Q 12-01-144JEE MainJEE Main 2019 (8 Apr, Shift 2)Medium
An electric dipole is formed by two equal and opposite charges $q$ with separation $d$. The charges have same mass $m$. It is kept in a uniform electric field $E$. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is
Answer: (B) $\sqrt{\dfrac{2qE}{md}}$
The dipole rotates about its centre. Moment of inertia: $I = 2m\left(\frac d2\right)^2 = \dfrac{md^2}{2}$.
Restoring torque for a small angle: $\tau = -pE\sin\theta \approx -qdE\,\theta$.
$$\omega = \sqrt{\frac{qdE}{md^2/2}} = \sqrt{\frac{2qE}{md}}$$
Solution by Sreeraj P, M.Sc Physics