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 :

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