An electric dipole of moment $\overrightarrow{\mathrm{P}}$ is lying along a uniform electric field $\overrightarrow{\mathrm{E}}$ . The work done in rotating the dipole by 90° is

When an electric dipole is placed in an electric field $\overrightarrow{\mathrm{E}}$ , a torque $\overrightarrow{\mathrm{\tau }}=\overrightarrow{\mathrm{p}}\times \overrightarrow{\mathrm{E}}$ acts on it. This torque tries to rotate the dipole through an angle. 

If the dipole is rotated from an angle ${\mathrm{\theta }}_1 \mathrm{to} {\mathrm{\theta }}_2$, then work done by external force is given by 

$$\begin{gathered} \mathrm{W}=\mathrm{pE}\left({\mathrm{cos\theta }}_1-{\mathrm{cos\theta }}_2\right) \left(\mathrm{i}\right) \\ \text{ Putting }{\mathrm{\theta }}_1=0°,{\mathrm{\theta }}_2=90°\text{ in the Eq. (i), we get } \\ \mathrm{W}=\mathrm{pE}\left(\cos 0°-\cos 90°\right) \\ =\mathrm{pE}(1-0)=\mathrm{pE} \end{gathered}$$