A charge $Q$ is distributed over two concentric hollow spheres of radii $r$ and $R$, where $R>r$, such that the surface charge densities are equal. Find the potential at the common centre.

Three concentric metallic shells $A, B$ and $C$ of radii, $a, b$ and $c\left(a<b<c\right)$ have surface charged densities $+\sigma , -\sigma$ and $+\sigma$ respectively, as shown in figure below. Find potential of three shells $A, B, C$.

Three concentric metallic shells $A, B$ and $C$ of radii, $a, b$ and $c\left(a<b<c\right)$ have surface charged densities $+\sigma , -\sigma$ and $+\sigma$ respectively, as shown in figure below. If shells $A$ and $C$ are at the same potential, obtain the relation between radii $a, b, c$.

In below image, the potentials at points $A$ and $B$ are $V_A$ and $V_B$ respectively. Calculate $V_A-V_B$ for the given arrangement.

Figure below shows some equipotential surfaces. What can you say about the magnitude and direction of the electric field?