Magnetic permeability of air than steel. Magnetic properties of matter

6. MAGNETIC MATERIALS

All substances are magnetic and are magnetized in an external magnetic field.

Based on their magnetic properties, materials are divided into weakly magnetic ( diamagnetic materials And paramagnets) and highly magnetic ( ferromagnets And ferrimagnets).

Diamagnetsμ r < 1, значение которой не зависит от напряженности внешнего magnetic field. Diamagnets are substances whose atoms (molecules) in the absence of a magnetizing field have a magnetic moment equal to zero: hydrogen, inert gases, most organic compounds and some metals ( Cu, Zn, Ag, Au, Hg), as well as IN i, Ga, Sb.

Paramagnets– substances with magnetic permeabilityμ r> 1, which is weak fields does not depend on the strength of the external magnetic field. Paramagnetic substances include substances whose atoms (molecules) in the absence of a magnetizing field have a magnetic moment different from zero: oxygen, nitrogen oxide, salts of iron, cobalt, nickel and rare earth elements, alkali metals, aluminum, platinum.

Diamagnetic and paramagnetic materials have magnetic permeabilityμ ris close to unity. Application in technology as magnetic materials is limited.

In highly magnetic materials, the magnetic permeability is significantly greater than unity (μ r >> 1) and depends on the magnetic field strength. These include: iron, nickel, cobalt and their alloys, as well as alloys of chromium and manganese, gadolinium, ferrites of various compositions.

6.1. Magnetic characteristics of materials

The magnetic properties of materials are assessed by physical quantities called magnetic characteristics.

Magnetic permeability

Distinguish relative And absolute magnetic permeabilities substances (materials) that are interconnected by the relationship

μa = μ o ·μ, Gn/m

μ o– magnetic constant,μ o = 4π ·10 -7 H/m;

μ – relative magnetic permeability (dimensionless quantity).

Relative magnetic permeability is used to describe the properties of magnetic materials.μ (more often called magnetic permeability), and for practical calculations, absolute magnetic permeability is usedμa, calculated by the equation

μa = IN /N,Gn/m

N– intensity of the magnetizing (external) magnetic field, A/m

IN – magnetic field induction in a magnet.

Large valueμ shows that the material is easily magnetized in weak and strong magnetic fields. The magnetic permeability of most magnets depends on the strength of the magnetizing magnetic field.

To characterize magnetic properties, a dimensionless quantity called magnetic susceptibility χ .

μ = 1 + χ

Temperature coefficient of magnetic permeability

The magnetic properties of a substance depend on temperatureμ = μ (T) .

To describe the nature of the changemagnetic properties with temperatureuse the temperature coefficient of magnetic permeability.

Dependence of the magnetic susceptibility of paramagnetic materials on temperatureTdescribed by Curie's law

Where C - Curie constant .

Magnetic characteristics of ferromagnets

The dependence of the magnetic properties of ferromagnets has more complex character, shown in the figure, and reaches a maximum at a temperature close toQ To.

The temperature at which the magnetic susceptibility decreases sharply, almost to zero, is called the Curie temperature -Q To. At temperatures higherQ To the process of magnetization of a ferromagnet is disrupted due to the intense thermal movement of atoms and molecules and the material ceases to be ferromagnetic and becomes paramagnetic.

For iron Q k = 768 ° C, for nickel Q k = 358 ° C, for cobalt Q k = 1131 ° C.

Above the Curie temperature, the dependence of the magnetic susceptibility of a ferromagnet on temperatureTdescribed by the Curie-Weiss law

The process of magnetization of highly magnetic materials (ferromagnets) has hysteresis. If a demagnetized ferromagnet is magnetized in an external field, it becomes magnetized according to magnetization curve B = B(H) . If then, starting from some valueHbegin to reduce the field strength, then inductionBwill decrease with some delay ( hysteresis) in relation to the magnetization curve. As the field increases opposite direction the ferromagnet is demagnetized, then remagnetizes, and with a new change in the direction of the magnetic field, it can return to the starting point from where the demagnetization process began. The resulting loop shown in the figure is called hysteresis loop.

At some maximum tensionN m magnetizing field, the substance is magnetized to a state of saturation, in which the induction reaches the valueIN N, which is calledinduction of saturation.

Residual magnetic induction IN ABOUT – observed in a ferromagnetic material, magnetized to saturation, during its demagnetization, when the magnetic field strength is zero. To demagnetize a material sample, the magnetic field strength must change its direction to the opposite direction (-N). Field strengthN TO , at which induction is equal to zero, is called coercive force(holding force) .

Magnetization reversal of a ferromagnet in alternating magnetic fields is always accompanied by thermal energy losses, which are caused by hysteresis losses And dynamic losses. Dynamic losses are associated with eddy currents induced in the volume of the material and depend on electrical resistance material, decreasing with increasing resistance. Hysteresis lossesW in one magnetization reversal cycle determined by the area of ​​the hysteresis loop

and can be calculated for a unit volume of a substance using the empirical formula

J/m 3

Where η – coefficient depending on the material,B N – maximum induction achieved during the cycle,n– exponent equal to 1.6 depending on the material¸ 2.

Specific energy losses due to hysteresis R G – losses spent on magnetization reversal of a unit mass per unit volume of material per second.

Where f – AC frequency,T– period of oscillation.

Magnetostriction

Magnetostriction – the phenomenon of changes in the geometric dimensions and shape of a ferromagnet when the magnitude of the magnetic field changes, i.e. when magnetized. Relative change in material dimensionsΔ l/ lcan be positive and negative. For nickel, magnetostriction is less than zero and reaches a value of 0.004%.

In accordance with Le Chatelier's principle of counteracting the influence of the system external factors, seeking to change this state, mechanical deformation of the ferromagnet, leading to a change in its size, should affect the magnetization of these materials.

If, during magnetization, a body experiences a reduction in its size in a given direction, then the application of a mechanical compressive stress in this direction promotes magnetization, and stretching makes magnetization difficult.

6.2. Classification of ferromagnetic materials

All ferro magnetic materials Based on their behavior in a magnetic field, they are divided into two groups.

Soft magnetic – with high magnetic permeabilityμ and low coercive forceN TO< 10A/m. They are easily magnetized and demagnetized. They have low hysteresis losses, i.e. narrow hysteresis loop.

Magnetic characteristics depend on the chemical purity and the degree of distortion of the crystal structure. The less impurities(WITH, R, S, O, N) , the higher the level of characteristics of the material, therefore it is necessary to remove them and oxides during the production of a ferromagnet, and try not to distort the crystalline structure of the material.

