Question

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:
$\left[\text{Mains-2019, April 8th, Shift 2}\right]$

• A. $\sqrt{\frac{2qE}{md}}$
• B. $2\sqrt{\frac{qE}{md}}$
• C. $\sqrt{\frac{qE}{2md}}$
• D. $\sqrt{\frac{qE}{md}}$

Answer 1

The correct option is A $\sqrt{\frac{2qE}{md}}$

As we know that,

$\tau =-PE\sin \theta$

When the angle $\theta$ is very small and expressed in radians,

$\Rightarrow I\alpha =-PE\left(\theta \right)$

$\alpha =\frac{PE}{I}(-\theta )$

Comparing the above equation with $\alpha =-{\omega }^2\theta$, we get,

$\omega =\sqrt{\frac{PE}{I}}=\sqrt{\frac{qdE}{2m{\left(\frac{d}{2}\right)}^2}}=\sqrt{\frac{2qE}{md}}$

Hence, $\left(B\right)$ is the correct answer.