Torque experienced by an electric dipole in the uniform electric field:
Consider an electric dipole of dipole moment \(\vec p\) placed in a uniform electric field \(\vec E\) whose field lines are equally spaced and point in the same direction. The charge +q will experience a force q \(\vec E\) in the direction of the field and charge -q will experience a force -q \(\vec E\) in a direction opposite to the field. Since the external field \(\vec E\) 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.
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
where θ is the angle made by \(\vec p\)with \(\vec E\).
Since p = 2aq, the torque is written in terms of the vector product as \(\vec {\tau}\) = \(\vec p\)x \(\vec E\)
The magnitude of this torque is τ = pE sin θ and is maximum when θ =90°.
This torque tends to rotate the dipole and align it with the electric field. Once \(\vec p \) is aligned with \(\vec E\), the total torque on the dipole becomes zero.
