An electric dipole of dipole moment p is placed in a uniform electric field E in stable equilibrium position. Its moment of inertia about the centroidal axis is I . If it is displaced slightly from its mean position, find the period of small oscillations.

Explanation

Let dipole be rotated by an angle `theta`, then the magnitude of torque acting on electric dipole can be written as follows :
`tau =pE sin theta`
This torque of electric force tries to realign it along the external field . It acts like restoring torque for electric dipole to oscillate.
`rArr I alpha =pE sin theta`
`rArr alpha = (pE)/I sin theta `
If `theta` is a very small angle, then we may approximate sin `theta approx theta`, hence we get :
`rArr alpha =(pE)/I theta`
In simple harmonic oscillation we can write magnitude of angular acceleration `alpha` as follows :
`|alpha|=omega^2 theta`
On comparing our result with standard equation of S.H.M., we have :
`omega^2=(pE)/I`
Time period of S.H.M is given by , `T=(2pi)/omega`, hence `T=2pisqrt(I/(pE))`