Question

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

• A. $\frac{\mu_0 n^2 e}{r}$
• B. $\frac{\mu_0 n e}{2r}$
• C. $\frac{\mu_0 n e}{2 \pi r}$
• D. Zero

Answer 1

Answer: (B)

Current in the orbit, $I=\frac{e}{T}$
$I=\frac{e}{(2 \pi/{\omega})}=\frac{\omega e}{2 \pi}=\frac{(2 \pi n)e}{2 \pi}=ne$
Magnetic field at centre of current carrying circular
coil is given by
$ \, \, \, \, B=\frac{\mu_0 I}{2r}=\frac{\mu_0 ne}{2r}$