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.

Options

A. `pi sqrt(I/(pE))`
B. `2pi sqrt(I/(pE))`
C. `pi sqrt((2I)/(pE))`
D. `2pi sqrt((2I)/(pE))`

Answer

B

Explanation

When displaced at an angle `theta` from its mean position, the magnitude of restoring torque is
`tau=-pE sintheta`
For small angular displacement `sintheta~~theta`
`tau=-pE theta`
The angular acceleration is `alpha=tau/I=-((pE)/I)theta=omega^2theta`
where `omega^2=(pE)/Iimplies T=(2pi)/omega=2pi sqrt(I/(pE))`