When a dipole is placed into an existing electric field, the dipole will rotate to align itself with the electric field lines. The rotation is caused by a torque(the net force on the dipole is 0 since the force acting on the charges are equal and opposite). The torques acting on each of the charges are of the same orientation, so the total torque is given by
Example:
If the above dipole is placed into an electric field of magnitude N/C such that the fields lines are aligned with the line joining P to the dipole, what torque acts on the dipole?