An isolated metal sphere of radius r is given a charge q. The potential energy of the sphere is :
q24πϵ0r
q4πϵ0r
q8πϵ0r
q28πϵ0r
A
q4πϵ0r
B
q8πϵ0r
C
q28πϵ0r
D
q24πϵ0r
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Solution
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Let at any instant q be the charge on the sphere Now potential of the sphere =kqr Work done to add a dq charge to this sphere dw=kqr⋅dq (As V∞=0) ∴ total work done to accumulate q charge is ∫dw=∫q0kqr⋅dq ⇒w=kr[q22]q0 ⇒w=kq22r ⇒w=q24πε0r⋅2 ⇒w=q28πε0r
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