If the electric potential of the inner metal sphere of radius $a$ is $10 \text{ V}$ and that of the outer spherical shell of radius $b$ is $5 \text{ V}$,then the potential at the centre will be ...... $\text{V}$.

The electric potential of the Earth is taken to be zero because the Earth is a good:

The figure shows a charge array known as an electric quadrupole. For a point on the axis of the quadrupole,obtain the dependence of potential on $r$ for $r / a >> 1,$ and contrast your results with that due to an electric dipole,and an electric monopole (i.e.,a single charge).

The work done in carrying a charge $Q$ once around a circle of radius $r$ about a charge $q$ at the centre is

Three concentric spherical shells have radii $a, b$ and $c$ $(a < b < c)$ and have surface charge densities $\sigma, -\sigma$ and $\sigma$ respectively. If $V_A, V_B$ and $V_C$ denote the potentials of the three shells,then,for $c = a + b$,we have

Three concentric spherical metallic shells $X$,$Y$,and $Z$ of radii $a$,$b$,and $c$ respectively $[a < b < c]$ have surface charge densities $\sigma$,$-\sigma$,and $\sigma$,respectively. The shells $X$ and $Z$ are at the same potential. If the radii of $X$ and $Y$ are $2\,cm$ and $3\,cm$,respectively,then the radius of shell $Z$ is $......\,cm$.