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# Magnetic field intensity H and magnetic induction intensity B, magnetization intensity M and magnetic polarization intensity J

Magnetic field intensity H, magnetic induction intensity B, magnetization intensity M and magnetic polarization intensity J are four very important basic concepts. They are related but sometimes easily confused. It is very important for practitioners in the magnetic material industry to distinguish these four concepts. Today, I will explain their identities and relationships in detail for everyone who understands Cidi.

## Magnetic field intensity H

The magnetic field strength H is actually a physical quantity with no practical meaning. When people defined it previously, they assumed that there was something like a magnetic charge, but later discovered that this thing does not exist, it is just the other side of the current.
In the 1820s, scientists made a series of revolutionary discoveries, which opened up modern magnetic theory.

• The Danish physicist Hans Oster discovered in July 1820 that the current of a current-carrying wire would exert a force on the magnetic needle, causing the magnetic needle to deflect and point. (Oersted experiment-the magnetic effect of electric current)
• In September, only a week after the news arrived at the French Academy of Sciences, Ampere successfully conducted experiments to show that if the current carried in the same direction, two parallel current-carrying wires will attract each other; otherwise, the current flows in the opposite direction and parallel wires. Will be mutually exclusive.
• In 1825, Ampere published Ampere’s Law, which is a rule about the relationship between current and the direction of magnetic lines of magnetic field excited by the current.

Through the measurement of mechanics, it can be concluded that the point where the distance between the long straight wire and the wire is equal, the strength of the “magnetic field” felt by the magnetic needle is the same, and the strength of the “magnetic field” at different distances is inversely proportional to the distance. In this way, we define the physical quantity of magnetic field strength H through mechanical measurement and current intensity. Its unit is A/m. In the Gauss unit system, the unit of H is Oe Oersted, 1A/m=4π×10-3Oe.

There are many explanations for the magnetic field strength H. We can simply understand H as an external magnetic field (analogous to the electric field strength, for example, using a current I to apply a magnetic field H to an object). ## Magnetic induction intensity B

The magnetic field strength is only a magnetic field given by an external current, and for ferromagnetic materials in the magnetic field, in addition to being affected by the external magnetic field H, the particles inside the material will also generate an induced magnetic field under the action of the external magnetic field. The magnetic induction intensity B indicates that a particle “feels” the total magnetic field, which is the sum of the external magnetic field H and the induced magnetic field M at this time.
In the vacuum, the magnetic induction intensity is proportional to the external magnetic field, B=μ0H, where μ0 is the vacuum permeability. The magnetic induction intensity B=μ0(H+M) inside the ferromagnetic substance, that is, the total magnetic field is equal to the sum of μ0 times the “magnetic field H generated by the current” plus the “magnetic field M generated by the medium magnetized by H”. The unit of B is Tesla T. In the Gauss unit system, the unit is Gauss Gs, 1T=10KGs.
In fact, the magnetic induction intensity is the real “magnetic field intensity” of a magnet, but since H has been called the magnetic field intensity in history, we can only give B another name called the magnetic induction intensity. Both B and H are talking about “magnetic field strength”, but due to the different definition and derivation methods, their units are different (under the Gaussian system, the unit of B is Gauss Gs, and the unit of H is Oe, 1Oe＝1×10-4Wb·m-2＝1×10-4T＝1Gs）.
The magnetic field intensity H is the magnetic field of the void space. It does not consider the material in the space. It focuses on the relationship between the magnetic field and the source that generates the magnetic field-current, while the magnetic induction intensity B is based on the magnetic field H of the void space. After adding the actual material to the final magnetic field strength, it focuses on the actual magnetic field strength of the material. ## Magnetization M

We have just mentioned the magnetization M, which is an induced magnetic field generated by the particles inside the substance under the action of an external magnetic field. Modern physics proves that every electron in an atom is in orbital motion and spin motion around the nucleus, both of which produce magnetic effects. If the molecule is regarded as a whole, the sum of the magnetic effects generated by each electron in the molecule can be represented by an equivalent circular current. This equivalent circular current is called molecular current, and its corresponding magnetic moment is called Molecular magnetic moment, expressed in pm, is the vector sum of the magnetic moment of each electron orbit and the magnetic moment of spin in the molecule.
When there is no external magnetic field, the vector sum of the magnetic moments of all molecules in any volume element inside the magnetic medium is zero, and the substance does not show magnetism to the outside; and when the magnetic medium is in an external magnetic field, each molecule receives a moment, which The molecular magnetic moment is forced to turn to the direction of the external magnetic field. Therefore, under the action 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 degree of magnetism to the outside, or the magnetic medium is magnetized. In order to describe the magnetization state (magnetization degree and magnetization direction) of the magnetic medium, we introduce the magnetization intensity vector M, which represents the vector sum of the magnetic moments of all molecules in a unit volume, and the unit is A/m (the unit of M under the Gaussian 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. A high magnetic susceptibility means that the same external magnetic field can produce more internally induced magnetic fields; a low magnetic susceptibility means that even if the external magnetic field is large, the material inside will “be too lazy to care about it” and only have a weak response. The magnetic susceptibility can be positive or negative. The positive magnetic susceptibility χ>0 indicates that the direction of the internal magnetic field M is the same as the external magnetic field H. If the negative magnetic susceptibility χ<0, the additional magnetic field M generated by H inside the material is opposite to the external field H.

## Magnetic polarization intensity J

In the above, we introduced the magnetic induction intensity B=μ0(H+M)=μ0H+μ0M, we call μ0M the magnetic polarization intensity of the material, that is, J=μ0M, and its unit is also T (Tesla). In a physical sense, the magnetic polarization intensity J is interpreted as the magnetic dipole moment per unit volume of the magnetic medium, also known as the intrinsic magnetic induction. The symbol is Bi or J. It is not difficult to see from J=μ0M that the difference between the magnetic polarization intensity J and the refinement intensity M is only that M is multiplied by a constant μ0.
In soft magnetic materials, the value of the magnetic field intensity is usually not more than 1000A/m, μ0 is 4×10-7H/m, and J=B-μ0H, so the difference between the magnetic induction intensity B and the magnetic polarization intensity J is very small; But in hard magnetic materials, this difference is very significant, so two relationship curves B=f(H) and J=f(H) are usually given.
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