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# Magnetic field intensity, magnetic induction, magnetization and magnetic polarization and their relations

The four basic concepts are magnetic field strength h, magnetic induction strength B, magnetic intensity m and magnetic polarization strength J. they are related but sometimes confused. It is very important for the industry practitioners to distinguish these four concepts. This paper explains the four concepts and their relationship.

## Magnetic field strength H

The magnetic field intensity H is actually a physical quantity without practical significance. When people defined it previously, it was assumed that there was a magnetic charge, but later it was found that this thing did not exist, it was just the other side of the current.
In the 1920s, scientists had a series of revolutionary discoveries, which opened up the theory of modern magnetism.
In July 1820, Danish physicist Hans Oster found that the current of the current carrying wire would exert force on the magnetic needle, which deflected the needle to point. (auste experiment – magnetic effect of current) in September, just a week after the news arrived at the French Academy of Sciences, ampere successfully conducted experiments showing that if the current flow is the same, two parallel current carrying wires attract each other; otherwise, the parallel wires will repel each other if the current flow is the same. In 1825, ampere published Ampere law, which is the rule of the relationship between current and magnetic direction of magnetic field excited by current. Through mechanical measurement, it can be concluded that the distance between the long straight wire and the conductor is the same, the magnetic field intensity felt by the magnetic needle is the same, and the intensity of the magnetic field at different points is inversely proportional with the distance. In this way, we define the physical quantity of magnetic field intensity H by mechanical measurement and current intensity. Its unit is a/ meter m, and in Gauss unit system, h is OE OSTE, 1a/m=4 π × 10-3oe.
There are many explanations for the intensity of the magnetic field H, and we can simply understand h as an external magnetic field (similar to the electric field strength, for example, applying a magnetic field H to an object by current I).

## Magnetic induction strength B

The magnetic field strength is only a magnetic field given by the external current. For ferromagnetic materials in the magnetic field, in addition to the influence of the external magnetic field H, the particles inside the material will also produce a induced magnetic field under the action of the external magnetic field. Magnetic induction intensity B indicates that a particle “senses” the total magnetic field, which is the sum of the applied magnetic field H and the induced magnetic field M.
In vacuum, the magnetic induction intensity is proportional to the external magnetic field, b= μ 0h, where μ 0 is the vacuum permeability. The magnetic induction strength b= μ 0 (h+m) in the ferromagnetic material, that is, the total magnetic field equals μ 0 times the sum of “magnetic field H generated by current” plus “the magnetic field m produced by the magnetization of medium by H”. B is in Tesla T, and in the Gauss unit system, it is Gauss GS, 1t = 10kgs.
In fact, magnetic induction strength is the real magnetic field strength of magnet. But since h has been called magnetic field strength in history, it can only be given another name of B called magnetic induction strength. B and H are all about “magnetic field strength”, but because of different methods of definition and export, their units are different (under Gaussian system, B is Gauss GS, h is in auste, 1oe = 1 × 10-4wb · m-2 = 1 × 10-4t = 1gs).
Magnetic field intensity H is a magnetic field in void space, which does not consider the matter in space, it focuses on the relationship between magnetic field and the source of magnetic field – current. While magnetic induction strength B is considered the strength and weakness of final magnetic field after adding actual material on the basis of virtual space magnetic field H, it focuses on the actual magnetic field strength of material.

## Magnetization M

We have just mentioned the magnetization m, which is a induced magnetic field produced by the particles inside the material under the action of the external magnetic field. Modern physics has proved that every electron in an atom is orbiting and spinning around the nucleus, both of which produce magnetic effects. If the molecule is regarded as a whole, the sum of the magnetic effects of each electron in the molecule can be expressed by an equivalent circular current. The equivalent circular current is called molecular current, and its corresponding magnetic moment is called molecular magnetic moment. In PM, it is the vector sum of the magnetic moment and spin magnetic moment of each electron in the molecule.

When there is no external magnetic field, the vector sum of all molecular magnetic moments in any volume element in the magnetic medium is zero, and the material does not show magnetism; while when the magnetic medium is in the external magnetic field, each molecule is subjected to a torque, which forces the molecular magnetic moment to turn to the direction of the outer magnetic field. In the presence of the external magnetic field, the vector sum of all molecular magnetic moments in any volume element is not zero. In this way, the magnetic medium shows a certain magnetic field, or the magnetic medium is magnetized. In order to describe the magnetization state (magnetization degree and direction of magnetization) of magnetic medium, we introduce the magnetization intensity vector m, which represents the vector sum of all molecular magnetic moments in unit volume, in a/m (the unit of m under Gauss system is Gauss GS). In order to study the relationship between the induced magnetic field m and the applied field H, we define the magnetic susceptibility χ = m / h. The high magnetic susceptibility indicates that the same external magnetic field can produce more internal induced magnetic field; the magnetic susceptibility shows that even if the external magnetic field is large, the material inside is “lazy to ignore it”, and only has a weak response. The magnetic susceptibility can be positive or negative, and the positive magnetic susceptibility χ > 0 indicates that the direction of the internal magnetic field m is the same as that of the external magnetic field h. If the negative magnetic susceptibility χ < 0, the direction of the additional magnetic field m generated by the internal magnetic field H is opposite to that of the external magnetic field H.

## Magnetic polarization J

Above, we introduced the magnetic induction B = μ 0 (H + m) = μ 0h + μ 0m. We call μ 0m the magnetic polarization of matter, that is, j = μ 0m, and its unit is t (Tesla). In physical sense, the magnetic polarization J is interpreted as the magnetic dipole moment of a unit volume of magnetic medium, also known as the intrinsic magnetic induction. The symbol is bi or J. It is not difficult to see from J = μ 0m that the difference between the magnetic polarization intensity J and the refinement intensity m lies in M multiplied by a constant μ 0.
In soft magnetic materials, the value of magnetic field intensity is usually no more than 1000A / m, μ 0 is 4 × 10-7h / m, and j = B – μ 0h, so the difference between magnetic induction intensity B and magnetic polarization intensity J is very small; but in hard magnetic materials, the difference is very significant, so the two curves of B = f (H) and j = f (H) are usually given.
In order to help you better understand the three concepts of B, J and m, here are three kinds of magnetization curves and three kinds of hysteresis loops of matter, from which you can more intuitively see their relationship and differences. (due to the limitation of drawing tools and drawing level, the curve is not completely accurate. It is only for you to understand B, J and m)
Source: China Permanent Magnet Manufacturer www.rizinia.com