Nine point charges are placed on a cube as shown in the figure. The charge $q$ is placed at the body centre whereas all other charges are at the vertices. The electrostatic potential energy of the system will be

If $50$ joule of work must be done to move an electric charge of $2 \,C$ from a point, where potential is $-10$ volt to another point, where potential is $V$ volt, the value of $V$ is ......... $V$

For an infinite line of charge having charge density $\lambda $ lying along $x-$ axis, the work required in moving charge $q$ from $C$ to $A$ along arc $CA$ is :-

There exists a uniform electric field $E=4 \times 10^5 \,Vm ^{-1}$ directed along negative $x$-axis such that electric potential at origin is zero. Acharge of $-200 \,\mu C$ is placed at origin, and a charge of $+200 \,\mu C$ is placed at $(3 \,m , 0)$. The electrostatic potential energy of the system is ...........$J$

The mean free path of electrons in a metal is $4 \times 10^{-8} \;m$. The electric field which can give on an average $2 \;eV$ energy to an electron in the metal will be in units of $V / m$

Derive the formula for the electric potential energy of system of two charges.