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

If an electron is doing $n$ revolutions per second then we can say the current is,
$i=\frac{q}{T}=\frac{e}{T} \text{we know that} T=\frac{1}{n}.$
$\Rightarrow i=\frac{e}{T}=ne$

Now, magnetic field at the center of a circular loop is
$B=\frac{{\mu }_{0}i}{2r}=\frac{{\mu }_{0}ne}{2r}$