Electrostatics Question 670
Question: An electric dipole is situated in an electric field of uniform intensity $ E $ whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is
Options:
A) $ {{( \frac{pE}{l} )}^{1/2}} $
B) $ {{( \frac{pE}{l} )}^{3/2}} $
C) $ {{( \frac{l}{pE} )}^{1/2}} $
D) $ {{( \frac{p}{lE} )}^{1/2}} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] When dipole is given a small angular displacement $ \theta $ about its equilibrium position, the restoring torque will be $ \tau =-pE\sin \theta =-pE\theta (assin\theta =\theta ) $
or $ I\frac{d^{2}\theta }{dt^{2}}=-pE\theta (as\tau =I\alpha =I\frac{d^{2}\theta }{dt^{2}}) $
or $ \frac{d^{2}\theta }{dt^{2}}=-{{\omega }^{2}}\theta \text{with}{{\omega }^{2}}=\frac{pE}{I}\Rightarrow \omega =\sqrt{\frac{pE}{I}} $
