Question

An electron of mass \( m \) is revolving around the nucleus in a circular orbit of radius \( r \) has angular momentum \( L \). The magnetic field produced by the electron at the centre of the orbit is

• A. \( \frac{\mu_0 e L}{4 \pi m r^2} \)
• B. \( \frac{\mu_0 e L}{4 \pi m r^3} \)
• C. \( \frac{\mu_0 e L}{2 \pi m r^2} \)
• D. \( \frac{\mu_0 e L}{2 \pi m r^3} \)

Hint:

The magnetic field due to an electron revolving in a circular orbit can be calculated using the formula derived from Ampère's law and the relation between charge, current, and angular momentum.

Answer 1

The Correct Option is B

Step 1: Formula for magnetic field due to revolving electron.
The magnetic field \( B \) produced at the centre of a circular orbit by a moving electron is given by the formula: \[ B = \frac{\mu_0 e L}{4 \pi m r^3} \] where \( \mu_0 \) is the permeability of free space, \( e \) is the charge of the electron, \( L \) is the angular momentum, \( m \) is the mass of the electron, and \( r \) is the radius of the orbit.
Step 2: Conclusion.
Thus, the correct answer is (B) \( \frac{\mu_0 e L}{4 \pi m r^3} \).