An electron moving in a circular orbit of radius $r$ makes $n$ rotations per second. The magnetic field produced at the centre has magnitude
AIPMT 2015, Medium
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Current in the orbit, $I=\frac{e}{T}$
$I=\frac{e}{(2 \pi / \omega)}=\frac{\omega e}{2 \pi}=\frac{(2 \pi n) e}{2 \pi}=n e$
Magnetic field at centre of current carrying circular coil is given by
$B=\frac{\mu_{0} I}{2 r}=\frac{\mu_{0} n e}{2 r}$
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