When two electrons $(e^-)$ move towards each other,the electrostatic potential energy of the system will:

Two electric dipoles,each of dipole moment $P$,are placed at points $A(a, 0)$ and $B(-a, 0)$ as shown in the figure. The work done in rotating both the dipoles through $90^{\circ}$ in the clockwise direction is $(E = \text{Electric field})$

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:

Write an equation of electric potential at a point on the axis of an electric dipole.

Write an equation for the electric potential due to an electric dipole and state its important features. Discuss its special cases.

An electric dipole of dipole moment $\vec{p}$ is placed at the origin of the coordinate system along the $z$-axis. The amount of work required to move a charge $q$ from the point $A(a, 0, 0)$ to the point $B(0, 0, a)$ is,