Q. An electric dipole is situated in an electric field of uniform intensity $E$ whose dipole moment is $p$ and moment of inertia is $I.$ If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is
A) $\left( \frac{pE}{I} \right)^{1/2}$
B) $\left( \frac{pE}{I} \right)^{3/2}$
C) $\left( \frac{I}{pE} \right)^{1/2}$
D) $\left( \frac{p}{IE} \right)^{1/2}$
Explanation
(a) When dipole is given a small angular displacement $\theta$ about it’s equilibrium position, the restoring torque will be
$\tau = - pE\sin\theta = - pE\theta\ \ \ \ \ \lbrack as\ sin\theta = \theta\rbrack$
or $I\frac{d^{2}\theta}{dt^{2}} = - pE\theta\ \ \ \left\lbrack as\ \tau = I\alpha = I\frac{d^{2}\theta}{dt^{2}} \right\rbrack$
or $\frac{d^{2}\theta}{dt^{2}} = - \omega^{2}\theta$ with $\omega^{2} = \frac{pE}{I} \Rightarrow \omega = \sqrt{\frac{pE}{I}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.