When a torque is exerted perpendicular to the angular momentum L, it produces a change in angular momentum ΔL which is perpendicular to L, causing it to precess about the z axis. Labeling the precession angle as φ, we can describe the effect of the torque as follows:
The precession angular velocity (Larmor frequency) is
These relationships for a finite current loop extend to the magnetic dipoles of electron orbits and to the intrinsic magnetic moment associated with electron spin. There is also a characteristic Larmor frequency for nuclear spins.
In the case of the electron spin precession, the angular frequency associated with the spin transition is usually written in the general form
where g is called the gyromagetic ratio (sometimes the magnetogyric ratio). This angular frequency is associated with the "spin flip" or spin transition, involving an energy change of 2μB. An example for magnetic field 1 Tesla follows.
The characteristic frequencies associated with electron spin are employed in electron spin resonance (ESR) experiments, and those associated with the nuclear spin in nuclear magnetic resonance (NMR) experiments.
Magnetic force applications
Magnetic field concepts
Rohlf, Sec 8-4