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 oscilliations is

Options

A. `((pE)/I)^(1//2)`
B. `((pE)/I)^(3//2)`
C. `(I/(pE))^(1//2)`
D. `(p/(IE))^(1//2)`

Answer

A

Explanation

Restoring torque
`tau =-pE sin theta implies tau =-pE theta " "` [As `sin theta ~~ theta` ]
`I alpha = -pE theta implies alpha = (-pE)/I theta " "....(i)`
For angular S. H. M.
`alpha =-omega^2 theta" ".....(ii)`
by (i) & (ii)
`omega^2 = (pE)/I implies omega = sqrt((pE)/I)`