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Magnetic Susceptibility and Permeability

### 29.18: Magnetic Susceptibility and Permeability

In linear magnetic materials, like paramagnets and diamagnets, magnetization is proportional to the magnetic field intensity. The constant of proportionality, a dimensionless number, is called magnetic susceptibility. The value of the susceptibility depends on the type of material.

When diamagnetic materials are placed under an external magnetic field, the moments opposite to the field are induced. Hence, the susceptibility for diamagnets has a minimal negative value of 10-5–10-6. Since diamagnetism occurs due to the orbital motion of electrons independent of temperature, the susceptibility value is also independent of temperature.

For paramagnets, a torque acts on the moments under the application of an external magnetic field that tends to align the moments along the external field's direction. However, the random thermal motion of electrons produces a torque opposite to the field and tries to disorient the moments. These competing effects align only a few moments along the field direction, causing magnetization. Thus, the susceptibility is a minimal positive value of the order of 10-5 to 10-6. Since temperature causes the randomization of the moments, the susceptibility is temperature-dependent.

Magnetic permeability is a material's ability to penetrate the magnetic field lines. The ratio of material permeability to vacuum permeability is called relative permeability. Since diamagnets repel the external magnetic field, the relative permeability is slightly less than unity. However, paramagnetic materials attract the external magnetic field. Hence, the relative permeability is slightly greater than unity for paramagnets.

Ferromagnetic materials exhibit hysteresis. Thus, a non-linear dependence of magnetization on the magnetic field intensity is observed, and the susceptibility and relative permeability values are not constant. However, these values are higher compared to paramagnets at any condition. The relative permeability of ferromagnets is much larger than unity, around 1,000–100,000. The susceptibility value is usually of the order of 103 to 104, depending on the history of the applied magnetic field.