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 âˆ’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 VA 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.VA−VB=VVA−VB=Q4πε0a.Q4πε0.bV=Q4πε0[1a−1b]. . . . . . .(1)Now, shell is given a charge −3Q,the,The new potential is,V′A=Q4πε0.a−3Q4πε0.bV′A=Q4πε0[1a−3b] and,V′B=Q4πε0b−3Q4πε0bV′B=Q4πε0[1b−3b]V′A−V′B=Q4πε0[1a−1b]=VThe correct option is C.

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