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The relationship is given by: [1] = where τ is the torque acting on the dipole, B is the external magnetic field, and m is the magnetic moment. This definition is based on how one could, in principle, measure the magnetic moment of an unknown sample.
Where is the elementary magnetic moment and is the volume element; in other words, the M-field is the distribution of magnetic moments in the region or manifold concerned. This is better illustrated through the following relation: m = ∭ M d V {\displaystyle \mathbf {m} =\iiint \mathbf {M} \,\mathrm {d} V} where m is an ordinary magnetic ...
The total magnetic dipole moment resulting from both spin and orbital angular momenta of an electron is related to the total angular momentum J by a similar equation: = . The g -factor g J is known as the Landé g -factor , which can be related to g L and g S by quantum mechanics.
More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion [note 1] of a general magnetic field. Both the torque and force exerted on a magnet by an external magnetic field are proportional to that magnet's magnetic moment.
The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small [note 6] straight magnet is proportional to the magnet's strength (called its magnetic dipole moment m). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet.
The magnetic moment of an object is an intrinsic property and does not change with distance, and thus can be used to measure "how strong" a magnet is. For example, Earth possesses an enormous magnetic moment, however we are very distant from its center and experience only a tiny magnetic flux density (measured in tesla ) on its surface.
Magnetic susceptibility is a dimensionless proportionality constant that indicates the degree of magnetization of a material in response to an applied magnetic field. A related term is magnetizability, the proportion between magnetic moment and magnetic flux density. [3]
Crucially, the Larmor frequency is independent of the polar angle between the applied magnetic field and the magnetic moment direction. This is what makes it a key concept in fields such as nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR), since the precession rate does not depend on the spatial orientation of the spins.
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