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Question

A solid conducting sphere of radius a is surrounded by a thin uncharged concentric conducting shell of radius 2a A point charge q is placed at a distance 4a from common centre of conducting sphere and shell.The inner sphere is then grounded.The potential of outer shell is found to be
qnπε0a





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Solution

Let the potential of the outer shell be VB.

Potential at outer shell due to point charge is given by V1=kq4a
Potential at outer shell due to inner sphere is given by V2=kq2aVB=V1+V2

VB=kq4a+(kq8a)

VB=q32πε0a

Comparing this with the data given in the question we get, n=32

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