Question 260 of 311

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$2\sqrt{\dfrac{qE}{md}}$B$\sqrt{\dfrac{2qE}{md}}$C$\sqrt{\dfrac{qE}{2md}}$D$\sqrt{\dfrac{qE}{md}}$

Show answer and solution▾

Answer: (B) $\sqrt{\dfrac{2qE}{md}}$

$\tau =pE\sin ⁡\theta$
For small angle,
$\tau =pE\theta$
$\alpha =\dfrac{\tau }{I}=\dfrac{pE}{I}\theta$
$\left(∵\alpha ={\omega }^{2}\theta \right)$ Angular frequency $=\sqrt{\dfrac{pE}{I}}$
$=\sqrt{\dfrac{\left(qd\right)E}{\left(m\dfrac{{d}^{2}}{4}+m\dfrac{{d}^{2}}{4}\right)}}$
$=\sqrt{\dfrac{2qE}{md}}$