$A$ molecule of a substance has a permanent dipole moment $p$. $A$ mole of this substance is polarized by applying a strong electrostatic field $E$. The direction of the field is suddenly changed by an angle of $60^{\circ}$. If $N$ is the Avogadro's number,the amount of work done by the field is:

The electric potential due to an electric dipole at a given point is .......

In bringing an electron towards another electron,the electrostatic potential energy of the system

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:

$A$ moving positive charge approaches a negative charge. What will happen to the potential energy of the system?

Three infinitely long linear charges of charge density $\lambda$,$\lambda$,and $-2\lambda$ are placed in space. $A$ point in space is specified by its perpendicular distances $r_1$,$r_2$,and $r_3$ respectively from the linear charges. For the points which are equipotential: