An electric dipole with dipole moment $4\times {10}^{-9}\mathrm{C}-\mathrm{m}$ is aligned at 30° with the direction of a uniform electric field of magnitude $5\times {10}^{-9}\mathrm{N}/\mathrm{C}.$ Calculate the magnitude of the torque acting on the dipole.

Given, dipole moment,

$\mathrm{p}=4\times {10}^{-9}\mathrm{C}-\mathrm{m}$

Electric field, $\mathrm{E}=5\times {10}^4 \mathrm{N}/\mathrm{C}$

Angle between electric field and the dipole moment $\mathrm{\theta }={30}^{\mathrm{o}}$

 Torque applied on a dipole in the electric fiels,

$$\begin{gathered} \mathrm{\tau }=\mathrm{p}\times \mathrm{E}=\mathrm{pE} \sin \mathrm{\theta } \\ =4\times {10}^{-9}\times 5\times {10}^4\times \sin 30°=\frac{20\times {10}^{-5}}{2} \\ ={10}^{-4}\mathrm{N}-\mathrm{m} \end{gathered}$$

 The direction of torque is perpendicular to both electric field and dipole moment.