Question

An electron revolving in circular orbit of radius \( r \) with velocity \( v \) and frequency \( \nu \) has orbital magnetic moment \( M \). If the frequency of revolution is doubled, then the new magnetic moment will be

• A. \( \dfrac{M}{4} \)
• B. \( 2M \)
• C. \( M \)
• D. \( \dfrac{M}{2} \)

Hint:

Orbital magnetic moment is directly proportional to frequency of revolution.

Answer 1

The Correct Option is B

Step 1: Write formula for orbital magnetic moment.
\[ M = I \times A \]
Step 2: Express current in terms of frequency.
\[ I = e\nu \]
Step 3: Area of orbit.
\[ A = \pi r^2 \]
Step 4: Write magnetic moment.
\[ M = e\nu \pi r^2 \]
Step 5: Effect of doubling frequency.
If \( \nu \to 2\nu \), then \[ M' = e(2\nu)\pi r^2 = 2M \]
Step 6: Conclusion.
The new magnetic moment becomes \( 2M \).