Hard magnetic materials – have greatN K > 0.5 MA/m and residual induction (IN ABOUT ≥ 0.1T). They correspond to a wide hysteresis loop. They are magnetized with great difficulty, but they can retain magnetic energy for several years, i.e. serve as a source of constant magnetic field. Therefore, permanent magnets are made from them.

Based on their composition, all magnetic materials are divided into:

· metal;

· non-metallic;

· magnetodielectrics.

Metal magnetic materials - these are pure metals (iron, cobalt, nickel) and magnetic alloys of some metals.

To non-metallic materials include ferrites, obtained from powders of iron oxides and other metals. They are pressed and fired at 1300 - 1500 °C and they turn into solid monolithic magnetic parts. Ferrites, like metal magnetic materials, can be soft magnetic or hard magnetic.

Magnetodielectrics – these are composite materials from 60–80% powdered magnetic material and 40–20% organic dielectric. Ferrites and magnetodielectrics have great value electrical resistivity (ρ = 10 ÷ 10 8 Ohm m), the high resistance of these materials ensures low dynamic energy losses in alternating electromagnetic fields and allows them to be widely used in high-frequency technology.

6.3. Metal magnetic materials

6.3.1. Metal soft magnetic materials

Metallic soft magnetic materials include carbonyl iron, permalloy, alsifer and low-carbon silicon steel.

Carbonyl iron – obtained by thermal decomposition of iron pentacarbonyl liquidF e( CO ) 5 to obtain particles of pure powdered iron:

F e( CO ) 5 → Fe+ 5 СО,

at a temperature of about 200°Cand pressure 15 MPa. Iron particles have a spherical shape with a size of 1 – 10 microns. To remove carbon particles, iron powder is subjected to heat treatment in an environment N 2 .

The magnetic permeability of carbonyl iron reaches 20000, the coercive force is 4.5¸ 6,2A/m. Iron powder is used to make high-frequency magnetodielectric cores, as filler in magnetic tapes.

Permalloi –ductile iron-nickel alloys. To improve properties, add Mo, WITH r, Cu, producing doped permalloys. They have high ductility and are easily rolled into sheets and strips up to 1 micron.

If the nickel content in permalloy is 40 - 50%, then it is called low-nickel, if 60 - 80% - high-nickel.

Permalloys have high level magnetic characteristics, which is ensured not only by the composition and high chemical purity of the alloy, but also by special thermal vacuum treatment. Permalloys have a very high level of initial magnetic permeability from 2000 to 30000 (depending on the composition) in the region of weak fields, which is due to the low magnitude of magnetostriction and isotropy of magnetic properties. Especially high performance has a supermalloy, the initial magnetic permeability of which is 100,000, and the maximum reaches 1.5· 10 6 at B= 0.3 T.

Permalloy is supplied in the form of strips, sheets and rods. Low-nickel permalloys are used for the manufacture of inductor cores, small-sized transformers and magnetic amplifiers, high-nickel permalloi – for equipment parts operating at sonic and supersonic frequencies. The magnetic characteristics of permalloys are stable at –60 +60°С.

Alsifera – non-malleable fragile alloys of composition Al – Si– Fe , consisting of 5.5 – 13%Al, 9 – 10 % Si, the rest is iron. Alsifer is similar in properties to permalloy, but is cheaper. Cast cores are made from it, magnetic screens and other hollow parts with a wall thickness of at least 2 - 3 mm are cast. The fragility of alsifer limits its areas of application. Taking advantage of the fragility of alsifer, it is ground into powder, which is used as a ferromagnetic filler in pressed high-frequency magnetodielectrics(cores, rings).

Silicon Low Carbon Steel (electrical steel) – alloy of iron and silicon (0.8 - 4.8%Si). The main soft magnetic material for mass use. It is easily rolled into sheets and strips of 0.05 - 1 mm and is a cheap material. Silicon, found in steel in a dissolved state, performs two functions.

· By increasing the resistivity of steel, silicon causes a reduction in dynamic losses associated with eddy currents. Resistance increases due to silica formation SiO 2 as a result of the reaction

2 FeO + S i→ 2Fe+ SiO 2 .

· The presence of silicon dissolved in steel promotes the decomposition of cementite Fe 3 C – harmful impurities that reduce magnetic characteristics, and the release of carbon in the form of graphite. In this case, pure iron is formed, the growth of crystals of which increases the level of magnetic characteristics of steel.

The introduction of silicon into steel in an amount exceeding 4.8% is not recommended, since, while helping to improve magnetic characteristics, silicon sharply increases the brittleness of steel and reduces it mechanical properties.

6.3.2. Metallic hard magnetic materials

Hard magnetic materials - these are ferromagnets with high coercive force (more than 1 kA/m) and a large value of residual magnetic inductionIN ABOUT. Used for the manufacture of permanent magnets.

Depending on the composition, condition and method of production, they are divided into:

· alloyed martensitic steels;

· cast hard magnetic alloys.

Alloy martensitic steels – this is about carbon steels and alloyed steelsCr, W, Co, Mo . Carbon steel ages quickly and change their properties, so they are rarely used for the manufacture of permanent magnets. For the manufacture of permanent magnets, alloy steels are used - tungsten and chromium (N C ≈ 4800 A/m,IN O ≈ 1 T), which are manufactured in the form of rods with various shapes sections. Cobalt steel has a higher coercivity (N C ≈ 12000 A/m,IN O ≈ 1 T) compared to tungsten and chromium. Coercive force N WITH cobalt steel increases with increasing content WITH O .

Cast hard magnetic alloys. The improved magnetic properties of the alloys are due to a specially selected composition and special treatment - cooling of the magnets after casting in a strong magnetic field, as well as special multi-stage heat treatment in the form of quenching and tempering in combination with magnetic treatment, called dispersion hardening.

Three main groups of alloys are used for the manufacture of permanent magnets:

· Iron – cobalt – molybdenum alloy type remalloy with coercive forceN K = 12 – 18 kA/m.

· Alloy group:

§ copper – nickel – iron;

§ copper – nickel – cobalt;

§ iron - manganese, alloyedaluminum or titanium;

§ iron – cobalt – vanadium (F e– Co – V).

The alloy copper - nickel - iron is called kunife (WITH u– Ni - Fe). Alloy F e– Co – V (iron - cobalt - vanadium) is called vikala . Alloys of this group have a coercive force N TO = 24 – 40 kA/m. Available in wire and sheet form.

