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The Larmor formula can only be used for non-relativistic particles, which limits its usefulness. The Liénard-Wiechert potential is a more comprehensive formula that must be employed for particles travelling at relativistic speeds. In certain situations, more intricate calculations including numerical techniques or perturbation theory could be ...
Larmor precession is important in nuclear magnetic resonance, magnetic resonance imaging, electron paramagnetic resonance, muon spin resonance, and neutron spin echo. It is also important for the alignment of cosmic dust grains, which is a cause of the polarization of starlight .
The derivation of this relation is as follows. It suffices to demonstrate this for an infinitesimally narrow circular ring within the body, as the general result then follows from an integration . Suppose the ring has radius r , area A = πr 2 , mass m , charge q , and angular momentum L = mvr .
The derivation given here was first published by J. J. Thomson (discoverer of the electron) in 1907. It is derived for the special case where the final velocity of the particle is zero but the Larmor formula is true for any sort of accelerated motion provided that the speed of the particle is always much less than the speed of light.
Two pairs of gauge transformed potentials (φ, A) and (φ′, A′) are called gauge equivalent, and the freedom to select any pair of potentials in its gauge equivalence class is called gauge freedom. Again by the Poincaré lemma (and under its assumptions), gauge freedom is the only source of indeterminacy, so the field formulation is ...
Note that this formula applies only for non-relativistic velocities. Physically, a time changing magnetic moment emits radiation similar to the Larmor formula of an accelerating charge. Since momentum is conserved, the magnetic moment is pushed in the direction opposite the direction of the emitted radiation.
The operating (or Larmor) frequency of a magnet (usually quoted as absolute value in MHz) is calculated from the Larmor equation [4] =, where B 0 is the induction of the magnet (SI units of tesla), and is the magnetogyric ratio of the nucleus — an empirically measured fundamental constant determined by the details of the structure of each nucleus.
The theory of special relativity plays an important role in the modern theory of classical electromagnetism.It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transformation from one inertial frame of reference to another.