# Larmor radius

From FusionWiki

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{m v^2}{r} $

one immediately obtains

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

where only the perpendicular component of the velocity (with respect to the magnetic field) enters.