Question

Magnetic moment ($\mu$) for an electron moving in a circular path of radius $r$ with frequency $\nu$ is:

• A. $e\nu\pi r^{2}$
• B. $e\nu/r$
• C. $\pi r^{2}/e\nu$
• D. $2\pi r e\nu$

Hint:

Moving charge acts as a current loop; Magnetic Moment = Current $\times$ Area.

Answer 1

The Correct Option is A

Step 1: Concept
Magnetic moment $\mu = IA$.
Step 2: Analysis
Current $I = e/T = e\nu$. Area $A = \pi r^{2}$.
Step 3: Conclusion
$\mu = (e\nu)(\pi r^{2}) = e\nu\pi r^{2}$.
Final Answer: (A)