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 charged with $Q$ and $q$ $(Q>q)$ and are insulated from each other. The potential difference between the spheres will be :

• A. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{q}{R})$
• B. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{R}-\frac{Q}{r})$
• C. $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{Q}{R})$
• D. $\frac{1}{4\pi {ϵ}_0}(\frac{Q}{R}+\frac{q}{r})$

Answer 1

The correct option is A $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{q}{R})$

$V_r=\frac{Kq}{r}+\frac{KQ}{R}$

$V_R=\frac{kq}{R}+\frac{kQ}{R}$

$V_r-V_R=k(\frac{q}{r}-\frac{q}{R})$