Question

An electric dipole of length 2 cm, when placed with its axis making an angle of ${60}^o$ with a uniform electric field, experiences a torque of $8\sqrt{3}$ Nm. Calculate the potential energy of the dipole, if it has a charge of $\pm$ 4nC.

Answer 1

Torque, $\tau =PEsin\theta =2Qlsin\theta$

Here $l$ is the length of the dipole, $Q$ is the charge and $E$ is the electric field.

Potential energy, $U=-PEcos\theta =-2Qlcos\theta$

$\frac{\tau }{U}=\frac{2Qlsin\theta }{-2Qlcos\theta }(whereP=qd)=-tan\theta \frac{\tau }{U}=-tan\theta U=\frac{\tau }{-tan{60}^0}=-\frac{8\sqrt{3}}{\sqrt{3}}=-8joule$