Question

An electric dipole with dipole moment $4\times {10}^{–9}$ C m is aligned at ${30}^{\circ }$ with the direction of a uniform electric field of magnitude $5\times {10}^{4}N{C}^{–1}$. Calculate the magnitude of the torque acting on the dipole.

Answer 1

Given, dipole moment, $\overrightarrow{p}=4\times {10}^{-9}C-m$
Electric field,$\overrightarrow{E}=5\times {10}^{4}N/C$
Angle between them, $\theta ={30}^{\circ }$
Torque applied on a dipole in the electric field
$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}\Rightarrow \tau =pEsin\theta or\tau =4\times {10}^{-9}\times 5\times {10}^{4}sin{30}^{\circ }=\frac{20\times {10}^{-5}}{2}={10}^{-4}N-m$
The direction of torque is perpendicular to both electric field and dipole moment.