· Alloys system iron – nickel – aluminum(F e – Ni– Al), previously known as alloy alni. Alloy contains 20 - 33% Ni + 11 – 17% Al, the rest is iron. Adding cobalt, copper, titanium, silicon, and niobium to alloys improves their magnetic properties, facilitates manufacturing technology, ensures repeatability of parameters, and improves mechanical properties. Modern marking of the brand contains letters indicating the added metals (Y - aluminum, N - nickel, D - copper, K - cobalt, T - titanium, B - niobium, C - silicon), numbers - the content of the element, the letter of which appears before the number, for example, UNDC15.

Alloys have a high coercivity value N TO = 40 – 140 kA/m and large stored magnetic energy.

6.4. Non-metallic magnetic materials. Ferrites

Ferrites are ceramic ferromagnetic materials with low electronic conductivity. Low electrical conductivity combined with high magnetic characteristics allows ferrites to be widely used in high frequencies Oh.

Ferrites are made from a powder mixture consisting of iron oxide and specially selected oxides of other metals. They are pressed and then sintered at high temperatures. General chemical formula has the form:

MeO Fe 2 O 3 or MeFe 2 O 4,

Where Mehdivalent metal symbol.

For example,

ZnO Fe 2 O 3 or

NiO Fe 2 O 3 or NiFe 2 O 4

Ferrites have a cubic spinel-type latticeMgOAl 2 O 3 - magnesium aluminate.Not all ferrites are magnetic. The presence of magnetic properties is associated with the arrangement of metal ions in the cubic spinel lattice. So the systemZnFe 2 O 4 does not have ferromagnetic properties.

Ferrites are produced according to ceramic technology. The original powdered metal oxides are crushed in ball mills, pressed and fired in furnaces. The sintered briquettes are ground into a fine powder, and a plasticizer, for example a solution of polyvinyl alcohol, is added. From the resulting mass, ferrite products are pressed - cores, rings, which are fired in air at 1000 - 1400 ° C. The resulting hard, brittle, mostly black products can only be processed by grinding and polishing.

Soft magnetic ferrites

Soft magneticFerrites are widely used in the field of high-frequency electronics and instrument making for the manufacture of filters, transformers for low- and high-frequency amplifiers, antennas for radio transmitting and receiving devices, pulse transformers, and magnetic modulators. Produced by industry the following types soft magnetic ferrites with wide range magnetic and electrical properties: nickel - zinc, manganese - zinc and lithium - zinc. The upper limit frequency of ferrite use depends on their composition and varies with different brands ferrites from 100 kHz to 600 MHz, the coercivity is about 16 A/m.

The advantage of ferrites is the stability of magnetic characteristics and the relative ease of manufacturing radio components. Like all ferromagnetic materials, ferrites retain their magnetic properties only up to the Curie temperature, which depends on the composition of the ferrites and ranges from 45 ° to 950 ° C.

Hard magnetic ferrites

For the manufacture of permanent magnets, hard magnetic ferrites are used; barium ferrites are most widely used (VaO 6 Fe 2 O 3 ). They have a hexagonal crystal structure with largeN TO . Barium ferrites are a polycrystalline material. They can be isotropic - the same properties of ferrite in all directions are due to the fact that the crystalline particles are oriented arbitrarily. If, during the process of pressing magnets, the powdery mass is exposed to an external magnetic field of high intensity, then the crystalline ferrite particles will be oriented in one direction, and the magnet will be anisotropic.

Barium ferrites are characterized by good stability of their characteristics, but are sensitive to temperature changes and mechanical stress. Barium ferrite magnets are cheap.

6.5. Magnetodielectrics

Magnetodielectrics - these are composite materials consisting of fine particles of soft magnetic material bound to each other by an organic or inorganic dielectric. Carbonyl iron, alsifer and some types of permalloy, crushed to a powder state, are used as soft magnetic materials.

Polystyrene, bakelite resins, liquid glass, etc. are used as dielectrics.

The purpose of a dielectric is not only to connect particles of magnetic material, but also to isolate them from each other, and, consequently, to sharply increase the electrical resistivity value magnetodielectric. Electrical resistivityrmagnetodielectricsis 10 3 – 10 4 Ohm× m

Magnetodielectricsused for the manufacture of cores for high-frequency radio equipment components. The process of manufacturing products is simpler than from ferrites, because they do not require high temperature heat treatment. Products from magnetodielectrics are characterized by high stability of magnetic properties, high class surface cleanliness and dimensional accuracy.

Magnetodielectrics filled with molybdenum permalloy or carbonyl iron have the highest magnetic characteristics.

If in the experiments described above, instead of an iron core, we take cores from other materials, then a change in the magnetic flux can also be detected. It is most natural to expect that the most noticeable effect will be produced by materials similar in their magnetic properties to iron, i.e. nickel, cobalt and some magnetic alloys. Indeed, when a core made of these materials is introduced into the coil, the increase in magnetic flux turns out to be quite significant. In other words, we can say that their magnetic permeability is high; for nickel, for example, it can reach a value of 50, for cobalt 100. All these materials with large values combined into one group of ferromagnetic materials.

However, all other “non-magnetic” materials also have some effect on magnetic flux, although the influence is significantly less than that of ferromagnetic materials. With the help of very careful measurements this change can be detected and the magnetic permeability can be determined various materials. However, it must be borne in mind that in the experiment described above, we compared the magnetic flux in a coil whose cavity is filled with iron with the flux in a coil with air inside. As long as we were talking about such highly magnetic materials as iron, nickel, cobalt, this did not matter, since the presence of air has very little effect on the magnetic flux. But when studying the magnetic properties of other substances, in particular air itself, we must, of course, make a comparison with a coil inside which there is no air (vacuum). Thus, for magnetic permeability we take the ratio of magnetic fluxes in the substance under study and in vacuum. In other words, we take the magnetic permeability for vacuum as one (if , then ).

Measurements show that the magnetic permeability of all substances is different from unity, although in most cases this difference is very small. But what is especially remarkable is the fact that for some substances the magnetic permeability is greater than one, while for others it is less than one, i.e., filling the coil with some substances increases the magnetic flux, and filling the coil with other substances reduces this flux. The first of these substances are called paramagnetic (), and the second - diamagnetic (). As the table shows. 7, the difference in permeability from unity for both paramagnetic and diamagnetic substances is small.

It should be especially emphasized that for paramagnetic and diamagnetic bodies, magnetic permeability does not depend on the magnetic induction of an external, magnetizing field, i.e., it is a constant value characterizing a given substance. As we will see in § 149, this is not the case for iron and other similar (ferromagnetic) bodies.

