Concentric metallic hollow spheres of radii R and 4R hold charges Q₁ and Q₂ respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference $\mathrm{V}\left(\mathrm{R}\right)-\mathrm{V}\left(4\mathrm{R}\right)$ is :

We have given two metallic hollow spheres of radii R and 4R having charges Q₁ and Q₂
respectively. Potential on the surface of inner sphere (at A)
${\mathrm{V}}_{\mathrm{A}}=\frac{{\mathrm{kQ}}_1}{\mathrm{R}}+\frac{{\mathrm{kQ}}_2}{4\mathrm{R}}$
Potential on the surface of outer sphere (at B)
${\mathrm{V}}_{\mathrm{B}}=\frac{{\mathrm{kQ}}_1}{4\mathrm{R}}+\frac{{\mathrm{kQ}}_2}{4\mathrm{R}}$Potential difference $\mathrm{\Delta V}={\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_{\mathrm{B}}=\frac{3}{4}\cdot \frac{{\mathrm{kQ}}_1}{\mathrm{R}}=\frac{3}{16{\mathrm{\pi ϵ}}_0}\cdot \frac{{\mathrm{Q}}_1}{\mathrm{R}}$