Permeability: concept, units, factors, examples

Regarding this last point, we speak of a magnetic permeability, denoted by the symbol μ. For a material to be permeable to flow, it must undergo a momentary change induced by the flow in question or be capable of modifying the flow itself.

Magnetic field permeability through materials. Source: MarLed, French capyions removed by [1] / CC BY (

The upper image compares the magnetic permeabilities of three materials. B is the density of the magnetic flux, represented by the number of lines. H is the intensity of the external magnetic field surrounding the material. Therefore, it is observed that the bluish material is not very permeable, while the yellow and pink are to a greater extent.


The SI unit of magnetic permeability is the Henry per meter, H / m or N · A 2 . Its formula is:

μ = B / H

This is regarding magnetic permeability. But what about a more material permeability? Like that of a liquid flow trying to move through the pores of a solid or a membrane.

For example, the permeability of the rocks that make up oil fields. For these types of phenomena, the cgs unit called Darcy, D (9.86923 · 10 -23 m 2 ) is used.

Unit D is reserved especially for geological sciences and the oil industry, especially when it comes to drilling of oil reservoirs.

Relative permeability

Returning to magnetic permeability, one material will be more permeable than the other if its value of μ r is greater. In turn, this value indicates how permeable the material is compared to vacuum. So if μ r is greater than 1, it means that the material is magnetized and is very permeable to magnetic field lines.

On the other hand, if μ r is less than 1, it means that its magnetization affects or reduces the magnetic field lines. It could be said that said material is “semipermeable” to the magnetic field. Meanwhile, a μ r equal to or very close to 1, indicates that the magnetic field passes through the material without being disturbed, as occurs in a vacuum.

Factors determining permeability

Affinity for flow

For a material to be permeable it must allow the flow in question to travel through it. Also, the material must undergo a change, albeit slight, in its properties due to this flow. Or seen in another way, the material has to modify or disturb the flow.

In magnetic permeability, one material will be more permeable than the other if its magnetization is greater when experiencing the external magnetic field.

Meanwhile, in a material permeability, more typical of engineering, it is necessary for the material to “wet” from the flow. For example, a material will be permeable to a certain liquid, to say water, if its surface and interstices manage to get wet. Otherwise, the water will never travel through the material. Much less if the material is hydrophobic and always remains dry.

This “affinity” of the material for flow is the main factor that determines whether or not it will be permeable in the first place.

Size and orientation of pores

Magnetic permeability aside, the permeability of materials to liquids or gases depends not only on the affinity of the material for the flow itself, but also on the size and orientation of the pores.

After all, the pores are the internal channels through which the flow will travel. If they are very small, less volume will pass through the material. Also, if the pores are oriented perpendicular to the flow direction, their movement will be slower and more rugged.


Temperature plays an important role in the permeability of materials. This affects the way in which materials are magnetized, and also how liquids and gases move within them.

Generally, the higher the temperature, the higher the permeability, since the viscosity of liquids decreases and the speed with which gases propagate increases.

Flow intensity

Magnetic permeability is affected by the intensity of the magnetic field. This is also true for flows of liquids and gases, in which their intensity is defined by the pressure that the flow exerts on the surface of the material.

Examples of permeability

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The magnetic permeability of the soil depends on its mineral composition and its types of magnetism. On the other hand, its liquid permeability varies depending on the size of its grains and its dispositions. Take a look at the following video for example:

It compares the permeabilities for different solids. Note that clay, as it has the smallest grains, is the one that allows water to pass through it the least.

Likewise, it should be observed that the water that comes out becomes cloudy because it has wet the respective solids; except for the stones, since the interstices between them were very large.


The magnetic permeability of the vacuum is around 12.57 × 10 −7 H / m, and is denoted as μ 0 . The permeabilities of the materials or propagation media, μ, are divided by this value to obtain μ r (μ / μ 0 ).


Based on the example of iron, we will talk exclusively about magnetic permeability. For this metal pure (99.95%), its μ r is 200 000. That is, the lines of the magnetic field transmitted hundred thousand times more intense through iron than in vacuum.


The relative permeability of water is 0.999 992. That is, it hardly differs from a vacuum with regard to the propagation of the magnetic field.


The μ r of copper is 0.999 994. It is almost the same as that of water. Why? Because copper is not magnetized, and by not doing so, the magnetic field is not increased through it.


The μ r timber 43. Almost 000 is 1000 is the same as that of the vacuum, as wood magnetizations even suffer negligible because of their impurities.

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