Understanding Magnetic Permeability

ideal knowledge base Magnetic Permeability

Magnetic Permeability is a value that expresses how a magnetic material responds to an applied magnetic field. 

If a material's internal dipoles become easily oriented to an applied magnetic field, that material is regarded as being a high-permeability material.  If the material's internal dipoles do not become easily oriented to an applied magnetic field, it is a low-permeability magnetic material.

Magnetic Permeability is simply the ability of the material to form an internal magnetic field within itself under the influence of an applied magnetic field. 

Another way to understand it is that Permeability is the ability of a material to become magnetized when exposed to a magnetic field.

But there's an even easier way to think of permeability.  If you ask the question, "How easily does the material become magnetized?", the answer has to do with the permeability of the material. The easier it is magnetized, the more permeable it is.  Keep in mind that "ease of magnetization" is different from "strength of magnetization" because most materials that become easily magnetized are not strong magnets.

The assumption is that you are trying to magnetize a material that is practical for magnetic purposes.  We could talk about the magnetic permeability of air, or of a vacuum.  The permeability of air or vacuum can be measured.  The permeability is very low, since air and vacuum don't have much mass.  However, the permeability of hard magnetic materials is also low, and there is plenty of mass.  So then, what accounts for the difference?  That will be explained below in the Permeability of Hard Magnetic Materials section.

Let's try to understand permeability better.  When we create a magnetic field with an electromagnetic coil, we have a choice to make regarding the core that goes inside the coil.  If the core is made of air- or even a vacuum- there isn't much material there to become magnetized.

Permeability of Soft Magnetic Materials

If you make the core out of a soft magnetic material like silicon steel, it is easy to magnetize, so silicon steels are regarded as very permeable.  In fact, many electromagnets and solenoids have cores made of iron or silicon steel, precisely because these materials are so permeable.

Here is a short list of soft magnetic materials:

Low-carbon steel
Silicon steel
Iron-aluminum-silicon alloys
Nickel-iron alloys
Iron-cobalt alloys
Ferrites, and amorphous alloys.

But that's not the whole story.  The permeability equation is as follows:

µ = B/H


µ = permeability
B = Flux Density, measured in Teslas or Gauss
H = Magnetizing Force, measured in Oersteds

So we can see that permeability is the flux density divided by the magnetizing force.  This means that if the Flux Density is high and the Magnetizing Force is low, the Permeability is low.  If the Flux Density is low and the Magnetizing Force is high, then the Permeability is high. 

While we're on the subject, iron and silicon steels also have low Remanence and low Coercivity, additional factors that make them great core materials.  They magnetize easily (low Coercivity) and then demagnetize easily (Low Remanence) in part because they are permeable.  Also, the silicon addition to silicon steels reduces eddy currents and improves the long-term stability of the steel so its characteristics remain the same for a long time.

Permeability of Hard Magnetic Materials

NdFeB rare earth magnets -for example-have very low permeability, because they have strong magnetic dipoles that resist an external magnetic field.  This means that these magnets strongly resist external magnetic fields, which means that they will not easily re-orient their domains while under the influence of an external magnetic field.

NdFeB magnets also have a high coercive force (Coercivity) which makes it difficult to demagnetize them.

It is typical then for low-permeability materials to be used as permanent magnets, and for high-permeability materials to be used as soft magnetic materials.  If we look at Figure 1 (below) we see typical hysteresis curves for both hard- and soft magnetic materials.

Here is a short list of hard magnetic materials:

NdFeB (Neodymium)
SmCo (Samarium Cobalt)
Alnico (Aluminum, Nickel, Cobalt Alloy)

ideal knowledge base explain Magnetic Permeability

B-H Curve of Magnetic Material. As we follow the letters from a through g we generate important magnetic data about the material that helps us understand the material's magnetic properties.

Permeability and the Hysteresis Loop

We can learn a lot about permeability of a material just by looking at the hysteresis loop.  Generally, a highly permeable material will have a tall, narrow hysteresis loop, while a low permeability material will have a wider hysteresis loop.

The shape of the hysteresis loop is governed by a variety of factors that influence the material's magnetic characteristics.  A magnetic material with a narrow hysteresis loop generally has higher permeability while a material with a wider hysteresis loop will have lower permeability. 

But a number of additional factors influence a material's hysteresis loop and identify that material's magnetic characteristics.  For example, materials with a wider hysteresis loop generally exhibit the following properties:

  • Higher Remanence (Residual Magnetism)
  • Lower Permeability
  • Higher Retentivity
  • Higher Coercive Force (Coercivity)
  • Higher Reluctance

Materials with a thinner hysteresis loop have:

  • Lower Remanence (Residual Magnetism)
  • Higher Permeability
  • Lower Retentivity
  • Lower Coercive Force (Coercivity)
  • Lower Reluctance

Why Do We Care About Magnetic Permeability?

A non-permeable material (think of air or even a vacuum) will allow magnetic field lines to enter it's space.  It has virtually no effect on its surroundings.  It does not store any energy.  A hard magnetic permeable material will not allow external field lines to enter its domain.  Hard magnets have very strongly oriented dipoles that do not easily change their orientation, while soft magnets will more easily change their orientation in the presence of an applied field.

Permeability of Selected Materials

If we view the relative permeability values of a few materials, we can make some fascinating observations.  Some materials that seem very similar actually have very different permeability values.  Highly purified iron, for example, has the highest permeability on the chart, and it's permeability is 50X's that of electrical steel.  At the other end of the spectrum is Neodymium (actually Nd2Fe14B) magnets.  It's interesting to note that the Relative Permeability of Neodymium magnets -at 1.05- is very similar to the Relative Permeability of air at 1.00.

Relative Permeability of Selected Materials

Relative Permeability of Selected Materials

Relative Permeability of Selected Materials. It's surprising to note that the permeability of an NdFeB Magnet is similar to air until we consider what is happening with the diples.

Let's Talk About Dipoles

How can we best understand these Relative Permeability values?  Remember that permeability is the ability of the material to form an internal magnetic field within itself under the influence of an applied magnetic field.  So materials that can easily orient their dipoles in the presence of an external magnetic field are permeable, and materials that do not easily orient their dipoles are not so permeable.

Pure iron (a soft magnetic material) re-orients it's dipoles easily in the presence of a magnetic field, but a Neodymium magnet maintains those dipoles in their orientation even under the influence of a strong external magnetic field. 

What's even more interesting is that the permeability of a Neodymium magnet is very close to the permeability of air.  So we have to ask the question -"How can the permeability of a dense permanent magnet material be so close to air -where there is so little mass?" 

The answer to this question comes back to our earlier premise about how materials orient their dipoles.  Neodymium magnets do not easily re-orient their dipoles in the presence of an applied magnetic field.  Air -since there is so little mass- does not have many dipoles to orient. 

So we can see that the reason Neodymium magnets have nearly the same Permeability as air is that while Neodymium magnets have a lot more dipoles than air, they only allow a very small amount of those dipoles to align to an external magnetic field.  The result is that Neodymium magnets have virtually the same Permeability as air.

Magnetic Reluctance

Magnetic Reluctance is the opposite of Magnetic Permeability.  We can think of it as magnetic resistance.  Materials that are highly permeable will have low reluctance.  Conversely, materials with low permeability will generally have low reluctance.

Test Your Knowledge

​What is Magnetic Permeability?

What is the difference between the hysteresis loop for a hard magnetic material and a soft magnetic material?

Why do Neodymium magnets have nearly the same relative permeability as air?

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