Question

An electron revolving round the nucleus acts as a magnetic dipole.

1. Which force provides the centripetal force for electron?

2. Write the expression for the magnetic dipole moment of electron in vector form. What is the angle between direction of the magnetic moment and direction of angular momentum?

3. A charge 2 mC is moving through a circular path of radius 0.15 m with frequency 1000 Hz. Find the magnetic moment associated with the charge path.

Answer 1

1. Electrostatic force between electron and the nucleus.

2. Vectorially

\(\overrightarrow \mu_1=\frac{-e}{2m_e}\overrightarrow I\)

The magnetic moment of the electron is opposite in direction to the angular momentum.

∴ Angle = 180°.

3. Revolving charge behaves as a current loop. Hence Magnetic field is given as

B = \(\frac{\mu_0}{2}\frac{1}{a}\)

I = \(\frac{q}{T}\) = qv = 2 × 10^-3 × 100 = 0.2 A

Magnetic moment = IA = 0.2 × π × 0.15² = 0.0141 Am.