Larmor equation

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

where ${\displaystyle {\vec {\tau }}}$ is the torque, ${\displaystyle {\vec {\mu }}}$ is the magnetic dipole moment, ${\displaystyle {\vec {J}}}$ is the angular momentum vector, ${\displaystyle {\vec {B}}}$ is the external magnetic field, ${\displaystyle \times }$ symbolizes the cross product, and ${\displaystyle \ \gamma }$ 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 torque-exerting gravitational field.

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