# What is Magnetic Permeability?

Magnetic permeability is a material property that describes the change in the magnetic field inside a material compared with the magnetization field in which it is located [1][2]. In other words, it indicates how easily a material is affected by an induced magnetic field.

The use of this material property has a high significance in diverse industries. Applications such as electromagnets, transformers, and inductors use materials with significantly high magnetic permeability values.

• What magnetic permeability is
• How materials classify based on their magnetic permeability
• Magnetic permeability measurements
• Current and future applications of magnetic permeability

## What is magnetic permeability?

When a material is subjected to a magnetic field, it tends to reorient in the direction of the applied field, which generates an induced magnetization process. The effect of in the induced magnetization into the magnetic flux can be described using the magnetic permeability as follows:

\mu =\frac{B}{H}

where \mu is the absolute permeability of the medium, B is the magnetic flux, and H is the induced magnetic field [1][2]. The value of m also represents the slope of the B-H curve, known as the magnetization curve [3]. The magnetic properties are also usually represented by the concept of relative magnetic permeability, defined as \mu_r=\frac{\mu}{\mu_0}, where \mu_0 is the permeability of the free space with a value of 4\pi \times 10^{-7} weber per ampere-meter (Wb/A.m) [1]. For free-space or vacuum, the value of the relative magnetic permeability is \mu_r= 1. The concept of relative magnetic permeability helps to quantify the change of the induced magnetization in the magnetic flux [2][3].

## Classification of materials based on magnetic permeability

Materials can be classified based on their relative magnetic permeabilities as:

• Non-permeable
• Diamagnetic
• Paramagnetic
• Ferromagnetic

Description and examples of materials based on this classification are shown in the table below [1][2].

Table 1. Material classifications based on their relative magnetic permeability.

 Material Type Description Relative magnetic permeability Examples of Materials Non-permeable Repel or provide opposition to the induced magnetic field \mu_r =1 Copper Aluminium Platinum Hydrogen Glass Diamond Teflon Concrete (dry) Wood Air Diamagnetic Weakly attracted by the magnetic field with constant relative permeability values lower than 1 \mu_r < 1 Bismuth Graphite Sapphire Copper Pyrolytic carbon Water Superconductors Paramagnetic Strongly attracted by the magnetic field with constant relative permeability values slightly higher than 1 1 < \mu_r < 100 Magnesium Molybdenum Tantalum Ferrite (Nickel Zinc) Lithium Ferromagnetic Strongly attracted by the magnetic field with nonlinear relative permeability values \mu_r ≥ 100 Iron Nickel Cobalt Steel Alloys

## Magnetic permeability measurements

Determining the magnetic permeability of a material is not an easy task as it depends on the value of the applied magnetic field, and this field has a history. Generally, the magnetic permeability is measured by using entirely magnetic methods. Other methods depend mainly on the type of sample. Some of the most common methods include [4]:

• The reflection method: used to measure permeability spectra of thin magnetic films and other small specimens
• The eddy current technique: used to measure the permeability of metallic plates, tubes, and pipes
• The inductance method: used to measure effective permeability of planar spirals or cylinders.

## Applications of magnetic permeability

The main application of magnetic permeability is the characterization of magnetic materials. Magnetic materials are defined by their magnetization curve (B vs. H) and relative magnetic permeability (\mu_r). Magnetic materials are generally associated with ferromagnetic materials as these exhibit significantly high magnetic permeability values \mu_r≥100.

Magnetic materials constitute key pieces in technology applications for industries, such as [5]:

• Generation, distribution and conversion of energy
• Storage and retrieval of information
• Media and telecommunications

One of the oldest known applications of a magnetic material is the compass, which was invented in the 200’s B.C. in China. The magnetic compass used a piece of magnetized lodestone, also known as magnetite, and was used for centuries as a navigation tool. Later with the discovery of electromagnetism, other applications were introduced related to the production of electricity such as generators. Another key technological application was the invention of the magnetic tape that was used to store information in a magnetic wire or tape. The magnetic tape opened the door to many other applications in computer technology. The recent applications of magnetic materials are based on nanostructured materials. Examples of these include thin films, multilayer structures, and nanowires [6].

## Sources

[1] GeoSci Developers, “Magnetic Permeability”, [Online].

[2] Encyclopedia Britannica (2020), “Magnetic permeability”, [Online].

[3] Regtien, P. Dertien, E. (2018), "Inductive and magnetic sensors", Sensors for Mechatronics, 2nd Edition, [Online].

[4] Ciu, Z., Zhang, W., and Wang, H. (2018), "Magnetic permeability measurement method for particle materials", EEE International Instrumentation and Measurement Technology Conference.

[5] Anglada, J.R. et al. (2018), "On the importance of magnetic material characterization for the design of particle accelerator magnets", Journal of Physics, Conference Series 1065, 052045 [Online].

[6] Morup, S. and Frandsen, C. (2019), Magnetic nanoparticles, Comprehensive Nanoscience and Nanotechnology, Second Edition, vol1, p. 89-140

## Fun Facts

• The term permeability in electromagnetism was proposed in 1885 by the English mathematician and physicist Oliver Heaviside, who is known for shaping the equations of Maxwell’s electromagnetic theory after about 50 years of Maxwell’s death [a].
• Most common materials considered non-magnetic (i.e., water, wood, plants...) are, in fact, very weakly diamagnetic. The forces produced in diamagnetism are very weak and significantly smaller than forces between magnets. Under certain arrangements, the influence of diamagnetic materials can make the effect of levitation possible [b].

[a] Hunt, B., Oliver Heaviside: A first-rate oddity, Physics Today, November 201, [Online].

[b] Simon M.D. and Geim A.K., 2000, Diamagnetic Levitation: Flying frogs and floating magnets (invited), Journal of Applied Physics, Vol 87, n9, May [Online]