NNPS en-wikipedia-org-2350 313 6 Contact Contact NNP en-wikipedia-org-2350 313 7 Wikipedia Wikipedia NNP en-wikipedia-org-2350 313 8 Mobile Mobile NNP en-wikipedia-org-2350 313 9 view view NN en-wikipedia-org-2350 313 10 Developers Developers NNP en-wikipedia-org-2350 313 11 Statistics Statistics NNP en-wikipedia-org-2350 313 12 Cookie Cookie NNP en-wikipedia-org-2350 313 13 statement statement NN