An electric dipole is placed at an angle of ${30}^{\circ }$ with an electric field intensity $2\times {10}^5\text{N/C}$. It experiences a torque equal to $4\text{N-m}$. The charge on the dipole, if the dipole length is $2\text{cm}$ is

The correct option is B $2\text{mC}$
Given:
$E=2\times {10}^5\text{N/C};\tau =4\text{N-m}$
$l=2\text{cm}=2\times {10}^{-2}\text{m}$

Torque experienced by a dipole placed in uniform electric field is
$\overrightarrow{\tau }=\overrightarrow{p}\times \overrightarrow{E}$

The magnitude of torque will be

$\tau =pE\sin \theta$

$\Rightarrow \tau =\left(ql\right)E\sin \theta$

$\Rightarrow q=\frac{\tau }{lE\sin \theta }$

$\Rightarrow q=\frac{4}{2\times {10}^{-2}\times 2\times {10}^5\times \frac{1}{2}}$

$\therefore q=2\times {10}^{-3}\text{C}=2\text{mC}$

Hence, option $\left(b\right)$ is correct.


$\begin{array}{c}\text{Why this question}?\\ \text{Tip: The torque acting on dipole is always}{\perp }_r\\ \text{to plane of}\overrightarrow{E}\text{and dipole moment vector}\left(\overrightarrow{P}\right).\end{array}$