The magnetic moment, alternately referred to as the magnetic dipole moment, is a vector characteristic of sources of magnetic fields, and characterises the tendency of the magnetic field source to align with an external magnetic field. The magnetic dipole moment is a characteristic of both forms of magnetic field source, namely the movement of charges (as in a current loop) and the fields produced by fundamental particles. The standard SI unit for magnetic moment is either square-meter amperes (m^2*A) or the equivalent, joules per tesla (J/T).
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Determine whether the magnetic source for which you are trying to obtain the magnetic moment is made up of moving charges. The magnetic moment is "calculated" only for magnetic sources made up from moving charges; the magnetic moment of fundamental particles must be determined experimentally.
Find the magnetic dipole moment by multiplying the current in the loop by the area, in the case of planar current loops. This is what we would expect from dimensional analysis, since the unit for magnetic moment is made up of the product of area (square meters) and current (amperes) units. The magnetic moment of an arbitrary (not necessarily planar) closed loop is calculated by finding the product of the current and the vector area integral (infinitesimal da) over the loop.
Find the magnetic moment for arbitrary charge distributions. It is more challenging, but still analytically possible. In this case, the desired quantity is found by first taking the volume integral (over the volume of the arbitrary charge distribution) in spherical coordinates of the vector cross-product of position and current density (r X J, where J is the product of charge density and linear velocity of a particular point). Dividing the result of this integral by 2 yields the magnetic dipole moment of the charge distribution.
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