por What is relative permeability?
The relative permeability It is the measure of the capacity of a certain material to be crossed by a flow —without losing its characteristics—, with respect to that of another material that serves as a reference. It is calculated as the ratio between the permeability of the material under study and that of the reference material. Therefore, it is a dimensionless quantity.
Generally, when speaking of permeability, one thinks of a flow of fluids, commonly water. But there are also other elements capable of passing through substances, such as magnetic fields. In this case, we speak of magnetic permeability and relative magnetic permeability.
The permeability of materials is a very interesting property, regardless of the type of flow that passes through them. Thanks to it, it is possible to anticipate how these materials will behave under various circumstances.
For example, the permeability of soils is essential when building structures such as drains, pavements, and more. Even for crops, soil permeability is relevant.
For life, the permeability of cell membranes allows the cell to be selective in allowing necessary substances such as nutrients to pass through and rejecting others that may be harmful.
Regarding the relative magnetic permeability, it provides us with information about the response of materials to magnetic fields caused by magnets or live wires. Such elements abound in the technology that surrounds us, so it is worth investigating what effects they have on materials.
relative magnetic permeability
A very interesting application of electromagnetic waves is to facilitate oil prospecting. It is based on knowing how much the wave is capable of penetrating the subsoil before being attenuated by it.
This provides a good idea of the type of rocks found in a given location, since each rock has a different relative magnetic permeability, depending on its composition.
As stated at the beginning, whenever we talk about relative permeability, the term «relative» requires comparing the magnitude in question of a certain material with that of another that serves as a reference.
This is always applicable, regardless of whether it is the permeability before a liquid or before a magnetic field.
The vacuum has permeability, since electromagnetic waves have no problem moving there. It is a good idea to take it as a reference value to find the relative magnetic permeability of any material.
The permeability of the vacuum is none other than the well-known constant of the Biot-Savart law, which is used to calculate the magnetic induction vector. Its value is:
μo = 4π . 10 -7 Mt/A (Tesla . meter/Ampere).
This constant is part of nature and is linked, together with the electrical permittivity, to the value of the speed of light in a vacuum.
To find relative magnetic permeability, one must compare the magnetic response of a material in two different media, one of which is a vacuum.
In calculating magnetic induction B. of a wire in a vacuum, its magnitude was found to be:
where B is the intensity of the magnetic field, I is the intensity of the current, and r is the radial distance from the wire. If the wire is immersed in a different medium, then the magnitude of the field there will be:
And the relative permeability μr of said medium is the quotient between B and Bo: μr=B/Bo. This is a dimensionless quantity, as you can see.
Classification of materials according to their relative magnetic permeability
Relative magnetic permeability is a dimensionless and positive quantity, being the quotient of two positive quantities in turn. Remember that the magnitude of a vector is always greater than 0.
μr=B/Bo = μ/μo
μ= μr . μo
This magnitude describes how the magnetic response of a medium is, compared to the response in a vacuum. Now, the relative magnetic permeability can be equal to 1, less than 1 or greater than 1. That depends on the material in question and also on the temperature.
Obviously yes μr= 1 the medium is the void.
If it is less than 1, it is a diamagnetic material.
If it is greater than 1, but not by much, the material is paramagnetic.
And if it is much greater than 1, the material is ferromagnetic.
Temperature plays an important role in the magnetic permeability of a material. In fact, this value is not always constant. As the temperature of a material increases, it becomes disordered internally, so its magnetic response decreases.
Diamagnetic and paramagnetic materials
Diamagnetic materials respond negatively to magnetic fields and repel them. Michael Faraday (1791-1867) discovered this property in 1846, when he found that a piece of bismuth was repelled by either pole of a magnet.
Somehow, the magnetic field of the magnet induces a field in the opposite direction inside the bismuth. However, this property is not unique to this element. All materials have it to some extent.
It is possible to show that the net magnetization in a diamagnetic material depends on the characteristics of the electron. And the electron is part of the atoms of any material, so everyone can have a diamagnetic response at some point.
Water, noble gases, gold, copper and many more are diamagnetic materials.
On the other hand, paramagnetic materials have some magnetization of their own. That is why they can respond positively to the magnetic field of a magnet, for example. They have a magnetic permeability similar to the value of μo.
Close to a magnet, they can also become magnetized and become magnets on their own, but this effect disappears when the real magnet is removed from the vicinity. Aluminum and magnesium are examples of paramagnetic materials.
The Truly Magnetic Materials: Ferromagnetism
Paramagnetic substances are the most abundant in nature. But there are materials that are easily attracted to permanent magnets.
They are capable of acquiring magnetization by themselves. These are iron, nickel, cobalt and rare earths such as gadolinium and dysprosium. Furthermore, some alloys and compounds between these and other minerals are known as ferromagnetic materials.
This type of material experiences a very intense magnetic response to an external magnetic field, such as that of a magnet, for example. That’s why nickels stick to bar magnets. And in turn bar magnets stick to refrigerators.
The relative magnetic permeability of ferromagnetic materials is much greater than 1. Inside they have small magnets called magnetic dipoles. By aligning these magnetic dipoles, they intensify the magnetic effect inside ferromagnetic materials.
When these magnetic dipoles are in the presence of an external field, they quickly line up next to it and the material sticks to the magnet. Although the external field is suppressed, moving the magnet away, there is a remnant magnetization inside the material.
High temperatures cause internal disorder in all substances, producing what is called “thermal agitation”. With heat, the magnetic dipoles lose their alignment and the magnetic effect gradually disappears.
The Curie temperature is the temperature for which the magnetic effect completely disappears from a material. At this critical value, ferromagnetic substances become paramagnetic.
Devices for storing data, such as magnetic tapes and magnetic memories, use ferromagnetism. High intensity magnets are also manufactured with these materials, with many uses in research.
References
Tipler, P., Mosca, G. Physics for Science and Technology, Volume 2. Editorial Reverte.
Zapata, F. Study of mineralogies associated with the Guafita 8x oil well belonging to the Guafita field (Apure State) by means of Magnetic Susceptibility measurements and Mossbauer Spectroscopy. Degree thesis. Central University of Venezuela.