Two isolated,concentric,conducting spherical shells have radii $R$ and $2R$ and uniform charges $q$ and $2q$ respectively. If $V_1$ and $V_2$ are potentials at points located at distances $3R$ and $\frac{R}{2}$,respectively,from the centre of the shells,then the ratio $\left(\frac{V_2}{V_1}\right)$ will be:

Consider a sphere of radius $R$ having charge $q$ uniformly distributed inside it. At what minimum distance from its surface is the electric potential half of the electric potential at its centre?

$A$ solid conducting sphere having a charge $Q$ is surrounded by an uncharged concentric conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be $V$. If the shell is now given a charge of $-3Q$,the new potential difference between the same two surfaces is......$V$

The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on a smooth fixed ring placed on a smooth horizontal plane. In the same plane,a charge $+Q$ has also been fixed as shown. The potential at point $P$ due to $+Q$ is $V$. The velocity with which the bead should be projected from point $P$ so that it can complete a circle should be greater than:

If on two concentric hollow spheres of radii $R$ and $r$ $(R < r)$,a total charge $Q$ is distributed such that their surface charge densities are equal,then the potential at their common centre is:

The work done in carrying a charge of $5\,\mu C$ from a point $A$ to a point $B$ in an electric field is $10\,mJ$. The potential difference $(V_B - V_A)$ is then