Question

An electric dipole of momentum $\overrightarrow{p}$ is placed in a uniform electric field. The dipole is rotated through a very small angle $\theta$ from equilibrium and is released, find the time period of simple harmonic motion.

Answer 1

Whendisplacedatanangletheta,fromitsmeanpositionthemagnitudeofrestoringtorqueis

$\tau =-Psin\theta$

For small angular displacements in $\theta \approx \theta$

$\tau =-PE\theta$

$\alpha =\frac{\tau }{I}=-\frac{PE}{I}\theta =-w^2\theta$

$w^2=\frac{PE}{I}$

$T=2\pi \sqrt{\frac{IP}{E}}$