$A$ charge of $10 \, \text{esu}$ is placed at a distance of $2 \, \text{cm}$ from a charge of $40 \, \text{esu}$ and at a distance of $4 \, \text{cm}$ from another charge of $-20 \, \text{esu}$. The potential energy of the $10 \, \text{esu}$ charge in ergs is:

$A$ unit positive point charge is taken slowly through an infinitesimally thin tube that is inside a charged dielectric sphere of radius $R$, having uniform positive charge density $\rho$. The initial and final positions of the charge are marked by $A$ and $B$ at distances $2R$ and $3R$ respectively, from the centre of the sphere. In this process, the magnitude of the total work done on the point charge is $\frac{\rho R^2}{n \epsilon_0}$. The value of $n$ is : ($\epsilon_0$ is the permittivity of vacuum)

$A$ 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 $-3Q$,the new potential difference between the same two surfaces is:

When a positive $q$ charge is taken from a lower potential point to a higher potential point,its potential energy will

Two charges $8 \ \mu C$ each are placed at the corners $A$ and $B$ of an equilateral triangle of side $0.2 \ m$ in air. The electric potential at the third corner $C$ is

$A$ thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell. The electrostatic potential at a point $P$ at a distance $R/2$ from the centre of the shell is: