Magnetic moment

The magnetic moment of a magnet is a quantity that determines the torque it will experience in an external magnetic field. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments.

The magnetic moment may be considered to be a vector having a magnitude and direction. The direction of the magnetic moment points from the south to north pole of the magnet. The magnetic field produced by the magnet is proportional to its magnetic moment. More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, which produces the first term in the multipole expansion of a general magnetic field. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.

The magnetic moment is defined as a vector relating the aligning torque on the object from an externally applied magnetic field to the field vector itself. The relationship is given by:

where τ is the torque acting on the dipole and B is the external magnetic field, and μ is the magnetic moment.

This definition is based on how one would measure the magnetic moment, in principle, of an unknown sample.

The unit for magnetic moment is not a base unit in the International System of Units (SI). As the torque is measured in newton-meters (N·m) and the magnetic field in teslas (T), the magnetic moment is measured in newton-meters per tesla. This has equivalents in other base units:

where A is amperes and J is joules.

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