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 $\omega$ will be -

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

Answer 1

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

$\tau =PE\theta$
$I\propto =PE\theta$
$\propto =\frac{PE\theta }{I}$
${\omega }^2=\frac{PE}{I}$
$\omega =\sqrt{\frac{PE}{I}}.....\left(1\right)$
$I=m{\left(\frac{d}{2}\right)}^2+m{\left(\frac{d}{2}\right)}^2=\frac{m{d}^2}{2}....\left(2\right)$
$\therefore P=q\times d....\left(3\right)$
(2) and (3) into (1)
we get, $\omega =\sqrt{\frac{2qE}{md}}$