Question

An electric dipole of dipole moment p and rotational inertia I is allowed to oscillate about its equilibrium position in a uniform electric field E. Then, for small amplitudes the frequency of oscillation will be

• A. $\sqrt{pE/I}$
• B. $\sqrt{I/pE}$
• C. $\frac{1}{2\pi }\sqrt{pE/I}$
• D. $2\pi \sqrt{pE/I}$

Answer 1

The correct option is C $\frac{1}{2\pi }\sqrt{pE/I}$

$pE\sin \theta =I\alpha$

For small angles $\sin \theta =\theta$

$\frac{pE}{I}\theta =\alpha$

Time period for the dipole oscillations is $T=\frac{2\pi }{\sqrt{\frac{pE}{I}}}$

Thus the frequency of the dipole oscillation is $f=\frac{1}{T}=\frac{\sqrt{\frac{pE}{I}}}{2\pi }$