Charge Q coulombs is uniformly distributed throughout the volume of a solid hemisphere of radius R metres. Then the potential at centre O of the hemisphere in volts is :

The potential at centre of sphere in which q charge is uniformly distributed throughout the volume is ${\mathrm{V}}_{\mathrm{c}}=\frac{1}{4{\mathrm{\pi ϵ}}_0}\frac{3\mathrm{q}}{2\mathrm{R}}$.

By symmetry the potential at centre due to half sphere will be half of the complete sphere.

$\therefore {\mathrm{V}}_{\mathrm{c}}=\frac{1}{4{\mathrm{\pi ϵ}}_0}\frac{3\mathrm{q}/2}{2\mathrm{R}}=\frac{1}{4{\mathrm{\pi ϵ}}_0}\frac{3\mathrm{Q}}{2\mathrm{R}}\left[\therefore \frac{\mathrm{q}}{2}=\mathrm{Q}\right]$