Question

A dipole consists of two particles one with charge $+1\mu C$ and mass $1\text{kg}$ and the other with charge $-1\mu C$ and mass $2\text{kg}$ separated by a distance of 3 m. For small oscillations about its equilibrium position, the angular frequency, when placed in a uniform electric field of $20\text{kV/m}$ is

• A. $0.1\text{rad/s}$
• B. $1.1\text{rad/s}$
• C. $10\text{rad/s}$
• D. $2.5\text{rad/s}$

Answer 1

The correct option is A $0.1\text{rad/s}$


$\tau =qE2\sin \theta +qE\sin \theta$
$=3qE\sin \theta$
${\tau }_{net}=3qE\theta$
$I\alpha =3qE\theta$
$\alpha =\frac{3qE\theta }{I}......\left(1\right)$
For angular SHM $\alpha =-{\omega }^2\theta .....\left(2\right)$
From (1) and (2)
$\omega =\sqrt{\frac{3qE}{I}}$
$=\sqrt{\frac{3\times 1\times {10}^{-6}\times 20\times {10}^3}{6}}$
$=\sqrt{\frac{1}{100}}=0.1\text{rad/sec}$