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Question

Inside a conducting spherical shell of inner radius 3R and outer radius 5R , a point charge Q is placed at a distance R from the centre of the shell. The electric potential at the centre of the shell will be.

A
14πϵ05Q6R
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B
14πϵ013Q15R
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C
14πϵ0QR
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D
14πϵ07Q9R
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Solution

The correct option is B 14πϵ013Q15R
From conservation of charge, the charge distribution on each surface is as shown in the figure.

Here in the figure , 1 represents the point charge, 2 represents inner surface of shell and 3 represents the surface of outer shell.

Electric potential at centre due to point charge,
V1=14πϵ0QR

Electric potential at centre due to inner surface of shell,
V2=14πϵ0(Q)3R

And, electric potential at centre due to outer surface of shell,
V2=14πϵ0(Q)5R

Net potential at the centre
V=V1+V2+V3

V=14πϵ0[QRQ3R+Q5R]

V=14πϵ0[QR(155+315)]

V=14πϵ013Q15R

Hence, option (c) is the correct answer.

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