Question

A dipole moment ‘$P$’ and moment of inertia $I$ is placed in a uniform electric field $\vec{E}$. If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is

• A. $\sqrt{\frac{PE}{I}}$
• B. $2\pi\sqrt{\frac{I}{PE}}$
• C. $ \frac {1}{2\pi} \sqrt{\frac{PE}{I}}$
• D. $ \pi \sqrt{\frac{I}{PE}}$

Answer 1

Answer: (B)

Dipole moment $= p$ electric field $= E$ centroid axis $= I$ Explanation When displaced at an angle $\theta$ from its mean position the magnitude of restoring torque is $T =$ $- p \sin \theta$ For small angular displacement $\sin \theta \approx \theta$ $ \begin{array}{l} T =- pE \theta \\ \alpha=\frac{ T }{ I }=-\left(\frac{ PE }{ I }\right) \theta \\ =- w ^2 \theta \\ w^2=\frac{P E}{I} \\ T =2 \pi \sqrt{\frac{ I }{ PE }} \\ \end{array} $ (P.E $=$ moment in electric field)