Two· concentric spheres kept in air have radii R and r. They have similar charge and equal surface charge density $\mathrm{\sigma }$. The electric potential at their common centre is ......

(where, ${\mathrm{\epsilon }}_0$ = permittivity of free space) 

Potential due to a uniformly charged sphere is

                           $\mathrm{V}=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{\mathrm{Q}}{\mathrm{R}}$                                                 …(i)

Also,                  $\mathrm{\sigma }=\frac{\mathrm{Q}}{4{\mathrm{\pi R}}^2}=\frac{{\mathrm{Q\epsilon }}_0}{4{\mathrm{\pi \epsilon }}_0{\mathrm{R}}^2}$

                          $\frac{{\mathrm{\sigma R}}^2}{{\mathrm{\epsilon }}_0}=\frac{1\times \mathrm{Q}}{4{\mathrm{\pi \epsilon }}_0}$                                                …(ii)

From Eqs. (i) and (ii), we get $\mathrm{V}=\frac{\mathrm{\sigma R}}{{\mathrm{\epsilon }}_0}$

Potential due to outer sphere, ${\mathrm{V}}_1=\frac{\mathrm{\sigma R}}{{\mathrm{\epsilon }}_0}$

Potential due to inner sphere, ${\mathrm{V}}_2=\frac{\sigma r}{{\mathrm{\epsilon }}_0}$

Net potential at centre, $\mathrm{V}={\mathrm{V}}_1+{\mathrm{V}}_2=\frac{\mathrm{\sigma }}{{\mathrm{\epsilon }}_0}(\mathrm{R}+\mathrm{r})$