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

moment of inertia about center:

$$I=2m\left(\frac{l}{2}\right)^2=\frac{ml^2}{2}$$

For small oscillations,

$$I\omega^2=−pE_0θ$$

with

p=ql

$$\omega=\sqrt{\frac{pE_0}{I}}=\sqrt{\frac{qlE_0}{ml^2/2}}=\sqrt{\frac{2qE_0}{ml}}$$

Hence

$$T=\frac{2\pi}{\omega}$$

$$T=2\pi\sqrt{\frac{ml}{2qE_0}}$$

Create a FREE account and get:

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now

Ask our AI anything

AI can make mistakes. Please verify important information.

Download resources