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. $\frac{1}{4\pi {\epsilon }_0}\left[\frac{q}{r}-\frac{q}{R}\right]$
• B. $\frac{1}{4\pi {\epsilon }_0}\left[\frac{q}{r}+\frac{q}{R}\right]$
• C. $\frac{1}{4\pi {\epsilon }_0}\left[\frac{q}{r}-\frac{Q}{R}\right]$
• D. $\frac{1}{4\pi {\epsilon }_0}\left[\frac{q}{r}+\frac{Q}{R}\right]$

Answer 1

Answer: (A)

First we calculate total potential on sphere A and B
$V_A=\frac{kq}{r}+\frac{kQ}{R}$
$V_B=\frac{kq}{R}+\frac{kQ}{R}$
$\therefore V_A-V_B=\frac{kq}{r}-\frac{kq}{R}$