Derive the expression for the torque acting on an electric dipole, when it is held in a uniform electric field. Identify the orientation of the dipole in the electric field, in which it attains stable equilibrium.

Explanation

Consider an electric dipole AB placed in a uniform electric field `vecE` oriented at an angle `theta` with the field.
As shown, forces qE and qE act on the two charges in mutually opposite directions. As the two forces act at two different points non-linearly, they constitute a couple whose torque is given by:

torque `tau =(qE).` Normal distance between the forces
=`qE 2a sin theta= pE sin theta " " [ :. p =q(2a)]`
The torque has a tendency to align the dipole along the direction of electric field. In vector notation, we can write that,
`vectau= vecpxxvecE.`
When electric dipole is parallel to the electric field `vecE, theta=0^(@)` and so the torque `vectau=vec0` . Moreover, potential energy of dipole [U= -pE sin `theta`] is minimum having a value U = -pE. So this represents the stable equilibrium position of dipole.