Question

An electron of charge \(e\) is revolving in a fixed orbit of radius \(r\) with frequency \(f\). Its magnetic dipole moment is

• A. \(\pi^2 efr^2\)
• B. \(\pi efr^2\)
• C. \(\pi efr\)
• D. \(\pi^2 efr\)

Hint:

For revolving charges, always remember: \[ \mu = I \times \text{Area} \]

Answer 1

The Correct Option is B

Step 1: Magnetic moment formula.
Magnetic dipole moment is given by:
\[ \mu = I \times A \]
Step 2: Calculating current.
\[ I = ef \]
Step 3: Area of circular orbit.
\[ A = \pi r^2 \]
Step 4: Substituting values.
\[ \mu = ef \times \pi r^2 = \pi efr^2 \]
Step 5: Conclusion.
The correct expression is \(\pi efr^2\).