An electron moves in a circular path with a speed of $1\mathrm{.}33107$ m$/$s in the presence of a uniform magnetic field with a magnitude of $1\mathrm{.}82$ mT$.$ The electron's path is perpendicular to the field.

$($a$)$

What is the radius $($in cm$)$ of the circular path?

cm

$($b$)$

How long $($in s$)$ does it take the electron to complete one revolution?