Obtain the expression of torque acting on electric dipole in uniform external electric field.

Explanation

Consider a permanent dipole of dipole moment `vecP` in a uniform external field `vecE` as shown in figure.
There is a force `-qvecE` on `-q` and a force `-qvecE` on - q. The net force on the dipole is zero, since `vecE` is uniform.
However, the charge are separated, 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) x (Perpendicular distance between the two forces)
`=qE xx 2a sin theta`
`=2qaEsin theta`
Its direction is normal to the plane of the paper, coming out of it.
`vectau = vecp xx vecE`
`therefore tau = pEsin theta`
This torque will tend to align the dipole with the field `vecE` . When `vecp` is aligned with `vecE` the torque is zero.