Prove that the frequency of oscillation of an electric dipole of moment p and rotational inertia `I` for small amplitudes about its equilibrium position in a uniform electric field strength E is `1/(2pi) sqrt(((pE)/I))`

Explanation

Let an electric dipole (charge q and -q at a distance 2a apart) placed in a uniform external electric field of strength E.

Restoring torque on dipole `" " tau=-pE sin theta=-pE theta("as " theta "is small")`
Here -ve sign shows the restoring tendendency of torque `:' tau =I alpha :.` angular acceleration `=alpha=tau/I=(PE)/I theta`
For SHM `alpha=-omega^(2) theta" "` comparing we get `omega=sqrt((pE)/(I))`
Thus frequency of oscillations of dipole `n=omega/(2pi)=1/(2pi)sqrt(((pE)/I))`