Table 7. Magnetic permeability for some paramagnetic and diamagnetic substances

Paramagnetic substances		Diamagnetic substances
Nitrogen (gaseous)		Hydrogen (gaseous)
Air (gaseous)
Oxygen (gaseous)
Oxygen (liquid)
Aluminum
Tungsten

The influence of paramagnetic and diamagnetic substances on the magnetic flux is explained, just like the influence of ferromagnetic substances, by the fact that the magnetic flux created by the current in the coil winding is joined by the flux emanating from elementary ampere currents. Paramagnetic substances increase the magnetic flux of the coil. This increase in flux when the coil is filled with a paramagnetic substance indicates that in paramagnetic substances, under the influence of an external magnetic field, elementary currents are oriented so that their direction coincides with the direction of the winding current (Fig. 276). A slight difference from unity only indicates that in the case of paramagnetic substances this additional magnetic flux is very small, i.e., that paramagnetic substances are magnetized very weakly.

A decrease in the magnetic flux when filling the coil with a diamagnetic substance means that in this case the magnetic flux from elementary ampere currents is directed opposite to the magnetic flux of the coil, i.e., that in diamagnetic substances, under the influence of an external magnetic field, elementary currents arise, directed opposite to the winding currents (Fig. 277). The smallness of deviations from unity in this case also indicates that the additional flow of these elementary currents is small.

Rice. 277. Diamagnetic substances inside the coil weaken the magnetic field of the solenoid. The elementary currents in them are directed opposite to the current in the solenoid

Determination of the magnetic permeability of a substance. Its role in describing the magnetic field

If you conduct an experiment with a solenoid that is connected to a ballistic galvanometer, then when the current in the solenoid is turned on, you can determine the value of the magnetic flux F, which will be proportional to the deflection of the galvanometer needle. Let's carry out the experiment twice, and set the current (I) in the galvanometer to be the same, but in the first experiment the solenoid will be without a core, and in the second experiment, before turning on the current, we will introduce an iron core into the solenoid. It is discovered that in the second experiment the magnetic flux is significantly greater than in the first (without a core). When repeating the experiment with cores of different thicknesses, it turns out that the maximum flow is obtained in the case when the entire solenoid is filled with iron, that is, the winding is tightly wound around the iron core. You can conduct an experiment with different cores. The result is that:

where $Ф$ is the magnetic flux in a coil with a core, $Ф_0$ is the magnetic flux in a coil without a core. The increase in magnetic flux when a core is introduced into the solenoid is explained by the fact that to the magnetic flux that creates the current in the solenoid winding, a magnetic flux created by a set of oriented ampere molecular currents was added. Under the influence of a magnetic field, molecular currents are oriented, and their total magnetic moment ceases to be equal to zero, and an additional magnetic field arises.

Definition

The quantity $\mu $, which characterizes the magnetic properties of the medium, is called magnetic permeability (or relative magnetic permeability).

This is a dimensionless characteristic of a substance. An increase in the flux Ф by $\mu $ times (1) means that the magnetic induction $\overrightarrow(B)$ in the core is the same number of times greater than in vacuum with the same current in the solenoid. Therefore, we can write that:

\[\overrightarrow(B)=\mu (\overrightarrow(B))_0\left(2\right),\]

where $(\overrightarrow(B))_0$ is the magnetic field induction in vacuum.

Along with magnetic induction, which is the main force characteristic of the field, an auxiliary vector quantity is used as magnetic field strength ($\overrightarrow(H)$), which is related to $\overrightarrow(B)$ by the following relation:

\[\overrightarrow(B)=\mu \overrightarrow(H)\left(3\right).\]

If formula (3) is applied to the experiment with a core, we obtain that in the absence of a core:

\[(\overrightarrow(B))_0=(\mu )_0\overrightarrow(H_0)\left(4\right),\]

where $\mu $=1. If there is a core, we get:

\[\overrightarrow(B)=\mu (\mu )_0\overrightarrow(H)\left(5\right).\]

But since (2) is satisfied, it turns out that:

\[\mu (\mu )_0\overrightarrow(H)=(\mu m)_0\overrightarrow(H_0)\to \overrightarrow(H)=\overrightarrow(H_0)\left(6\right).\]

We found that the magnetic field strength does not depend on what kind of homogeneous substance the space is filled with. The magnetic permeability of most substances is about unity, with the exception of ferromagnets.

Magnetic susceptibility of a substance

Usually the magnetization vector ($\overrightarrow(J)$) is associated with the intensity vector at each point of the magnet:

\[\overrightarrow(J)=\varkappa \overrightarrow(H)\left(7\right),\]

where $\varkappa $ is magnetic susceptibility, a dimensionless quantity. For non-ferromagnetic substances and in small fields $\varkappa $ does not depend on the strength and is a scalar quantity. In anisotropic media, $\varkappa $ is a tensor and the directions of $\overrightarrow(J)$ and $\overrightarrow(H)$ do not coincide.

Relationship between magnetic susceptibility and magnetic permeability

\[\overrightarrow(H)=\frac(\overrightarrow(B))((\mu )_0)-\overrightarrow(J)\left(8\right).\]

Let us substitute the expression for the magnetization vector (7) into (8), and obtain:

\[\overrightarrow(H)=\frac(\overrightarrow(B))((\mu )_0)-\overrightarrow(H)\left(9\right).\]

Expressing the tension, we get:

\[\overrightarrow(H)=\frac(\overrightarrow(B))((\mu )_0\left(1+\varkappa \right))\to \overrightarrow(B)=(\mu )_0\left( 1+\varkappa \right)\overrightarrow(H)\left(10\right).\]

Comparing expressions (5) and (10), we obtain:

\[\mu =1+\varkappa \left(11\right).\]

Magnetic susceptibility can be either positive or negative. From (11) it follows that the magnetic permeability can be either greater than unity or less than it.

Example 1

Task: Calculate the magnetization in the center of a circular coil of radius R=0.1 m with a current of strength I=2A, if it is immersed in liquid oxygen. The magnetic susceptibility of liquid oxygen is equal to $\varkappa =3.4\cdot (10)^(-3).$

As a basis for solving the problem, we will take an expression that reflects the relationship between magnetic field strength and magnetization:

\[\overrightarrow(J)=\varkappa \overrightarrow(H)\left(1.1\right).\]

Let's find the field in the center of the coil with current, since we need to calculate the magnetization at this point.

