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Question

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge 3Q, the new potential difference between the same two surfaces is :

A
V
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B
2V
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C
4V
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D
2V
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Solution

The correct option is A V
The electric field in between the shell and sphere is
E.πx2=Qenϵ0=Qϵ0 (using Gauss's law)
E=Q4πϵ0x2
The potential difference between the shells is dV=VrVR=RrEdx=RrQ4πϵ0x2dx=Q4πϵ0(1/r1/R)
Thus, V=Q4πϵ0(1/r1/R)
As the potential difference between solid sphere and hollow shell depends on the radii of two spheres and charge on the inner sphere, Since the two values have not changed, potential difference does not change. Hence the potential difference remains V.

203514_142392_ans.png

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