question_answer

An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency \[\omega \]is :- [JEE Main 8-4-2019 Afternoon]

A) \[\sqrt{\frac{qE}{2md}}\]

B) \[\sqrt{\frac{qE}{md}}\]

C) \[\sqrt{\frac{2qE}{md}}\]

D) \[\sqrt{\frac{qE}{md}}\]

Correct Answer: C

Solution :

[c]

moment of inertia \[(I)=m{{\left( \frac{d}{2} \right)}^{2}}\times 2=\frac{m{{d}^{2}}}{2}\]

Now by \[\tau =I\alpha \]

\[(qE)(dsin\theta )=\frac{m{{d}^{2}}}{2}.\alpha \]

\[\alpha =\left( \frac{2qE}{md} \right)\sin \theta \]

for small \[\theta \]

\[\Rightarrow \]\[\alpha =\left( \frac{2qE}{md} \right)\theta \]

\[\Rightarrow \]Angular frequency \[\omega =\sqrt{\frac{2qE}{md}}\]