Let us select an elementary section on the current-carrying conductor (Fig. 1); as a basis for solving the problem, we use the formula for the strength of the current-carrying coil element:

where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the element of the conductor with current (the direction is specified by the direction of the current), $\vartheta$ is the angle between $ \overrightarrow(dl)$ and $\overrightarrow(r)$. Based on Fig. 1 $\vartheta=90()^\circ $, therefore (1.1) will be simplified, in addition, the distance from the center of the circle (the point where we are looking for the magnetic field) of the conductor element with current is constant and equal to the radius of the turn (R), therefore we have:

The resulting magnetic field strength vector is directed along the X axis, it can be found as the sum of individual vectors $\ \ \overrightarrow(dH),$ since all current elements create magnetic fields in the center of the turn, directed along the normal of the turn. Then, according to the principle of superposition, the total magnetic field strength can be obtained by passing to the integral:

Substituting (1.3) into (1.4), we get:

Let's find the magnetization if we substitute the intensity from (1.5) into (1.1), we get:

All units are given in the SI system, let’s carry out the calculations:

Answer: $J=3.4\cdot (10)^(-2)\frac(A)(m).$

Example 2

Task: Calculate the fraction of the total magnetic field in a tungsten rod that is in an external uniform magnetic field, which is determined by molecular currents. The magnetic permeability of tungsten is $\mu =1.0176.$

The magnetic field induction ($B"$), which accounts for the molecular currents, can be found as:

where $J$ is magnetization. It is related to the magnetic field strength by the expression:

where the magnetic susceptibility of a substance can be found as:

\[\varkappa =\mu -1\ \left(2.3\right).\]

Therefore, we find the magnetic field of molecular currents as:

The total field in the rod is calculated according to the formula:

We use expressions (2.4) and (2.5) to find the required relationship:

\[\frac(B")(B)=\frac((\mu )_0\left(\mu -1\right)H)(\mu (\mu )_0H)=\frac(\mu -1) (\mu).\]

Let's carry out the calculations:

\[\frac(B")(B)=\frac(1.0176-1)(1.0176)=0.0173.\]

Answer:$\frac(B")(B)=0.0173.$

Magnetic permeability- physical quantity, coefficient (depending on the properties of the medium) characterizing the relationship between magnetic induction texvc not found; See math/README for setup help.): (B) and magnetic field strength Unable to parse expression (Executable file texvc not found; See math/README for setup help.): (H) in matter. For different environments this coefficient is different, so they talk about the magnetic permeability of a particular medium (meaning its composition, state, temperature, etc.).

First found in Werner Siemens's 1881 work "Beiträge zur Theorie des Elektromagnetismus" ("Contribution to the Theory of Electromagnetism").

Usually denoted Greek letter Unable to parse expression (Executable file texvc . It can be either a scalar (for isotropic substances) or a tensor (for anisotropic substances).

In general, the relationship between magnetic induction and magnetic field strength through magnetic permeability is introduced as

Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \vec(B) = \mu\vec(H),

And Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \mu in the general case, this should be understood as a tensor, which in component notation corresponds to:

Unable to parse expression (Executable file texvc not found; See math/README - help with setup.): \ B_i = \mu_(ij)H_j

For isotropic substances the ratio:

Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \vec(B) = \mu\vec(H)

can be understood in the sense of multiplying a vector by a scalar (magnetic permeability is reduced in this case to a scalar).

Often the designation Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \mu is used differently than here, namely for relative magnetic permeability (in this case Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \mu coincides with that in the GHS).

The dimension of absolute magnetic permeability in SI is the same as the dimension of the magnetic constant, that is, Gn / or / 2.

Relative magnetic permeability in SI is related to magnetic susceptibility χ by the relation

Unable to parse expression (Executable file texvc not found; See math/README - help with setup.): \mu_r = 1 + \chi,

Classification of substances by magnetic permeability value

The vast majority of substances belong either to the class of diamagnets ( Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \mu \lessapprox 1), or to the class of paramagnets ( Unable to parse expression (Executable file texvc not found; See math/README for setup help.): \mu \gtrapprox 1). But a number of substances (ferromagnets), for example iron, have more pronounced magnetic properties.

In ferromagnets, due to hysteresis, the concept of magnetic permeability, strictly speaking, is not applicable. However, in a certain range of changes in the magnetizing field (so that the residual magnetization can be neglected, but before saturation), it is still possible, to a better or worse approximation, to present this dependence as linear (and for soft magnetic materials, the lower limit may not be too significant in practice), and in In this sense, the value of magnetic permeability can also be measured for them.

Magnetic permeability of some substances and materials

Magnetic susceptibility of some substances

Magnetic susceptibility and magnetic permeability of some materials

Medium	Susceptibility χ m (volume, SI)	Permeability μ [H/m]	Relative permeability μ/μ 0	Magnetic field	Maximum frequency
Metglas (English) Metglas )		1,25	1 000 000	at 0.5 T	100 kHz
Nanoperm Nanoperm )		10×10 -2	80 000	at 0.5 T	10 kHz
Mu metal		2.5×10 -2	20 000	at 0.002 T
Mu metal			50 000
Permalloy		1.0×10 -2	70 000	at 0.002 T
Electrical steel		5.0×10 -3	4000	at 0.002 T
Ferrite (nickel-zinc)		2.0×10 -5 - 8.0×10 -4	16-640		100 kHz ~ 1 MHz [[K:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]][[K:Wikipedia:Articles without sources (country: Lua error: callParserFunction: function "#property" was not found. )]]
Ferrite (manganese-zinc)		>8.0×10 -4	640 (or more)		100 kHz ~ 1 MHz
Steel		8.75×10 -4	100	at 0.002 T
Nickel		1.25×10 -4	100 - 600	at 0.002 T
Neodymium magnet			1.05	up to 1.2-1.4 T
Platinum		1.2569701×10 -6	1,000265
Aluminum	2.22×10 -5	1.2566650×10 -6	1,000022
Tree			1,00000043
Air			1,00000037
Concrete			1
Vacuum	0	1.2566371×10 -6 (μ 0)	1
Hydrogen	-2.2×10 -9	1.2566371×10 -6	1,0000000
Teflon		1.2567×10 -6	1,0000
Sapphire	-2.1×10 -7	1.2566368×10 -6	0,99999976
Copper	-6.4×10 -6 or -9.2×10 -6	1.2566290×10 -6	0,999994
Water	-8.0×10 -6	1.2566270×10 -6	0,999992
Bismuth	-1.66×10 -4		0,999834
Superconductors	−1	0	0

