A point charge q is placed inside a conducting spherical shell of inner radius 2R and outer radius 3R, at a distance of R from the centre of the shell. The electric potential at the centre of shell will be

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$\frac{q}{3 π ε_{0} R}$

$\frac{q}{6 π ε_{0} R}$

$\frac{q}{8 π ε_{0} R}$

$\frac{5 q}{24 π ε_{0} R}$

answer is D.

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Detailed Solution

$Electric potential due to point charge = \frac{kq}{R}$

$Electric potential due to inner surface of shell = - \frac{kq}{2 R}$

$Electric potential due to outer surface of shell = \frac{kq}{3 R}$

$V = \frac{kq}{R} - \frac{kq}{2 R} + \frac{kq}{3 R} = \frac{kq}{R} [1 - \frac{1}{2} + \frac{1}{3}]$

$= \frac{5 k q}{6 R} = \frac{5 q}{24 π ε_{0} R}$

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