magnetization - Magnetization in Maxwell's equations

Magnetic moment per unit volume, resulting from the individual magnetic moments contributed by atoms or molecules of the material; symbol M, units A/m (amps per metre); expresses how much a material is magnetized. For diamagnetic materials, magnetization opposes the external field; for paramagnetic materials, it reinforces it. In these cases, the magnetization is proportional to the external field. For ferromagnets this proportionality fails, and M can be large, even with no external field.

magnets) that describes to what extent they are affected by magnetic fields, and also determines the magnetic field that the material itself creates. The origin of the magnetic moments that create the magnetization can be either microscopic electric currents corresponding to the motion of electrons in atoms, or the spin of the electrons.

In some materials (e.g., ferromagnets) magnetization can exist even without an external magnetic field (spontaneous magnetization). In other types of materials, magnetization is induced only when an external magnetic field is present.

Magnetization in Maxwell's equations

The behavior of magnetic fields (, ), electric fields (, ), charge density (), and current density () is described by Maxwell's equations.

Relations between B, H and M

The magnetization defines the auxiliary magnetic field as

which is convenient for various calculations.

Magnetization current

The magnetization makes a contribution to the current density , known as the magnetization current or bound current:

so that the total current density that enters Maxwell's equations is given by

where is the electric current density of free charges, the second term is the contribution from the magnetization, and the last term is related to the electric polarization .

Magnetostatics

In the absence of free electric currents and time-dependent effects, Maxwell's equations describing the magnetic quantities reduce to

These equations can be easily solved in analogy with electrostatic problems where

In this sense plays the role of a "magnetic charge density" analogous to the electric charge density .

Magnetization is volume density of magnetic moment. That is: if a certain volume has magnetization then volume element dV has magnetic moment of . The diamagnetic magnetization is proportional and opposing to the applied magnetic field. The magnitude of induced magnetic moment is very small and in a direction opposite to that of applied field.Therefore, relative permeability is less than 1 and magnetic susceptibilty is negative.

Ferromagnetism

Ferromagnetic materials present a magnetization much larger than other materials. Ferromagnetic materials can be characterized by their permeability, Curie temperature (temperature of the phase change to paramagnetic behavior), coercive field (field strength needed do demagnetize the material) and remnant magnetization (magnetization at zero external field).