Question

A particle of charge \( q \) and mass \( m \) moves in a circular orbit of radius \( r \) with angular speed \( \omega \). The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

• A. \( \omega \) and \( q \)
• B. \( q \) and \( m \)
• C. \( \omega \) and \( m \)
• D. \( q \) and \( r \)

Hint:

The ratio of magnetic moment to angular momentum depends on the charge and mass of the particle.

Answer 1

The Correct Option is B

Step 1: Magnetic Moment and Angular Momentum.
For a charged particle moving in a circular orbit, the magnetic moment \( \mu \) is given by: \[ \mu = \frac{q v r}{2} \] where \( v = r \omega \). The angular momentum \( L \) is: \[ L = m r^2 \omega \] Thus, the ratio of the magnetic moment to angular momentum depends on \( q \) and \( m \).
Step 2: Conclusion.
The correct answer is (B), \( q \) and \( m \).