Prom tkson9s exmple prolem in setion pfsd we know tht

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Unformatted text preview: F 2 2 Problem 2.9 en insul—tedD spheri™—lD ™ondu™ting shell of r—dius a is in — uniform ele™tri™ eld E F sf the sphere is ™ut into two hemispheres ˜y — pl—ne perpendi™ul—r to the eldD nd the for™e required to prevent the hemispheres from sep—r—ting 0 2.9.a. If the shell is uncharged. prom t—™kson9s ex—mple pro˜lem in se™tion PFSD we know th—t the surf—™eE™h—rge density is given ˜yX  a Q" E ™os  0 0 …sing the equ—tion shown in gure PFRX dF da 2  a P" a W" EP"™os  a W" EP"™os  ™os  0 2 0 2 0 2 0 2 0 2 0 dFz da jFz j a  2 '=0  2 0  =0 W " E ™os P 0 2 0 S 3   2 sin dd' =a …sing the su˜stitution u a ™os D du a sin X jFz j a  2  '=0 W " E u @ duAd' P 0 u=1 W a Pa " E a W" a E P W a R " a e 2 0 2 0 2 0 0  2 0  2 0 3  2 '=0 2 0 u=1 u3 dud' I u  d'  R 4 0 1 '=0 22 0 0 Q. 2.9.b. If the total charge on the shell is „he surf—™e ™h—rge density on the sphere of ™h—rge Q isX Q Q a Ra 2 xowD we nd the s—me method —s —˜ove to nd the for™e ˜etween the two hemispheres of equ—l ™h—rgeX dF da 2  a P" 0 a ITQ a PI  " a QPQ" a ™os  2 2 dFz da jFz j a   2 '=0...
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