Question

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. ${\left(\frac{p}{IE}\right)}^{1/2}$

Answer 1

The correct option is A ${\left(\frac{pE}{I}\right)}^{1/2}$

When dipole is given a small angular displacement $\theta$ about it's equilibrium position, the restoring torque will be
$\tau =-pEsin\theta =-pE\theta$ (as $sin\theta =\theta$)
or $I\frac{d^2\theta }{d{t}^2}=-pE\theta$ (as $\tau =I\alpha =I\frac{d^2\theta }{d{t}^2}$)
or $\frac{d^2\theta }{d{t}^2}=-{\omega }^2\theta$ with ${\omega }^2=\frac{pE}{I}\Rightarrow \omega =\sqrt{\frac{pE}{I}}$