Question

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

Answer 1

Correct Answer - a
When dipole is given a small angular displacement `theta` about its equilibrium position, the restoring torque will be
`tau= -pE sin theta= -pE theta(as sin theta= theta)`
or `I(d^(2)theta)/(dt^(2))= -pE theta(as tau= I alpha= 1 (d^(2)theta)/(dt^(2)))`
or `(d^(2)theta)/(dt^(2))= -omega^(2) theta` with `omega^(2)= (pE)/(I)implies omega= sqrt((pE)/(I))`