Derive an expression for the work done in rotating an electric dipole of dipole moment 'p' in a uniform electric field 'E' from an orientation `theta_1" to " theta_2`.

Explanation

Consider an electric dipole of dipole moment `vecp` placed in a uniform electric field `vecE` oriented at an angle `theta` with the direction of electric field. The torque acting on the dipole is
`tau = pE sin theta`
Elementary work done in rotating the dipole further through a small angle `d theta` against the torque is
`dW = tau d theta = pE sin theta d theta`
`:.` Total work done in rotating the dipole from orientation `theta_1 " to " theta_2` will be
`W = underset(theta_1)overset(theta_2)int pE sin theta d theta= pE [ -costheta]_(theta_1)^(theta_2)=pE[cos theta_1 - costheta_2]`