Obtain the expression for the torque acting on an electric dipole in a uniform external electric field.

(N/A) Consider a permanent dipole of dipole moment $\vec{p}$ in a uniform external field $\vec{E}$.
There is a force $q\vec{E}$ on charge $+q$ and a force $-q\vec{E}$ on charge $-q$. The net force on the dipole is zero,since $\vec{E}$ is uniform.
However,the charges are separated by a distance $2a$,so the forces act at different points,resulting in a torque on the dipole.
When the net force is zero,the torque (couple) is independent of the origin.
Magnitude of torque = (Magnitude of each force) $\times$ (Perpendicular distance between the two forces)
$= qE \times (2a \sin \theta)$
$= (2qa) E \sin \theta$
Since the dipole moment $p = 2qa$,we have:
$\tau = pE \sin \theta$
In vector form,the torque is given by:
$\vec{\tau} = \vec{p} \times \vec{E}$
This torque will tend to align the dipole with the field $\vec{E}$. When $\vec{p}$ is aligned with $\vec{E}$,the torque is zero.