10b show that the total charge on the boss has the

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Unformatted text preview: ™—n ˜e —pproxim—ted ˜y grounded sphere in — uniform ele™tri™ eld @we —re given th—t the purpose of the nonEgrounded pl—te is to ™—use the ele™tri™ eld ˜etween the pl—tes to ˜e ™onst—nt —nd uniformAF ren™eD equ—tion PFIR from t—™kson gives the ele™tri™ potenti—l ˜etween the pl—tesX ¨ a E  0 r a3 r2  ™os  yn the ˜ossD the surf—™eE™h—rge density is the s—me —s equ—tion PFIS from t—™ksonX  a Q" E ™os  0 U 0 @PA „o nd the surf—™eE™h—rge density on the grounded pl—ne @lo™—ted —t z a HAD we rst ™onvert equ—tion @PA to g—rtesi—n ™oordin—tesX ¨a a   a3 E0 r ™os  I | {z } r3 z   a 3  E0 z I r   @¨  "0  @z z =0   a 3  E0 I r a a 2.10.b. Show that the total charge on the boss has the magnitude "0 E0 a2 . Q ‡e will integr—te the surf—™eE™h—rge density over the surf—™e —re— of the ˜oss to nd its net ™h—rgeX Q a  Q" E ™os da 0 a Q" E 0 0  0 a Qa " E 2 0  2  2 '=0 ==2 2    0 '=0  ™os  sin dd'  =a ==2 ™os  sin dd' …sing the su˜stitution u a sin D du a ™os X Q a Qa " E 2 0 a Qa " E 2 0  0 0 2 '=0  2 '=0 I a Qa " E P P a Qa " E 2 0 2 0 0 0 V  1 u=0 udud' I u   P u 2 1 =0 d' 2.10.c. sfD inste—d of the other ™ondu™ting sheet —t — dierent potenti—lD — point ™h—rge q is pl—™ed dire™tly —˜ove the hemispheri™—l ˜oss —t — dist—n™e d from its ™enterD...
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This note was uploaded on 12/08/2011 for the course PHYSICS 505 taught by Professor Liu during the Winter '08 term at University of Michigan.

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