Permeability

The Basics

Permeability (Latin permeare = to let through) generally refers to the permeability of matter. Accordingly, magnetic permeability μ refers to the permeability of matter to magnetic flux.

The magnitude of a magnetic field H can be expressed using the magnetic flux density B and the magnetic permeability μ.

In general, the following applies:

\(H=\frac{1}{\mu}B\).

The magnetic permability is scaled via a physical constant, the so-called magnetic field constant \(\mu_0=4\pi\cdot10^{-7}Vs/Am\). The magnetic permeability can then be defined for each material using a relative magnetic permeability (also known as the permeability number) μ_r and the magnetic field constant μ₀: μ=μ_r•μ₀.

For a vacuum, by definition, μ_r = 1 and therefore:

\(H_0=\frac{1}{\mu_0}B_0\).

The magnetic flux density in a vacuum (B₀) can be divided by the magnetic field constant μ₀ to obtain the corresponding magnetic field in a vacuum (H₀). So, in a vacuum, a magnetic flux density of B₀ = 1 tesla ( 1 Vs/m²) corresponds to a magnetic field of \(H_0=\frac{10^7}{4\pi} A/m\).

Matter influences magnetic fields in such a way that, under the influence of an external magnetic field, a magnetic flux density is formed in matter that depends on the magnetic permeabilityμ of the material. The magnetic flux density in matter is particularly high if the magnetic permeability μ is particularly high.

The permeability number μ_r can be defined by the vacuum flux density B₀ using the relationship B=μ_r•B₀. B corresponds to the magnetic flux density that arises due to the influence of matter.

With the definition B=μ_r•B₀, it follows that matter strengthens magnetic fields if μ_r is greater than 1 and weakens magnetic fields if μ_r is less than 1. Both cases are known.

Permeability of ferromagnetic materials

Ferromagnetic materials have microscopic electron spins that are aligned in an external magnetic field. This results in an additional magnetic field in the external space, which is caused by the aligned magnetic moments of the electron spins. This magnetic field can be many orders of magnitude stronger than the external magnetic field that has aligned the electron spins.

Once the electron spins are aligned, the alignment in ferromagnets is stabilised by the so-called exchange interaction. As a result, μ_r becomes very high and in special ferromagnetic materials (so-called amorphous metals) is up to μ_r = 150 000. Iron has a permeability of around μ_r = 10 000.

Strictly speaking, these integer values in the literature are always values of the relative permeability or permeability number μ_r. The term μ is often used in literature to simplify matters. However, what is actually meant is μ_r.

Permeability of paramagnetic materials

Besides the above, there are paramagnets , which also contain electron spins that can be aligned. However, in paramagnets, this alignment is not stabilised. Paramagnets are therefore only light magnetic field amplifiers. μ_r here is in the order of 1,00001.

Permeability of diamagnetic materials

Lastly, there are also diamagnets. These weaken the external magnetic field because there are no permanent resulting electron spins inside that could be aligned in the external magnetic field. Instead, when an external magnetic field penetrates, a current is induced which, according to Lenz's law, is directed in the opposite direction to its cause and therefore weakens the external magnetic field. Diamagnetism generally occurs in matter, but the diamagnetism in para- and ferromagnets is superimposed by the aligned elementary magnets.

Special case: superconductors

Superconductors are a special case. This is because superconductors have a permeability factor of zero. This means that the magnetic flux density in the superconductor disappears. Superconductors therefore have no permeability for magnetic flux. The field lines are completely displaced from the superconductor and run around it.

Superconductors are therefore also called perfect diamagnets.