Two charges $5 \text{ nC}$ and $-2 \text{ nC}$ are placed at points $(5 \text{ cm}, 0, 0)$ and $(23 \text{ cm}, 0, 0)$ in a region of space where there is no other external field. The electrostatic potential energy of this charge system is

In the figure shown,the electric potential energy of the system is: ($q$ is at the centre of the conducting neutral spherical shell of inner radius $a$ and outer radius $b$)

Write the $SI$ unit of electrostatic potential energy and its dimensional formula.

Obtain the equation of electric potential energy of a dipole from the equation of potential energy of a system of two electric charges.

An electric dipole with dipole moment $\vec{p}_i = (3\hat{i} + 4\hat{j}) \times 10^{-30} \, \text{C-m}$ is placed in an electric field $\vec{E} = 4000 \hat{i} \, \text{N/C}$. An external agent turns the dipole slowly until its electric dipole moment becomes $\vec{p}_f = (-4\hat{i} + 3\hat{j}) \times 10^{-30} \, \text{C-m}$. The work done by the external agent is equal to:

The work done required to assemble the four charges at the corners of a square of side $a$, as shown in the figure, is: