Torque experienced by an electric dipole in the uniform electric field: Consider an electric dipole of dipole moment `vecp` placed in a uniform electric field `vecE` whose field lines are equally spaced and point in the same direction. The charge +q will experience a force `qvecE` in the direction of the field and charge -q will experience a force `-qvecE` in a direction opposite to the field. Since the external field `vecE` is uniform, the total force acting on the dipole is zero. These two forces acting at different points will constitute a couple and the dipole experience a torque. This torque tends to rotate the dipole. (Note that electric field lines of a uniform field are equally spaced and point in the same direction). The total torque on the dipole about the point O
`tau=vec(OA)xx(-qvecE)+vec(OB)xxqvecE`
Using right-hand corkscrew rule, it is found that total torque is perpendicular to the plane of the paper and is directed into it.
The magnitude of the total torque
`tau=|vec(OA)|(-qvecE)sintheta+|(vec(OB)||qvecE|sintheta`
`tau=qE 2a sintheta`
where theta is the angle made by `vecp` with `vecE`.Since p = 2aq, the torque is written in terms of the vector product as
`vectau=vecpxxvecE`
The magnitude of this torque is `tau=pEsintheta` and is maximum when `theta=90^(@)`.
This torque tends to rotate the dipole and align it with the electric field `vecE`. Once `vecp` is aligned with `vecE`, the total torque on the dipole becomes zero.
