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(C) The work done in bringing the charges from infinity to their respective positions is equal to the change in the electrostatic potential energy of

Vedclass · Accepted Answer

$q^2 / 4 \pi \varepsilon_0 a$

Vedclass · Answer

(C) The work done in bringing the charges from infinity to their respective positions is equal to the change in the electrostatic potential energy of the system.Let the shell be charge $1$,the charge $+q$ be charge $2$,and the charge $-q$ be charge $3$.The potential inside a uniformly charged spherical shell is constant and equal to $V = kQ/R$,where $k = 1 / (4 \pi \varepsilon_0)$.$1$. Work done to bring charge $+q$ to $x = -a/2$: $W_1 = q 	imes V_{	ext{shell}} = q(kQ/R)$.$2$. Work done to bring charge $-q$ to $x = +a/2$: $W_2 = (-q) 	imes V_{	ext{shell}} + (-q) 	imes V_{	ext{charge } q} = (-q)(kQ/R) + (-q)(kq / a) = -kQq/R - kq^2/a$.Total work done $W = W_1 + W_2 = (kQq/R) - (kQq/R) - kq^2/a = -kq^2/a$.The magnitude of the work done is $|W| = | -kq^2/a | = q^2 / (4 \pi \varepsilon_0 a)$.

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