Larmor radius

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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.

See also