An electric dipole of moment $$p$$ is lying along a uniform electric field $$E.$$ The work done in rotating the dipole by $${90^ \circ }$$ is

Solution :
When an electric dipole is placed in an electric field $$E,$$ a torque $$\tau = p \times E$$   acts on it. This torque tries to rotate the dipole.
If the dipole is rotated from an angle $${\theta _1}$$ to $${\theta _2}$$ then work done by external force is given by
$$W = pE\left( {\cos {\theta _1} - \cos {\theta _2}} \right)\,......\left( {\text{i}} \right)$$
Putting $${\theta _1} = {0^ \circ },{\theta _2} = {90^ \circ }$$    in the Eq. (i), we get
$$\eqalign{ & W = pE\left( {\cos {0^ \circ } - \cos {{90}^ \circ }} \right) \cr & = pE\left( {1 - 0} \right) = pE \cr} $$