Question

A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass ‘m’ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance ‘l’. If the dipole is placed in a uniform electric field ‘\(\overrightarrow{E}\); such a way that dipole axis makes a very small angle with the electric field, ‘\(\overrightarrow{E}\)'. The angular frequency of the oscillations of the dipole when released is given by.

• A. \(\sqrt{\frac{4qE}{3ml}}\)
• B. \(\sqrt{\frac{8qE}{3ml}}\)
• C. \(\sqrt{\frac{4qE}{ml}}\)
• D. \(\sqrt{\frac{8qE}{ml}}\)

Answer 1

The Correct Option is A

In this case, since masses of both charges are not the same, we need to find center of mass (COM), about which dipole will oscillate and then we will find moment of inertia about this axis, to find torque and hence angular frequency \( \omega \). Given, the mass of positive charge is \(m\), so the center of mass will be at a distance \(L\) from the negative charge: \[ \frac{L}{3} = \frac{2m}{3m} = \frac{2L}{3} \] The moment of inertia about the axis is \(I = \frac{2mL^2}{3}\). Hence, angular frequency: \[ \omega = \sqrt{\frac{qE}{I}} = \frac{4qE}{3ml} \]