Question

A small conducting sphere of radius $r$ is lying concentrically with a bigger hollow conducting sphere of radius $R$. The bigger and smaller spheres are charged with $Q$ and $q$ respectively $(Q>q)$. The two spheres are insulated from one another. 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 B $\frac{1}{4\pi {ϵ}_0}(\frac{q}{r}-\frac{q}{R})$

$V_{inner}=\frac{q}{4\pi {ϵ}_{o}r}+\frac{Q}{4\pi {ϵ}_{o}R}$

$V_{outer}=\frac{q}{4\pi {ϵ}_{o}R}+\frac{Q}{4\pi {ϵ}_{o}R}$

$\Delta V=V_{inner}-V_{outer}=\frac{1}{4\pi {ϵ}_o}(\frac{q}{r}-\frac{q}{R})$

Answer-(B)