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Phys_322_HW4

# Phys_322_HW4 - Physics 322 HW4 Solution 1(a If the charge...

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Physics 322 HW4 Solution 1. (a) If the charge is uniformly distributed, 3 0 4 3 e a . Since the energy required bringing a charge is   0 1 4 q r dq dE r  ,   3 4 3 q r r , 2 4 dq r dr , So the total energy of the sphere is 0 2 2 4 2 5 0 0 0 0 0 0 4 4 3 3 15 20 a e E r dr a a  So the frequency is 2 0 0 3 20 E e h h a   (b)   0 3 0 4 exp 2 / e r r a a ,   0 1 4 q r dq dE r    2 0 ' 4 ' ' r q r r r dr ,   2 4 dq r r dr ,   0 2 2 0 3 0 0 0 2 2 2 0 2 0 0 0 4 ' 4 ' ' exp 2 '/ 4 ' ' 2 2 2 4 exp 2 / 1 4 r r r x a e q r r r dr r a r dr a r r e x e dx e r a e a a   2 2 0 0 3 2 0 0 0 0 16 2 2 exp 2 / 1 1 exp 2 / e r r dE r a r a rdr a a a

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Phys_322_HW4 - Physics 322 HW4 Solution 1(a If the charge...

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