Question

The frequency of oscillation of an electric dipooemoment having dipole moment $p$ and rotationa inertia $/$ oscillating in a uniform electric field $E_0$given

• A. $\left(1/2\pi \right)\sqrt{1/pE}$
• B. $\left(1/2\pi \right)\sqrt{pE/l}$
• C. (2\pi) $\sqrt{pE/l}$
• D. (2\pi) $\sqrt{1/pE}$

Answer 1

Answer: (B)

$\left(1/2\pi \right)\sqrt{pE/l}$

$\text{Solution}:$

Let an electric dipole (charge q and -q at a distance 2a apart) placed in a uniform external electric field of strength E. Restoring torque on dipole

$\tau =-pEsin\theta =-pE\theta$ (as $\theta$ is small)

Here -ve sign shows the restoring tendency of torque

$\tau =I\alpha$

angular acceleration =$\alpha =\frac{\tau }{I}=\frac{PE}{I}\theta$

For SHM $\alpha =-{\omega }^2\theta$

comparing we get

$\omega =\sqrt{\frac{pE}{I}}$

Thus frequency of oscillations of dipole

$n=\frac{\omega }{2\pi }=\frac{1}{2\pi }\sqrt{\frac{pE}{I}}$

$\text{Hence B is the correct option}$