Magnetization of steel. Magnetic permeability

 § 40. Magnetization of steel. Magnetic permeability

Ferromagnetic materials, such as iron, cobalt, nickel and their alloys, steel, etc., are widely used in various electrical machines and apparatuses to amplify the magnetic field and give it a certain shape.

If a ferromagnetic material is placed in a coil and an electric current is passed through its turns, then under the influence of the magnetic field created by the current, the material is magnetized. This means that the material has its own magnetic field, obtained as a result of the addition of magnetic fields (magnetic moments) of individual atoms.

A change in the current strength in the coil leads to a change in the strength of its magnetic field H, which causes a change in the magnetic induction B in the core of this coil.

On fig. 36 shows graphs of changes in magnetic induction depending on the intensity of the magnetizing magnetic field. Such graphs are called magnetization curves. For different materials and their grades, the magnetization curves are different. At low values ​​of the field strength H, the magnetic induction in the material increases rapidly, magnetization occurs approximately in proportion to the change in strength, and then, as the magnetic field strength increases, the increase in the magnetic induction of the material slows down.

The state of a material in which a further increase in the magnetic field strength does not lead to an increase in its magnetization is called magnetic saturation.

The magnetic properties of materials are characterized by their absolute magnetic permeability μA. It is determined by the ratio of the magnetic induction B to the magnetic field strength H and is measured in henry/meter (gn/m).

Absolute magnetic permeability of vacuum μa = 4π 10-7 gn/m. For air and other non-ferromagnetic materials, it slightly differs from μa and, in technical calculations, is taken equal to 4π · 10-7 gn/m.

Since the absolute magnetic permeability for vacuum and the above materials is practically the same, then μa is called the magnetic constant μ0.

The absolute magnetic permeability μa of ferromagnetic materials is not constant and is many times higher than the magnetic permeability of vacuum.

The number showing how many times the absolute magnetic permeability μа of a ferromagnetic material is greater than the magnetic constant μ0 is called the relative magnetic permeability μ or, in short, magnetic permeability (Table 5).

Example. Steel under certain conditions has an absolute magnetic permeability (μа = 0.0008792 gn/m. Calculate the relative magnetic permeability μ of this steel.

Solution. Magnetic constant μ0 = 4π 10-7 gn/m, then the relative magnetic permeability

As can be seen from the magnetization curves (see Fig. 36), the ability of materials to be magnetized - their magnetic permeability - is large in weak magnetic fields, and then gradually decreases with increasing induction.

Consequently, the magnetic permeability of ferromagnetic materials is a variable value, depending on the degree of their magnetization.

                                                                   Table 5

The highest relative magnetic permeability of some materials

Material                  - μ

Cobalt                    - 174

Steel Transformer - 7500

Nickel                   -1120

Permalloy C          -115 000

With the same magnetic field strength, the magnetic induction in steel is greater than in cast iron. This is due to the fact that the magnetic permeability of steel is greater than the magnetic permeability of cast iron.

The magnetic induction is directly proportional to the field strength H and the absolute magnetic permeability μa of the magnetized material:

B = μaH. (35)

Example. The magnetic field strength of the coil is H = 750 A/m, and the absolute magnetic permeability of the core is μа = 0.0008792 gn/m. Determine the magnetic induction of the core.

Solution. Magnetic induction B = μa H = 0.0008792 750 = 0.65 T. Since 1 t = 10,000 gauss, then 0.65 

T = 6500 gauss.

*******

Magnetic field strength, also calledmagnetic intensity or magnetic field intensity, the part of the magnetic field in a material that arises from an external current and is not intrinsic to the material itself. It is expressed as the vector H and is measured in units of amperes per metre. The definition of H is H = B/μ − M, where B is the magnetic flux density, a measure of the actual magnetic field within a material considered as a concentration of magnetic field lines, or flux, per unit cross-sectional area; μ is the magnetic permeability; and M is the magnetization. The magnetic field H might be thought of as the magnetic field produced by the flow of current in wires and the magnetic field B as the total magnetic field including also the contribution M made by the magnetic properties of the materials in the field. When a current flows in a wire wrapped on a soft-iron cylinder, the magnetizing field H is quite weak, but the actual average magnetic field (B) within the iron may be thousands of times stronger because B is greatlyenhanced by the alignment of the iron’s tiny natural atomic magnets in the direction of the field.

*******

Let me explain what is "surprising" about this issue, about which everyone knows and no one sees point-blank, that this is Super Singularity. Imagine the winding of a toroidal transformer with an iron core and an air frame.

The magnetic field strength H, which is created in the ring core when current I flows through the winding, can be calculated by the formula: H = N*I/l, where: N is the number of turns; I - current strength in the wire, Ampere; l is the length of the ring along the midline, meters.

Let's say we have 75 turns, with a current in the wire equal to 1 Ampere and a length of the middle line of the ring core 100 mm (0.1 meter):

H = N * I / l = 75 * 1 / 0.1 = 750 A / m

Source voltage U= 5 V, power equal to

P=UI=5*1=5W

Absolute magnetic permeability: air = 1.25663753 * 10−6 (0.000001257) gn / m, core = 0.0008792 gn / m, it remains only to calculate the magnetic induction at a magnetic field strength of the winding equal to 750 A / m:

Without core: B = μаH = 0.00000125663753 *750 = 0.000942478 T,

With a core: B = μaH = 0.0008792 * 750 = 0.6594 T.

With the same expended source power of 5 W, we obtained an increase in the resulting magnetic induction by 700 times.

Serge Rakarskiy