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From the expression for the torque on a current loop, the characteristics of the current loop are summarized in its magnetic moment
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The magnetic moment can be considered to be a vector quantity with direction perpendicular to the current loop in the right-hand-rule direction. The torque is given by
As seen in the geometry of a current loop, this torque tends to line up the magnetic moment with the magnetic field B, so this represents its lowest energy configuration. The potential energy associated with the magnetic moment is
so that the difference in energy between aligned and anti-aligned 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. Also important are nuclear magnetic moments.
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In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system (such as a
loop of electric current, a bar magnet, an electron, a molecule, or a planet) usually refers to its magnetic dipole
moment, and is a measure of the strength of the system's net magnetic source. Specifically, magnetic dipole
moment quantifies the contribution of the system's internal magnetism to the external dipolar magnetic field
produced by the system (i.e. the component of the external magnetic field that drops off with distance as the
inverse cube) !!!!!
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