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Question

Two concentric spherical conducting shells of radii R and 2R carry charges Q and 2Q respectively. Change in electric potential on the outer shell when both are connected by a conducting wire is:
(Where K=14πϵ0)

A
Zero
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B
KQR
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C
3KQ2R
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D
2KQR
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Solution

The correct option is A Zero

Case 1: Net potential (V0) on the outer shell when both shells are not connected,

V0=V1+V2
Here,
V1=Potential on outer shell due to shell 1,
V2=Potential on outer shell due to shell 2,

Substituting the values of V1 and V2 from figure we get,
V0=14πϵ0(Q2R)+14πϵ0(2Q2R)

V0=14πϵ0(3Q2R) (1)

Case 2:After connecting, all charges in the inner shell come to outer shell.

Net potential (V0) on the outer shell when both shells are connected by conducting wire,

V0=14πϵ0(Q+2Q)2R

V0=14πϵ03Q2R (2)

From (1) and (2),
The change in potential, V0V0=0

Hence option (a) is the correct answer.

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