Question

Two concentric spheres kept in air have radii 'R' and 'r'. They have similar charge and equal surface charge density '$\sigma$'. The electric potential at their common centre is ______. (${ϵ}_0=$permittivity of free space)

• A. $\frac{\sigma (R+r)}{{ϵ}_0}$
• B. $\frac{\sigma (R-r)}{{ϵ}_0}$
• C. $\frac{\sigma (R+r)}{2{ϵ}_0}$
• D. $\frac{\sigma (R+r)}{4{ϵ}_0}$

Answer 1

Answer: (A)

$\frac{\sigma (R+r)}{{ϵ}_0}$

The potential at the centre of a sphere of radius $r$ and surface charge $q$ is
$V=\frac{1}{4\pi {ϵ}_0}\frac{q}{r}$

$V=\frac{r}{{ϵ}_0}\left(\frac{q}{4\pi r^2}\right)=\frac{\sigma r}{{ϵ}_0}$

The potential at centre of two concentric spheres of radii $r$ and $R$ is addition of individual potentials by each shell.

$V=\frac{\sigma (R+r)}{{ϵ}_0}$