problem23_52

University Physics with Modern Physics with Mastering Physics (11th Edition)

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23.52: From Problem 22.51, the electric field of a sphere with radius R and q distributed uniformly over its volume is for 4 and for 4 2 0 3 0 R r r πε q E R r R πε qr E = = = - b a b a b Edr V V Take . at infinity and . 0 = V Let point a be a distance R r < from the center of the sphere. - = + = R r R r R r R πε q dr r πε q dr R πε qr V 2 2 0 2 0 3 0 3 8 4 4 Set e q 2 + = to get r V for the sphere. The work done by the attractive force of the sphere when one electron is removed from is to = d r - - = - = 2 2 0 2 sphere 3 8 2 R d R πε e eV W r The total work done by the attractive force of the sphere when both electrons are removed is twice this, . 2 sphere W The work done by the repulsive force of the two electrons is ) 2 ( 4 0 2 d πε e W ee = The total work done by the electrical forces is . 2 sphere ee W W + The energy required to remove the two electrons is the negative of this,
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