Magnetic dipole moment (Ampère model)

Description

Far away from a magnet, its magnetic field is almost always described (to a good approximation) by a dipole field characterized by its total magnetic dipole moment, m. This is true regardless of the shape of the magnet, so long as the magnetic moment is non-zero. One characteristic of a dipole field is that the strength of the field falls off inversely with the cube of the distance from the magnet’s center.

The magnetic moment of a magnet is therefore a measure of its strength and orientation. A loop of electric current, a bar magnet, an electron, a molecule, and a planet all have magnetic moments. 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.

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 vector: it has both a magnitude and direction. The direction of the magnetic moment points from the south to north pole of a magnet (inside the magnet). For example, the direction of the magnetic moment of a bar magnet, such as the one in a compass is the direction that the north poles points toward.

In the physically correct Ampère model, magnetic dipole moments are due to infinitesimally small loops of current. For a sufficiently small loop of current, I, and area, A, the magnetic dipole moment is calculated by the shown formula