A uniform magnetic field B is present in a region. An electron is...

When an electron moves in a circular path in a uniform magnetic field, the magnetic force provides the necessary centripetal force.

$e v B = \dfrac{m v^2}{r}$

$m v = e B r$

According to Bohr's quantization rule, the angular momentum of the electron is an integral multiple of $\dfrac{h}{2\pi}$.

$m v r = \dfrac{n h}{2\pi}$

Substituting $m v = e B r$ into the quantization condition:

$(e B r) r = \dfrac{n h}{2\pi}$

$e B r^2 = \dfrac{n h}{2\pi}$

$r = \sqrt{\dfrac{n h}{2\pi e B}}$