The electric potential at a distance of $3 \, m$ on the axis of a short dipole of dipole moment $4 \times 10^{-12} \, C \cdot m$ is ......... $mV$.

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 an equation of electric potential at a point due to an electric dipole.

Two equal charges $q$ of opposite sign separated by a distance $2a$ constitute an electric dipole of dipole moment $p$. If $P$ is a point at a distance $r$ from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole,then the potential at $P$ is given by $(r \gg 2a)$ (where $p = 2qa$).

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:

In the figure,the value of $Q$ so that the electrostatic potential energy of the system becomes zero is