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Susceptibility

What is magnetic susceptibility?

Magnetic susceptibility χ (Latin suscipere = to take on) describes, similar to magnetic permeability, how well a magnetic flux can penetrate a material. While permeability indicates the total flux inside a solid material, susceptibility only describes the proportion of the magnetic flux taken on by the matter. The susceptibility χ is therefore smaller by exactly 1 than the permeability μ: χ=μ-1.
Table of Contents
Susceptibility (Latin suscipere = to take on) is closely related to permeability (Latin permeare = to pass through). Susceptibility describes the magnetic polarisation at an external magnetic flux density, i.e. the magnetisation in the external magnetic field. Susceptibility is abbreviated with the Greek letter χ.

Permeability describes the entire field as it exists under the influence of polarised matter.

Determining the magnetic susceptibility

When we consider the magnetisation M of a material in an external magnetic field H0, the magnetisation is directly specified by the susceptibility χ. The following applies M= χ•H0.

The total magnetic field H is, therefore, the sum of the magnetisation and the incident magnetic field H0: H= M+H0=χ•H0+H0=(χ+1)•H0.

You can also write H=μ•H0. This equation expresses the fact that the total magnetic field inside or on the surface of matter is proportional to the incident field. The proportionality factor is the permeability. An observer would measure this field strength at the surface of the material. However, if an observer could distinguish between the part of the original incident field and the field caused by the magnetisation, he would find that the magnetisation is described precisely by the susceptibility as a proportionality factor.

Therefore, M= χ•H0 applies. The susceptibility indicates the part that has been "absorbed" by the matter. Subsequently, the sum of this part and the part originally present is the magnetic field H that is "allowed to pass through".

Therefore, H= M+H0=χ•H0+H0=(χ+1)•H0=μ•H0 applies.

And so, the simple relationship μ=χ+1 between the permeability μ and the susceptibility χ applies.

The illustration shows the course of the field lines of the magnetic field H through a para- or ferromagnetic material with (μ =2,χ=1) (links) (left) and around a superconductor with (μ =0, χ =-1) (right). The original incident field is shown as a blue arrow, and the magnetisation as a red arrow. In a ferromagnetic material, the magnetisation is positive and therefore aligned with the original field. This is always the case if χ > 0, i.e. if the material
The illustration shows the course of the field lines of the magnetic field H through a para- or ferromagnetic material with (μ =2,χ=1) (links) (left) and around a superconductor with (μ =0, χ =-1) (right). The original incident field is shown as a blue arrow, and the magnetisation as a red arrow. In a ferromagnetic material, the magnetisation is positive and therefore aligned with the original field. This is always the case if χ > 0, i.e. if the material "absorbs" the magnetic field in the same direction and thus amplifies it. In a diamagnet, on the other hand, the magnetisation is pointed in the opposite direction to the incident field. The absorbed field is negative and therefore χ < 0. While the positive field amplification can be many times greater than the incident field, negative attenuation is only possible up to the point of complete compensation of the field. This complete compensation occurs in superconductors. For the superconductor, χ = -1 applies, i.e. μ = 0. The superconductor, therefore, does not allow any field to pass through. Hence, a superconductor is a "perfect diamagnet".
The positive or negative absorption of the magnetic field can be conceptualised by considering the reason for paramagnetism, ferromagnetism or diamagnetism.

If a material has elementary magnets, so-called magnetic moments, which can align themselves in the external field (these are generally unpaired electron spins), the material itself becomes a magnet that has been "activated" by the external field. The total magnetic field can be many times greater than the incident field.

If there are no single electron spins in the material, the material has no magnetic moments. In this case, a weak effect that is always present prevails, namely diamagnetism. It corresponds to the induction of a circular current when the material is introduced into the magnetic field. According to Lenz's law, this circular current is pointed in the opposite direction to the external magnetic field (its cause) and hence the magnetisation of the diamagnet is also pointed in the opposite direction to the external field.


Portrait of Dr Franz-Josef Schmitt
Author:
Dr Franz-Josef Schmitt

Dr Franz-Josef Schmitt is a physicist and academic director of the advanced practicum in physics at Martin Luther University Halle-Wittenberg. He worked at the Technical University from 2011-2019, heading various teaching projects and the chemistry project laboratory. His research focus is time-resolved fluorescence spectroscopy in biologically active macromolecules. He is also the Managing Director of Sensoik Technologies GmbH.

The copyright for all content in this compendium (text, photos, illustrations, etc.) remains with the author, Franz-Josef Schmitt. The exclusive rights of use for this work remain with Webcraft GmbH, Switzerland (as the operator of supermagnete.nl). Without the explicit permission of Webcraft GmbH, the contents of this compendium may neither be copied nor used for any other purpose. Suggestions to improve or praise for the quality of the work should be sent via e-mail to [email protected]
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