Question

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

• A. q and m
• B. \(ω\) and m
• C. \(ω\) and q
• D. \(ω\) , q and m

Hint:

For a charge in a circular orbit, M/L = q/2m, which depends on q and m only.

Answer 1

The Correct Option is A

Step 1: Use the vector relation:
For an orbiting charge, $\vec M = \dfrac{q}{2m}\vec L$.

Step 2: Verify by dimensions:
$\dfrac{M}{L} = \dfrac{q}{2m}$ has units of C/kg, the same as charge per mass, which matches $\dfrac{\text{A m}^2}{\text{kg m}^2/\text{s}} = \dfrac{\text{C}}{\text{kg}}$.

Step 3: Conclusion:
The radius and the angular speed do not appear. Only the charge and the mass matter, so the answer is (A).

Final Answer:
Option (A). \[ \boxed{\frac{M}{L}=\frac{q}{2m} \text{ (A)}} \]