Two concentric spheres of radii R and r have similar charges with equal surface density (σ). The electric potential at their common centre is

$\frac{\sigma}{\varepsilon_0}(R+r)$

Let q₁ and q₂ be charges on spheres.

Then potential at the common centre

$v=\frac{k q_1}{R}+\frac{k q_2}{r}=\frac{1}{e_0}\left[\frac{1}{4 \pi R^2} \times R+\frac{q_2}{4 \pi r^2} \times r\right]$

But $\frac{q_1}{4 \pi R^2}=\frac{q_2}{4 \pi r^2}=\sigma \quad ∴ \quad v=\frac{1}{\varepsilon_0}[\sigma R+\sigma r]=\frac{\sigma}{\varepsilon_0}[R+r]$