See also

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Notes

Excerpt characterizing Magnetic permeability

I felt so sorry for him!.. But, unfortunately, I was not in my power to help him. And I honestly really wanted to know how this extraordinary little girl helped him...
- We found them! – Stella repeated again. – I didn’t know how to do it, but my grandmother helped me!
It turned out that Harold, during his lifetime, did not even have time to find out how terribly his family suffered while dying. He was a warrior knight, and died before his city fell into the hands of the “executioners,” as his wife predicted.
But as soon as he found himself in this unfamiliar, wondrous world of “gone” people, he was immediately able to see how mercilessly and cruelly evil fate dealt with his “only and loved ones.” Afterwards, like one possessed, he spent an eternity trying somehow, somewhere to find these people, the most dear to him in the whole wide world... And he searched for them for a very long time, more than a thousand years, until one day, some completely unfamiliar person, sweet girl Stella didn’t offer to “make him happy” and didn’t open that “other” door to finally find them for him...
- Do you want me to show you? - the little girl suggested again,
But I was no longer so sure whether I wanted to see something else... Because the visions she had just shown hurt my soul, and it was impossible to get rid of them so quickly to want to see some kind of continuation...
“But you want to see what happened to them!” – little Stella confidently stated the “fact”.
I looked at Harold and saw in his eyes complete understanding of what I had just unexpectedly experienced.
– I know what you saw... I watched it many times. But they are happy now, we go to look at them very often... And at their “former” ones too... - the “sad knight” said quietly.
And only then I realized that Stella, simply, when he wanted it, transferred him to his own past, just like she had just done!!! And she did it almost playfully!.. I didn’t even notice how this wonderful, bright girl began to “tie me to her” more and more, becoming for me almost a real miracle, which I endlessly wanted to watch... And whom I didn’t want to leave at all... Then I knew almost nothing and couldn’t do anything except what I could understand and learn myself, and I really wanted to learn at least something from her while there was still such an opportunity.
- Please come to me! – Stella, suddenly saddened, whispered quietly, “you know that you can’t stay here yet... Grandma said that you won’t stay for a very, very long time... That you can’t die yet.” But you come...
Everything around suddenly became dark and cold, as if black clouds had suddenly covered such a colorful and bright Stella world...
- Oh, don’t think about such terrible things! – the girl was indignant, and, like an artist with a brush on a canvas, she quickly “painted over” everything again in a light and joyful color.
- Well, is this really better? – she asked contentedly.
“Was it really just my thoughts?..” I didn’t believe it again.
- Well, of course! – Stella laughed. “You’re strong, so you create everything around you in your own way.”
– How then to think?.. – I still couldn’t “enter” the incomprehensible.
“Just shut up and show only what you want to show,” my amazing friend said, as a matter of course. “My grandmother taught me that.”
I thought that apparently it was time for me, too, to “shock” my “secret” grandmother a little, who (I was almost sure of this!) probably knew something, but for some reason did not want to teach me anything yet.. .
“So you want to see what happened to Harold’s loved ones?” – the little girl asked impatiently.
To be honest, I didn’t have too much desire, since I wasn’t sure what to expect from this “show.” But in order not to offend the generous Stella, she agreed.
– I won’t show you for a long time. I promise! But you should know about them, right?.. – the girl said in a happy voice. - Look, the son will be first...

To my greatest surprise, unlike what I had seen before, we found ourselves in a completely different time and place, which was similar to France, and the clothes were reminiscent of the eighteenth century. A beautiful covered carriage was driving along a wide cobbled street, inside of which were sitting a young man and a woman in very expensive suits, and apparently in a very bad mood... The young man stubbornly proved something to the girl, and she, not listening to him at all, hovered calmly somewhere in your dreams than young man very annoying...
- You see, it’s him! This is the same " little boy“... only after many, many years,” Stella whispered quietly.
- How do you know that it’s really him? – still not quite understanding, I asked.
- Well, of course, it’s very simple! – the little girl stared at me in surprise. – We all have an essence, and the essence has its own “key” by which each of us can be found, you just need to know how to look. Look...
She showed me the baby again, Harold's son.
– Think about his essence, and you will see...
And I immediately saw a transparent, brightly glowing, surprisingly powerful entity, on whose chest an unusual “diamond” energy star was burning. This “star” shone and shimmered with all the colors of the rainbow, now decreasing, now increasing, as if slowly pulsating, and sparkled so brightly, as if it had really been created from the most stunning diamonds.
– Do you see this strange inverted star on his chest? - This is his “key”. And if you try to follow him, like a thread, then it will lead you straight to Axel, who has the same star - this is the same essence, only in its next incarnation.
I looked at her with all my eyes, and apparently noticing this, Stella laughed and cheerfully admitted:
– Don’t think that it was me myself – it was my grandmother who taught me!..
I was very ashamed to feel like a complete incompetent, but the desire to know more was a hundred times stronger than any shame, so I hid my pride as deeply as possible and carefully asked:
– But what about all these amazing “realities” that we are seeing here now? After all, this is someone else’s, specific life, and you don’t create them in the same way as you create all your worlds?
- Oh no! – the little girl was again glad to have the opportunity to explain something to me. - Of course not! This is just the past in which all these people once lived, and I’m just taking you and me there.
- And Harold? How does he see all this?
- Oh, it’s easy for him! He’s just like me, dead, so he can move wherever he wants. He doesn't have it anymore physical body, so his essence does not know any obstacles here and can walk wherever it wants... just like me... - the little girl finished more sadly.
I sadly thought that what was for her just a “simple transfer into the past”, for me, apparently for a long time will be a “mystery behind seven locks”... But Stella, as if hearing my thoughts, immediately hastened to reassure me :
- You'll see, it's very simple! You just have to try.
– And these “keys”, are they never repeated by others? – I decided to continue my questions.
“No, but sometimes something else happens...” for some reason, the little one answered, smiling funny. “That’s exactly how I got caught at the beginning, for which they even beat me up very badly... Oh, that was so stupid!..”
- How? – I asked, very interested.
Stella immediately answered cheerfully:
- Oh, that was very funny! - and after thinking a little, she added, “but it’s also dangerous... I was looking on all the “floors” for the past incarnation of my grandmother, and instead of her, a completely different entity came along her “thread”, which somehow managed to “copy” my grandmother’s “ flower" (apparently also a "key"!) and, just as I had time to rejoice that I had finally found it, this unfamiliar entity mercilessly hit me in the chest. Yes, so much that my soul almost flew away!..
- How did you get rid of her? – I was surprised.
“Well, to be honest, I didn’t get rid of it...” the girl became embarrassed. - I just called my grandmother...
– What do you call “floors”? – I still couldn’t calm down.
– Well, these are different “worlds” where the essences of the dead live... In the most beautiful and highest live those who were good... and, probably, the strongest too.
- People like you? – I asked, smiling.
- Oh, no, of course! I probably got here by mistake. – The girl said completely sincerely. – Do you know what’s most interesting? From this “floor” we can walk everywhere, but from the others no one can get here... Isn’t that interesting?..
Yes, it was very strange and very excitingly interesting for my “starved” brain, and I really wanted to know more!.. Maybe because until that day no one had ever really explained anything to me, but just sometimes someone - gave (like, for example, my “star friends”), and therefore, even such a simple childish explanation already made me unusually happy and made me delve even more furiously into my experiments, conclusions and mistakes... as usual, finding in everything that was happening even more unclear. My problem was that I could do or create “unusual” very easily, but the whole problem was that I also wanted to understand how I create it all... And this is precisely what I have not been very successful in yet ...

