A point charge $q$ is placed inside a conducting spherical shell of inner radius $2 R$ and outer radius $3 R$ at a distance of $R$ from the center of the shell. Find the electric potential at the center of the shell.

Question

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Answer 1

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

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

and electric potential due to outer surface of shell $= \frac{k q}{3 R}$

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

$= \frac{k 5 q}{6 R}$

Answer 2

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

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

and electric potential due to outer surface of shell $= \frac{k q}{3 R}$

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

$= \frac{k 5 q}{6 R}$