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Question

A large hollow metallic sphere A (of radius R ) is positively charged to a potential of 100 V and a small sphere B (of radius R5) is also positively charged to a potential of 100 V. Now B is placed inside A and they are connected by a wire. The final potential of A will be:

A
200 V
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B
150 V
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C
120 V
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D
none of above
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Solution

The correct option is C 120 V
The charge on sphere A and B is :
V=14πϵ0qr

qA=(4πϵ0R)V
and qB=(4πϵ0)R5V
When they are connected by conducting wire, the entire charge will flow to outer sphere, so that their potentials become equal. Thus
q=qA+qB=(4πϵ0)6R5.V
The final potential of A now,
V=14πϵ0qR=(4πϵ0)(6R5V)4πϵ0R
=6V5=6005=120 V

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