An electric dipole of moment $\vec{P}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole through $\frac{\pi}{3}$ radians is:

An electric dipole with dipole moment $2 \times 10^{-10} \text{ C m}$ is aligned at an angle $30^{\circ}$ with the direction of a uniform electric field of $10^4 \text{ N C}^{-1}$. The magnitude of the torque acting on the dipole is:

An electric dipole,when placed in a uniform electric field $E$,will have minimum potential energy when the angle made by the dipole moment with the field $E$ is

$A$ dipole with two electric charges of $2 \ \mu C$ magnitude each,with separation distance $0.5 \ \mu m$,is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of $5 \ V$ is applied. Separation between the plates is $0.5 \ mm$. If the dipole is rotated by $30^{\circ}$ from the axis,it tends to realign in the direction due to a torque. The value of torque is $:$

An electric dipole with dipole moment $4 \times 10^{-9} \text{ Cm}$ is aligned at $60^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^4 \text{ NC}^{-1}$. Calculate the magnitude of the torque acting on the dipole.

$A$ and $B$ are two points on the axis and the perpendicular bisector respectively of an electric dipole. $A$ and $B$ are far away from the dipole and at equal distance from it. The electric fields at $A$ and $B$ are $\vec{E}_A$ and $\vec{E}_B$.