Spin and Orbital Motions of a Particle in a Homogeneous Magnetic Field

Abstract

The spin and orbital motions of a particle in a homogeneous magnetic field are examined in a classical approximation. Application is made to the determination of the $g$-factor anomalies of the electron and muon. It is found that the experimentally observed difference frequency between the spin and orbital motions depends on the component of particle velocity parallel to the magnetic field, and is proportional to ${(1\ensuremath{-}\frac{{{v}_{z}}^{2}}{{c}^{2}})}^{\frac{1}{2}}$, where the magnetic field defines the $z$ axis.