Magnetic Susceptibility and Permeability

Magnetic susceptibility is a dimensionless constant of proportionality between magnetization and magnetic field intensity in linear magnetic media. For diamagnets, susceptibility is a small negative value around 10-5 to 10-6 and remains independent of temperature. For paramagnets, susceptibility is a small positive value of similar magnitude but temperature-dependent due to competing thermal randomization effects.

Diamagnetism arises from the orbital motion of electrons, which is independent of temperature. When diamagnetic materials are placed in an external magnetic field, induced moments oppose the field. Since this orbital mechanism does not depend on thermal energy, the susceptibility value remains stable regardless of temperature changes.

In paramagnets, an external magnetic field exerts a torque that aligns moments along the field direction, but random thermal motion produces an opposing torque that disorients them. These competing effects mean only a few moments align, making susceptibility temperature-dependent. As temperature increases, thermal randomization strengthens, reducing the net magnetization and susceptibility.

Magnetic permeability describes a material's ability to penetrate magnetic field lines. Relative permeability is the ratio of material permeability to vacuum permeability. For diamagnets, relative permeability is slightly less than unity because they repel external fields. For paramagnets, it is slightly greater than unity since they attract external fields.

Ferromagnetic materials exhibit hysteresis, meaning magnetization depends not only on the current magnetic field intensity but also on the material's magnetic history. This non-linear dependence causes susceptibility and relative permeability values to vary and remain non-constant. However, ferromagnetic relative permeability values are much larger than unity, ranging from 1,000 to 100,000.

Diamagnetic and paramagnetic materials have minimal susceptibility values around 10-5 to 10-6. Ferromagnetic materials exhibit dramatically higher susceptibility, typically 10³ to 10⁴, depending on the applied magnetic field history. This difference reflects ferromagnets' strong ability to become magnetized compared to the weak responses of diamagnets and paramagnets.

In linear magnetic media, the magnetic field is proportional to magnetic field intensity, with magnetic susceptibility determining this proportionality. The magnetic field equals the product of vacuum permeability, field intensity, and the sum of one plus susceptibility. This relationship breaks down in ferromagnets due to hysteresis effects.