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. ${\left(\frac{\text{pE}}{\text{I}}\right)}^{\text{1/2}}$
• B. ${\left(\frac{\text{pE}}{\text{I}}\right)}^{\text{3/2}}$
• C. ${\left(\frac{\text{I}}{\text{pE}}\right)}^{\text{1/2}}$
• D. ${\left(\frac{\text{p}}{\text{IE}}\right)}^{\text{1/2}}$

Answer 1

Answer: (A)

$\tau =\text{P}\times \text{E}=\text{P}\text{E}\text{sin}\theta \text{.... (i)}$
$-PEsin\theta =I\alpha$
[ $I$ is the moment of inertia and α the angular acceleration]
Since displacement is small sin $\theta \stackrel{sim}{=}\theta$
$\therefore I\alpha =-\text{PE}\theta \Rightarrow \text{α}=-\frac{\text{PE}}{\text{I}}\theta$
The angular frequency of oscillation is given by
$\omega =\sqrt{\frac{\text{PE}}{I}}$
The potential energy is lowest when the dipole moment is aligned with the field and highest when the two are antialigned.