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. zero
• B. $\frac{{\mu }_{0}ne}{2\pi r}$
• C. $\frac{{\mu }_{0}ne}{2r}$
• D. $\frac{{\mu }_0{n}^{2}e}{2r}$

Answer 1

The correct option is C $\frac{{\mu }_{0}ne}{2r}$

Current in the orbit is $I=\frac{e}{T}=\frac{e\omega }{2\pi }=\frac{e2\pi n}{2\pi }=ne$

Magnetic field at centre us
$B=\frac{{\mu }_{0}I}{2r}=\frac{{\mu }_{0}ne}{2r}$