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 :

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

Answer 1

Answer: (C)

$\sqrt{\frac{2qE}{md}}$

Answer 2

moment of inertia (I) $= m\left(\frac{d}{2}\right)^{2} \times2 = \frac{md^{2}}{2}$
Now by $\tau =I\alpha$
$\left(qE\right) \left(d \sin\theta\right) = \frac{md^{2}}{2}.\alpha$
$\alpha = \left(\frac{2qE}{md}\right)\sin\theta$
for small $\theta$
$\Rightarrow \alpha = \left(\frac{2qE}{md}\right)\theta$
$\Rightarrow$ Angular frequency $\omega = \sqrt{\frac{2qE}{md}}$