The Classical Motion of a Rigid Charged Body in a Magnetic Field

Abstract

A frequently used classical analog to the quantum precession of a magnetic moment in a magnetic field is the motion in a uniform static magnetic field of a symmetrical rigid body charged so that the ratio of charge to mass density is uniform. In general, the figure axis of such a magnetic top both precesses and nutates, and the mechanism producing the nutation is qualitatively different from that responsible for the nutation of the familiar gravitational top. Unless the body is spherical the angular momentum vector also nutates in the course of the precession, a phenomenon caused by the deviation of the torque on the body from the customary, but here incorrect, expression M×B. The uniform precession frequency of the magnetic top is not the Larmor frequency but involves in addition terms depending on higher powers of the magnetic field, a correction which corresponds to the quadratic Zeeman effect.