Magnetisation

The magnetisation ($\vec{M}$) of a material is the state of magnetic polarisation due to an external magnetic field. In essence, it is the magnetic dipole moment per unit volume. In paramagnetic and diamagnetic materials, the magnetisation is sustained by the field, such that when $\vec{B}$ is removed, $\vec{M}$ disappears. For many materials, $\vec{M}\propto \vec{B}$:

$$\vec{M}={\chi }_m\vec{H}$$

where ${\chi }_m$ is the magnetic susceptibility. This is a dimensionless, material-dependent value. It’s positive for paramagnets, and negative for diamagnets. For superconductors, ${\chi }_m\approx -1$.

Any materials that obey the equation above are linear media. For instance, ferromagnets have a non-linear relation between $\vec{M}$ and $\vec{H}$.

See also

• Polarisation, the electrostatics analogue