Larmor radius

The Larmor radius is the radius of gyration of a charged particle moving in a magnetic field. Balancing the Lorentz Force

$\overrightarrow{F}=q\overrightarrow{v}\times \overrightarrow{B}$

with the centripetal force, whose magnitude is

$F=\frac{m{v}^2}{r}$

One immediately obtains

$r_L=\frac{m}{q}\frac{v_{\perp }}{B}$

where only the perpendicular component of the velocity enters.