Two concentric hollow conducting spheres of radius $r$ and $R$ are shown. The charge on outer shell is $Q$. What charge should be given to inner sphere so that the potential at any point $P$ outside the outer sphere is zero?

Two charged spherical conductors of radius $R_{1}$ and $\mathrm{R}_{2}$ are connected by a wire. Then the ratio of surface charge densities of the spheres $\left(\sigma_{1} / \sigma_{2}\right)$ is :

Figure shows three concentric metallic spherical shells. The outermost shell has charge $q_2$, the inner most shell has charge $q_1$, and the middle shell is uncharged. The charge appearing on the inner surface of outermost shell is

Show that electrostatic potential is constant throughout the volume of the conductor and has the same value (as inside) on its surface.

A metallic spherical shell has an inner radius $R_1$ and outer radius $R_2$. A charge $Q$ is placed at the centre of the spherical cavity. What will be surface charge density on the inner surface

A thin metallic spherical shell contains a charge $Q$ on it. A point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in fig. All  the three charges are positive. The force on the central charge due to the shell is :-