The magnetization vector field M represents how strongly a region of material is magnetized. It is defined as the net magnetic dipole moment per unit volume of that region. The magnetization of a uniform magnet, therefore, is a constant in the material equal to its magnetic moment, m, divided by its volume. Since the SI unit of magnetic moment is ampere-turn meter2, the SI unit of magnetization M is ampere-turn per meter which is identical to that of the H-field.
The magnetization M field of a region points in the direction of the average magnetic dipole moment in that region. Magnetization field lines, therefore, begin near the magnetic south pole and ends near the magnetic north pole. (Magnetization does not exist outside of the magnet.)
In the Amperian loop model, the magnetization is due to combining many tiny Amperian loops to form a resultant current called bound current. This bound current, then, is the source of the magnetic B field due to the magnet. (See Magnetic dipoles below and magnetic poles vs. atomic currents for more information.) Given the definition of the magnetic dipole, the magnetization field follows a similar law to that of Ampere's law:
where the integral is a line integral over any closed loop and Ib is the 'bound current' enclosed by that closed loop.
In the magnetic pole model, magnetization begins at and ends at magnetic poles. If a given region, therefore, has a net positive 'magnetic pole strength' (corresponding to a north pole) then it will have more magnetization field lines entering it than leaving it. Mathematically this is equivalent to:
where the integral is a closed surface integral over the closed surface S and qM is the 'magnetic charge' (in units of magnetic flux) enclosed by S. (A closed surface completely surrounds a region with no holes to let any field lines escape.) The negative sign occurs because the magnetization field moves from south to north.