Question

workdone an rotating electric dipole​

Answer 1

Torque=r x Force, here force is simply qE(since this E is uniform).

Torque=rqE sin(theta), now this rq is nothing but the dipole moment p.

Torque=pE sin(theta)

Work done by the torque is given by Integration[Torque. d(theta)] with upper limit Beta(final angle) and lower limit Alpha(initial angle).

This turns out to be, Work done=p.E

Integration[sin(theta).d(theta)] with the same limits of integration as stated above.