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

Answer: (A)

When dipole is given a small angular displacement $\theta$ about its equilibrium position, the restoring torque will be
$\tau = -pE sin\theta $(as $ sin\theta = \theta)$
or $I \frac{d^2\theta}{dt^2} = - pE \theta $( as $\tau = I\alpha = I \frac{d^2\theta}{dt^2})$
or $\frac{d^2\theta}{dt^2} = -\omega^2 \theta$ with $\omega^2 = \frac{pE}{I} $
$\Rightarrow \omega = \sqrt{\frac{pE}{I}}$