Larmorprecession

Larmor precession is the phenomenon of a magnetic moment precessing around an external magnetic field. It occurs when a charged particle, such as an electron or a proton, possesses a magnetic dipole moment and is placed in a static magnetic field. The magnetic moment experiences a torque due to the interaction with the external field, causing it to rotate around the direction of the field. This rotation is analogous to the wobble of a spinning top when subjected to gravity.

The angular frequency of this precession, known as the Larmor frequency, is directly proportional to the strength of the applied magnetic field and the gyromagnetic ratio of the particle. The gyromagnetic ratio is a fundamental property of the particle that relates its magnetic moment to its angular momentum. For a free electron, this ratio is approximately 2.802 x 10^10 radians per second per tesla.

Larmor precession is a cornerstone of nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI). In these techniques, a sample is placed in a strong magnetic field, and the nuclei of its atoms, which have magnetic moments, precess at the Larmor frequency. By applying radiofrequency pulses that match this frequency, the nuclei can be excited, and their subsequent relaxation back to equilibrium emits signals that are detected and used to create detailed images or analyze molecular structures. The phenomenon also finds applications in electron paramagnetic resonance (EPR) spectroscopy and in understanding the behavior of charged particles in planetary magnetospheres.