The potential difference between the center and the surface of a sphere of radius $R$ with a uniform volume charge density $\rho$ within it will be:

There are three concentric conducting spherical shells $A$,$B$,and $C$ of radii $a$,$b$,and $c$ respectively. The potentials of the spheres $A$,$B$,and $C$ respectively are:

Calculate the work done in taking a charge $q_0 = -2 \times 10^{-9} \, C$ from point $A$ to point $B$ via point $C$,as shown in the diagram. The source charge $q = 8 \, mC$ is located at the origin $O$. (in $, J$)

The electric potentials at two points $P$ and $Q$ are $10 \ V$ and $-4 \ V$ respectively. The work done in moving $100$ electrons from $P$ to $Q$ is:

$A$ thin conducting spherical shell (center at $O$) having charge $Q_0$,radius $R$ and three point charges $Q_0$,$-2Q_0$,$3Q_0$ are kept at points $A$,$B$,and $C$ respectively as shown in the figure. Find the potential at any point on the conducting shell. (Potential at infinity is assumed to be zero)

Two particles $A$ and $B$ having the same mass have charges $+q$ and $+4q$ respectively. When they are allowed to fall from rest through the same electric potential difference,the ratio of their speeds $v_A$ to $v_B$ will be: