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Larmor precession

In physics, Larmor precession (named after Joseph Larmor) is the precession of the magnetic moment of any object with a magnetic moment about an external magnetic field. Objects with magnetic moments have angular momentum and internal currents of electric charge related to their angular momentum; these include electrons, protons, other fermions, many atomic and nuclear systems, as well as classical macroscopic systems. The magnetic field exerts a torque on the magnetic moment,


τ⃗ = μ⃗ × B⃗ = γJ⃗ × B⃗

where τ⃗ is the torque, μ⃗ is the magnetic dipole moment, J⃗ is the angular momentum vector, B⃗ is the external magnetic field,  ×  symbolizes the cross product, and γ is the gyromagnetic ratio which gives the proportionality constant between the magnetic moment and the angular momentum. The phenomenon is similar to the precession of a tilted classical gyroscope in an external gravitational field.