Question

A large isolated metal sphere of radius r carries a fixed charge. A small charge is placed at a distance s from its surface. It experiences a force which is
a) inversely proportional to (r + s)
b) inversely proportional to s
c) inversely proportional to s2
d) inversely proportional to (r + s)2
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Answer 1

Answer:

LetatanyinstantqbethechargeonthesphereNowpotentialofthesphere=rkqWorkdonetoaddadqchargetothisspheredw=rkq⋅dq(AsV∞=0)∴totalworkdonetoaccumulateqchargeis∫dw=∫0qrkq⋅dq⇒w=rk[2q2]0q⇒w=2rkq2⇒w=4πε0r⋅2q2⇒w=8πε0rq2