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

Answer 1

Answer: (A)

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