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. \( \omega, q \) and \( m \)
• C. \( q \) and \( m \)
• D. \( \omega \) and \( m \)

Hint:

Orbiting charge: \begin{itemize} \item \( \mu/L = q/(2m) \) independent of radius and speed. \end{itemize}

Answer 1

The Correct Option is C

Concept: Magnetic moment of revolving charge: \[ \mu = \frac{q\omega r^2}{2} \] Angular momentum: \[ L = m\omega r^2 \] Step 1: {\color{red}Ratio.} \[ \frac{\mu}{L} = \frac{q\omega r^2 /2}{m\omega r^2} = \frac{q}{2m} \] Step 2: {\color{red}Conclusion.} Depends only on charge and mass.