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

(1) ${\left(\frac{pE}{I}\right)}^{1/2}$

(2) ${\left(\frac{pE}{I}\right)}^{3/2}$

(3) ${\left(\frac{I}{pE}\right)}^{1/2}$

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

(1) When dipole is given a small angular displacement θ about it's equilibrium position, the restoring torque will be

$\tau =-\text{\hspace{0.17em}}pE\mathrm{sin}\theta =-\text{\hspace{0.17em}}pE\theta$   (as sinθ = θ)

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}$$\omega =\sqrt{\frac{pE}{I}}$

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