Larmor radius

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

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

with the centripetal force, whose magnitude is

$F={\frac {mv^{2}}{r}}$

One immediately obtains

$r_{L}={\frac {m}{q}}{\frac {v_{\perp }}{B}}$

where only the perpendicular component of the velocity enters.