Numerous experiments indicate that all substances placed in a magnetic field are magnetized and create their own magnetic field, the action of which is added to the action of an external magnetic field:

$$\boldsymbol(\vec(B)=(\vec(B))_(0)+(\vec(B))_(1))$$

where $\boldsymbol(\vec(B))$ is the magnetic field induction in the substance; $\boldsymbol((\vec(B))_(0))$ - magnetic induction of the field in vacuum, $\boldsymbol((\vec(B))_(1))$ - magnetic induction of the field arising due to the magnetization of matter . In this case, the substance can either strengthen or weaken the magnetic field. The influence of a substance on an external magnetic field is characterized by the magnitude μ , which is called magnetic permeability of a substance

$$ \boldsymbol(\mu =\frac(B)((B)_(0)))$$

• Magnetic permeability is a physical scalar quantity that shows how many times the magnetic field induction in a given substance differs from the magnetic field induction in a vacuum.

All substances are made up of molecules, molecules are made up of atoms. The electron shells of atoms can be conventionally considered to consist of circular electric currents formed by moving electrons. Circular electric currents atoms must create their own magnetic fields. Electric currents must be affected by an external magnetic field, as a result of which one can expect either an increase in the magnetic field when the atomic magnetic fields are aligned with the external magnetic field, or a weakening when they are in the opposite direction.
Hypothesis about existence of magnetic fields in atoms and the possibility of changing the magnetic field in matter is completely true. All substances by the action of an external magnetic field on them can be divided into three main groups: diamagnetic, paramagnetic and ferromagnetic.

Diamagnets are called substances in which the external magnetic field is weakened. This means that the magnetic fields of the atoms of such substances in an external magnetic field are directed opposite to the external magnetic field (µ< 1). Изменение магнитного поля даже в самых сильных диамагнетиках составляет лишь сотые доли процента. Например, висмут обладает magnetic permeability µ = 0.999826.

To understand the nature of diamagnetism consider the motion of an electron that flies in at a speed v into a uniform magnetic field perpendicular to the vector IN magnetic field.

Under the influence Lorentz forces the electron will move in a circle, the direction of its rotation is determined by the direction of the Lorentz force vector. The resulting circular current creates its own magnetic field IN" . This is a magnetic field IN" directed opposite to the magnetic field IN. Consequently, any substance containing freely moving charged particles must have diamagnetic properties.
Although the electrons in the atoms of a substance are not free, the change in their motion inside the atoms under the influence of an external magnetic field turns out to be equivalent to the circular motion of free electrons. Therefore, any substance in a magnetic field necessarily has diamagnetic properties.
However, diamagnetic effects are very weak and are found only in substances whose atoms or molecules do not have their own magnetic field. Examples of diamagnetic materials are lead, zinc, bismuth (μ = 0.9998).

The first explanation of the reasons why bodies have magnetic properties was given by Henri Ampère (1820). According to his hypothesis, elementary electric currents circulate inside molecules and atoms, which determine the magnetic properties of any substance.

Let us consider the reasons for the magnetism of atoms in more detail:

Let's take some solid substance. Its magnetization is related to the magnetic properties of the particles (molecules and atoms) of which it is composed. Let's consider what current circuits are possible at the micro level. The magnetism of atoms is due to two main reasons:

1) the movement of electrons around the nucleus in closed orbits ( orbital magnetic moment) (Fig. 1);

Rice. 2

2) the intrinsic rotation (spin) of electrons ( spin magnetic moment) (Fig. 2).

For the curious. Magnetic moment of the circuit equal to the product current strength in the circuit per area covered by the circuit. Its direction coincides with the direction of the magnetic field induction vector in the middle of the current-carrying circuit.

Since the orbital planes of different electrons in an atom do not coincide, the magnetic field induction vectors created by them (orbital and spin magnetic moments) are directed at different angles to each other. The resulting induction vector of a multielectron atom is equal to the vector sum of the field induction vectors created by individual electrons. Atoms with partially filled electron shells have uncompensated fields. In atoms with filled electron shells, the resulting induction vector is 0.

In all cases, the change in the magnetic field is caused by the appearance of magnetization currents (the phenomenon of electromagnetic induction is observed). In other words, the superposition principle for the magnetic field remains valid: the field inside the magnet is a superposition of the external field $\boldsymbol((\vec(B))_(0))$ and the field $\boldsymbol(\vec(B"))$ of magnetizing currents i" , which arise under the influence of an external field. If the field of magnetization currents is directed in the same way as external field, then the induction of the total field will be greater than the external field (Fig. 3, a) - in this case we say that the substance enhances the field; if the field of magnetization currents is directed opposite to the external field, then the total field will be less than the external field (Fig. 3, b) - it is in this sense that we say that the substance weakens the magnetic field.

Rice. 3

IN diamagnetic materials molecules do not have their own magnetic field. Under the influence of an external magnetic field in atoms and molecules, the field of magnetization currents is directed opposite to the external field, therefore the modulus of the magnetic induction vector $ \boldsymbol(\vec(B))$ of the resulting field will be less than the modulus of the magnetic induction vector $ \boldsymbol((\vec(B ))_(0)) $ outer field.

Substances in which the external magnetic field is enhanced as a result of the addition of the electronic shells of the atoms of the substance to the magnetic fields due to the orientation of atomic magnetic fields in the direction of the external magnetic field are called paramagnetic(µ > 1).

