Question

A uniform magnetic field B exists in a region. An electron projected perpendicular to the field goes in a circle. Assuming Bohr's quantization rule, calculate the radius of $n$th orbit and the minimum possible speed of electron.

Answer 1

$r=\frac{mv}{eB}$ From Bohr's theory
$mvr=nh$ or $mv=\frac{nh}{r}$
Thus $r=\frac{nh}{reB}$ or r=$\sqrt{\frac{nh}{eB}}$ and $v=\frac{nh}{mr}$=$\frac{nh}{m\sqrt{\frac{nh}{eB}}}$
$v=\sqrt{\frac{nheB}{m^2}}$