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Question

A solid conducting sphere having a charge Q is surrounded by an uncharged concentric conducting spherical shell. The potential difference between the surface of solid sphere and the shell is V. The shell is now given a charge 3Q. The new potential difference between the same surfaces will be :

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

The correct option is C V
A solid conducting sphere having a charge Q is surrounded by an uncharged concentric spherical shell, The potential difference between the solid sphere and hallow shell is V.
VAVB=V
VAVB=Q4πε0a.Q4πε0.b
V=Q4πε0[1a1b]. . . . . . .(1)
Now, shell is given a charge 3Q,the,
The new potential is,
VA=Q4πε0.a3Q4πε0.b
VA=Q4πε0[1a3b] and,
VB=Q4πε0b3Q4πε0b
VB=Q4πε0[1b3b]
VAVB=Q4πε0[1a1b]=V
The correct option is C.


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