$A$ dipole having a dipole moment $p = 4 \, C-m$ is placed at the origin along the $x$-axis. $A$ point charge $q = 8 \, \mu C$ is fixed at $(4, 0, 0)$. Now,the dipole is rotated by an angle of $\frac{\pi}{2}$. Find the work done (in $mJ$) in rotating the dipole.

Five identical small electric dipoles are placed at a distance $r$ from an infinitely long straight wire carrying a uniform charge density $\lambda$. If they experience forces of magnitude $F_1, F_2, F_3, F_4$ and $F_5$ respectively,then:

For a short dipole placed at origin $O$,the dipole moment $P$ is along the $x$-axis,as shown in the figure. If the electric potential and electric field at point $A$ (at distance $r$ on the $x$-axis) are $V_0$ and $E_0$,respectively,then the correct combination of the electric potential and electric field,respectively,at point $B$ (at distance $2r$ on the $y$-axis) is given by

The dipole moment of a system of charge $+q$ distributed uniformly on an arc of radius $R$ subtending an angle $\pi /2$ at its centre, where another charge $-q$ is placed at the centre, is:

An electric dipole is placed at an angle $60^{\circ}$ with an electric field of strength $4 \times 10^5 \,N/C$. It experiences a torque equal to $8 \sqrt{3} \,Nm$. Calculate the charge on the dipole,if the dipole length is $4 \,cm$.

$A$ neutral water molecule $(H_2O)$ in its vapor state has an electric dipole moment of magnitude $6.4 \times 10^{-30} \ C \cdot m$. How far apart are the molecule's centers of positive and negative charge?