Relative and absolute magnetic permeability
Relative and absolute magnetic permeabilityDate of publication: 24-10-2025 🕒 5 min read
Magnetism is a phenomenon that is the foundation of modern technology. Without it, there would be no Electric Motors, transformers, hard disks, magnetic resonances or modern transport systems based on magnetic levitation. Although we rarely think about it on a daily basis, the magnetic properties of materials determine the efficiency of equipment, the safety of installations, and even the quality of imaging in medicine. One of the key parameters describing these phenomena is magnetic permeability - a value, which tells, how materials interact with a magnetic field. In this article we will look at, what magnetic permeability is, what its types are and how it affects practical applications in engineering and technology.
Highlights
- Magnetic permeability (μ) describes a material's ability to conduct a magnetic field.
- Relative permeability (μr) is the ratio of μ of a material to the permeability of a vacuum (μ₀ = 4π × 10-⁷H/m).
- Substances are divided into diamagnetics (μr < 1), paramagnetics (μr > 1) and ferromagnets (μr ≫ 1).
- High magnetic permeability allows the construction of efficient transformers, solenoids and magnetic screens.
- The highest values are reached by soft magnetic alloys, such as permalloy and mumetal.
- Magnetic properties depend on temperature, the crystal structure and processing of the material.
Causes of magnetism and basic properties
Magnetism is one of the fundamental physical phenomena, the source of which is electromagnetic interactions at the atomic level. The key role is played by the motion of electrons - both orbital, as well as spin. Orbital motion around the nucleus creates microscopic electric currents that generate the magnetic field, while the spin of the electron is responsible for the formation of elementary magnetic moments. In atoms, in which the electrons are paired, the spins cancel each other out. In the case of unpaired electrons, the magnetic moments do not compensate for each other, which leads to the appearance of macroscopic magnetism.
Macroscopic magnetic properties depend on the collective behavior of electrons in the crystal. An important role is played by the exchange interaction, which is responsible for the ordering of spins in ferromagnetics, and the spin-orbit interaction, which determines magnetic anisotropy. The influence of temperature is equally important - as the thermal energy increases, the ordering of spins disappears, and above the Curie temperature ferromagnets lose their properties and become paramagnets.
The basic parameters describing magnetism include: magnetic moment (μ), magnetization (M), magnetic induction (B), and magnetic susceptibility (χ). The relationship between them is described by the equation B = μ₀(H + M). Magnetic susceptibility, which is the ratio of magnetization to external field strength (χ = M/H), is a key parameter determining the magnetic permeability of materials.
Division of magnetic substances and bodies
Magnetic substances differ in their response to an external field, which is reflected in the relative magnetic permeability (μr).
- Diamagnetics have μr less than unity and are weakly repelled by the field - these include copper, silver, gold, bismuth or water.
- Paramagnetics have permeabilities slightly greater than unity and are weakly attracted - examples include aluminum, platinum or oxygen. Their susceptibility decreases with increasing temperature, according to the Curie-Weiss law (χ = C / (T - Tc)).
- The strongest interaction with the magnetic field is with ferromagnets. They have a relative permeability much greater than unity, can be permanently magnetized and lose these properties only above the Curie temperature. This group includes, among others.inter alia. iron, cobalt and nickel.
Magnetic permeability - meaning and types
Magnetic permeability μ determines, how a given material reacts to a magnetic field. The basic reference value is the absolute permeability of the vacuum μ₀, which is a universal physical constant equal to 4π × 10-⁷H/m. Based on it, the relative magnetic permeability μr is defined, which is the ratio of the permeability of the material to the permeability of the vacuum.
In practice, several types of this parameter are distinguished. Initial permeability applies to very weak fields, maximum permeability is the highest value achieved in the magnetization process, while relative permeability is the most commonly used comparative quantity. High permeability means, that the magnetic field lines "prefer" to pass through a given material instead of through a vacuum. This is why the cores of of transformers are made of materials with high μr, which allows to efficiently conduct the field and minimize energy losses.
Effect of structure and processing
The magnetic properties of materials depend not only on their chemical composition, but also on the mechanical processing. Bending or rolling changes the crystal structure of the metal, which lowers its magnetic permeability and increases its magnetic hardness. An example is stainless steels. Austenitic steels (e.g. 304, 316) are generally non-magnetic, and their μr is close to unity, although they may locally exhibit magnetism after cold working. Ferritic steels (e.g. 430) are typical ferromagnets with high permeability, therefore they strongly attract a magnet.
Demagnetization
In many applications it is necessary to remove residual magnetism, i.e. demagnetization. It consists in dispersion of the ordering of magnetic domains, which makes it impossible to continue acting as a magnet. In industry this applies for example to. tools made of steel, which cannot attract shavings, in medicine - surgical tools, which must be non-magnetic, and in electronics - cores coils or shielding elements. Demagnetization is carried out by heating the material above the Curie temperature or by applying an alternating magnetic field of decreasing amplitude.
Magnetic properties and examples of materials
Paramagnetics (μr > 1) are weakly attracted, diamagnetics (μr < 1) – słabo odpychane, while ferromagnets (μr ≫ 1) react very strongly and can reach permeabilities in the hundreds of thousands. The highest values are obtained by soft magnetic materials, such as permalloy or mumetal, whose μr reaches 100,000-500 000. For comparison, air has a permeability almost identical to vacuum - μr ≈ 1,00000037. Typical values of permeability are: approx 0,999994 for copper, 1,000022 for aluminum, about 600 for nickel and about 5000 for pure iron.
Table of magnetic permeabilities of selected materials
The magnetic permeability table below shows typical values of relative magnetic permeability for different classes of materials.
| Material | Type of magnetism | Relative magnetic permeability (μr) |
|---|---|---|
| Bismuth | Diamagnetic | 0,999834 |
| Copper | Diamagnetic | 0,999994 |
| Water | Diamagnetic | 0,999992 |
| Vacuum ( | Reference) | 1 (exactly) |
| Air | Paramagnetic | 1,00000037 |
| Aluminum | Paramagnetic | 1,000022 |
| Platinum | Paramagnetic | 1,000265 |
| Cobalt | Ferromagnetic | ~250 |
| Nickel | Ferromagnetic | ~600 |
| Steel | Ferromagnetic | ~1 500 |
| Iron (99.8% purity) | Ferromagnetic | ~5 000 |
| Permalloy (78% Ni, 22% Fe) | Ferromagnetic | ~100 000 |
| Mu}-metal | Ferromagnetic | ~100 000 - 500 000 |
Significance and prospects
Knowledge and control of magnetic permeability are of great practical importance. In power engineering, suitable materials ensure high efficiency of transformers and generators. In medicine, austenitic steels are used in magnetic resonance and surgery. In electronics, precise control of magnetism underlies the operation of hall Sensors, magnetic memories or field shielding.
Research focuses on new alloys and composites, magnetic nanostructures and the use of magnetism in green energy. Of particular interest are spintronics and topological materials, which could revolutionize electronics.
Magnetism is thus not only a subject of theoretical research, but also the foundation of modern technology. From simple compasses, by electric machines, to advanced medical devices, control of magnetic properties paves the way for further innovations.
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