Question

A electric dipole having charge $q$ and $-q$ are placed at distance ${}^{\prime }{d}^{\prime }$ is in equilibrium in a uniform electric filed $E$. Each charge has mass ${}^{\prime }{m}^{\prime }$. If dipole is displayed by small angle. Then its angular frequency of oscillation is:

• A. $\sqrt{\frac{3qE}{md}}$
• B. $\sqrt{\frac{qE}{2md}}$
• C. $\sqrt{\frac{2qE}{md}}$
• D. $\sqrt{\frac{2qE}{3md}}$

Answer 1

The correct option is C $\sqrt{\frac{2qE}{md}}$

${\omega }^2=\frac{pE}{I}=\frac{qd\left(E\right)}{\frac{m{d}^2}{4}+\frac{m{d}^2}{4}}=\frac{2qdE}{m{d}^2}$
${\omega }^2=\frac{2qE}{md}$
$\omega =\sqrt{\frac{2qE}{md}}$