Question

An electric dipole of mass \( m \), charge \( q \), and length \( l \) is placed in a uniform electric field \( E = E_0 \hat{i} \). When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:

• A. \( \frac{2\pi}{\frac{q m l}{q E_0}} \)
• B. \( \frac{1}{2\pi} \frac{q^2 m l}{q E_0} \)
• C. \( \frac{1}{2\pi} \frac{q m l}{2 q E_0} \)
• D. \( 2\pi \frac{q m l}{2 q E_0} \)

Hint:

For oscillations of a dipole in a uniform electric field, the time period depends on the moment of inertia of the dipole and the torque due to the electric field.

Answer 1

The Correct Option is D

The time period \( T \) for oscillations of an electric dipole in a uniform electric field is given by: \[ T = 2\pi \sqrt{\frac{I}{\tau}} \] where \( I \) is the moment of inertia and \( \tau \) is the torque. After simplifying, we find that the time period of oscillation is \( T = 2\pi \frac{q m l}{2 q E_0} \).