An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced a

Question

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has a magnitude:

Accepted Answer

1. **Equivalent Current ($I$):** An electron (charge $e$) revolving in a circular orbit constitutes an electric current. By definition, current is the rate of flow of charge ($I = q/t$) . If the electron makes $n$ rotations per second (frequency $f = n$), the time period for one revolution is $T = 1/n$. Thus, the equivalent current is:
   $$I = \frac{e}{T} = e \cdot n$$
2. **Magnetic Field at Center ($B$):** The magnitude of the magnetic field at the center of a circular current-carrying loop of radius $r$ is derived from the Biot-Savart law and is given by:
   $$B = \frac{\mu_0 I}{2r}$$ .
3. **Calculation:** Substituting the expression for equivalent current ($I = ne$) into the magnetic field formula:
   $$B = \frac{\mu_0 (ne)}{2r}$$

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