We have to find the frequency of oscillation of an electric dipole, of moment p and rotational inertia I, for small amplitudes of oscillation about its equilibrium position in a uniform electric field E.

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We consider an electric dipole of dipole moment in an electric field . When the dipole is disturbed from its equilibrium position in electric field , it will experience a restoring torque of magnitude

.

If the displacement is small we may approximate

.

If the moment of inertia of the dipole is I, its equation of motion for small displacements will be

Equation of motion has the simple harmonic motion form

The frequency of oscillation will therefore be

.