JEE Main & Advanced
JEE Main Paper (Held on 08-4-2019 Afternoon)
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 \[\omega =\sqrt{\frac{2qE}{md}}\]