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In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude of torque the object experiences in a given magnetic field. When the same magnetic field is applied ...
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.
Assuming the external magnetic field is uniform and shares a common axis with the paramagnet, the extensive parameter characterizing the magnetic state is , the magnetic dipole moment of the system. The fundamental thermodynamic relation describing the system will then be of the form = (,,,).
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 ...
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 moment is a ...
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.
The Hamiltonian of a system represents the total energy of the system; that is, the sum of the kinetic and potential energies of all particles associated with the system. . The Hamiltonian takes different forms and can be simplified in some cases by taking into account the concrete characteristics of the system under analysis, such as single or several particles in the system, interaction ...
While the magnetic moments (the black arrows) are oriented the same for both cases of γ, the precession is in opposite directions. Spin and magnetic moment are in the same direction for γ > 0 (as for protons). Protons, neutrons, and many nuclei carry nuclear spin, which gives rise to a gyromagnetic ratio as above. The ratio is conventionally ...