Question

A small conducting sphere of radius $r$ is lying concentrically inside a bigger hollow conducting sphere of radius $R$ . The bigger and smaller spheres are insulated from each other and are charged to $Q$ and $q\left(Q > q\right)$ respectively. The potential difference between the sphere will be

• A. $\frac{1}{4 \pi ε_{0}}\left[\frac{q}{r} - \frac{q}{R}\right]$
• B. $\frac{1}{4 \pi ε_{0}}\left[\frac{q}{r} + \frac{q}{R}\right]$
• C. $\frac{1}{4 \pi ε_{0}}\left[\frac{q}{r} - \frac{Q}{R}\right]$
• D. $\frac{1}{4 \pi ε_{0}}\left[\frac{q}{r} + \frac{Q}{R}\right]$

Answer 1

Answer: (A)

First we calculate total potential on sphere A and B
$V_{A}=\frac{k q}{r}+\frac{k Q}{R}$
$V_{B}=\frac{k q}{R}+\frac{k Q}{R}$
$\therefore \, V_{A}-V_{B}=\frac{k q}{r}-\frac{k q}{R}$