Paramagnets very weakly enhance the external magnetic field. The magnetic permeability of paramagnetic materials differs from unity by only a fraction of a percent. For example, the magnetic permeability of platinum is 1.00036. Due to the very small values ​​of the magnetic permeability of paramagnetic and diamagnetic materials, their influence on an external field or the effect of an external field on paramagnetic or diamagnetic bodies is very difficult to detect. Therefore, in ordinary everyday practice, in technology, paramagnetic and diamagnetic substances are considered as non-magnetic, that is, substances that do not change the magnetic field and are not affected by the magnetic field. Examples of paramagnetic materials are sodium, oxygen, aluminum (μ = 1.00023).

IN paramagnets molecules have their own magnetic field. In the absence of an external magnetic field, due to thermal motion, the induction vectors of the magnetic fields of atoms and molecules are randomly oriented, so their average magnetization is zero (Fig. 4, a). When an external magnetic field is applied to atoms and molecules, a moment of force begins to act, tending to rotate them so that their fields are oriented parallel to the external field. The orientation of the paramagnetic molecules leads to the fact that the substance is magnetized (Fig. 4, b).

Rice. 4

The complete orientation of molecules in a magnetic field is prevented by their thermal motion, therefore the magnetic permeability of paramagnetic materials depends on temperature. It is obvious that with increasing temperature the magnetic permeability of paramagnetic materials decreases.

Ferromagnets

Substances that significantly enhance an external magnetic field are called ferromagnets(nickel, iron, cobalt, etc.). Examples of ferromagnets are cobalt, nickel, iron (μ reaches a value of 8·10 3).

The very name of this class of magnetic materials comes from Latin name iron - Ferrum. Main feature These substances are able to maintain magnetization in the absence of an external magnetic field; all permanent magnets belong to the class of ferromagnets. In addition to iron, its “neighbors” on the periodic table - cobalt and nickel - have ferromagnetic properties. Ferromagnets find wide practical application in science and technology, therefore a significant number of alloys with various ferromagnetic properties have been developed.

All given examples of ferromagnets refer to transition group metals, electron shell which contains several unpaired electrons, which leads to the fact that these atoms have a significant magnetic field of their own. IN crystalline state Due to the interaction between atoms in crystals, areas of spontaneous magnetization - domains - arise. The dimensions of these domains are tenths and hundredths of a millimeter (10 -4 − 10 -5 m), which significantly exceeds the size of an individual atom (10 -9 m). Within one domain, the magnetic fields of atoms are oriented strictly parallel; the orientation of the magnetic fields of other domains in the absence of an external magnetic field changes arbitrarily (Fig. 5).

Rice. 5

Thus, even in a non-magnetized state, strong magnetic fields exist inside a ferromagnet, the orientation of which changes in a random, chaotic manner during the transition from one domain to another. If the dimensions of a body significantly exceed the dimensions of individual domains, then the average magnetic field created by the domains of this body is practically absent.

If you place a ferromagnet in an external magnetic field B 0 , then the magnetic moments of the domains begin to rearrange. However, mechanical spatial rotation of sections of the substance does not occur. The process of magnetization reversal is associated with a change in the movement of electrons, but not with a change in the position of atoms at nodes crystal lattice. Domains that have the most favorable orientation relative to the direction of the field increase their size at the expense of neighboring “wrongly oriented” domains, absorbing them. In this case, the field in the substance increases quite significantly.

Properties of ferromagnets

1) the ferromagnetic properties of a substance appear only when the corresponding substance is located V crystalline state ;

2) the magnetic properties of ferromagnets strongly depend on temperature, since the orientation of the magnetic fields of the domains is prevented by thermal motion. For each ferromagnet there is a certain temperature at which the domain structure is completely destroyed and the ferromagnet turns into a paramagnet. This temperature value is called Curie point . So for pure iron the Curie temperature is approximately 900°C;

3) ferromagnets are magnetized until saturation in weak magnetic fields. Figure 6 shows how the magnetic field induction modulus changes B in steel with a change in external field B 0 :

Rice. 6

4) the magnetic permeability of a ferromagnet depends on the external magnetic field (Fig. 7).

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This is explained by the fact that initially with an increase B 0 magnetic induction B grows stronger, and therefore μ will increase. Then, at the value of magnetic induction B" 0 saturation occurs (μ at this moment is maximum) and with further increase B 0 magnetic induction B 1 in the substance ceases to change, and the magnetic permeability decreases (tends to 1):

$$\boldsymbol(\mu = \frac B(B_0) = \frac (B_0 + B_1)(B_0) = 1 + \frac (B_1)(B_0);) $$

5) ferromagnets exhibit residual magnetization. If, for example, a ferromagnetic rod is placed in a solenoid through which current passes and magnetized until saturation (point A) (Fig. 8), and then reduce the current in the solenoid, and with it B 0 , then you can notice that the field induction in the rod during the process of its demagnetization remains always greater than during the magnetization process. When B 0 = 0 (the current in the solenoid is turned off), the induction will be equal to B r (residual induction). The rod can be removed from the solenoid and used as a permanent magnet. To finally demagnetize the rod, you need to pass a current in the opposite direction through the solenoid, i.e. apply an external magnetic field with the opposite direction of the induction vector. Now increasing the modulus of the induction of this field to B oc , demagnetize the rod ( B = 0).

• Module B oc the induction of a magnetic field that demagnetizes a magnetized ferromagnet is called coercive force .

Rice. 8

With further increase B 0 you can magnetize the rod until saturation (point A" ).

Reducing now B 0 to zero, we get a permanent magnet again, but with induction –B r (opposite direction). To demagnetize the rod again, the current in the original direction must be turned on again in the solenoid, and the rod will demagnetize when the induction B 0 will become equal B oc . Continuing to increase I B 0 , magnetize the rod again until saturation (point A ).

Thus, when magnetizing and demagnetizing a ferromagnet, the induction B lags behind B 0. This lag is called the phenomenon of hysteresis . The curve shown in Figure 8 is called hysteresis loop .

Hysteresis (Greek ὑστέρησις - “lagging behind”) - a property of systems that do not immediately follow the applied forces.

The shape of the magnetization curve (hysteresis loop) varies significantly for different ferromagnetic materials, which have been found to be very wide application in scientific and technical applications. Some magnetic materials have a wide loop with high values residual magnetization and coercive force, they are called magnetically hard and are used to make permanent magnets. Other ferromagnetic alloys are characterized by low coercive force values; such materials are easily magnetized and remagnetized even in weak fields. Such materials are called magnetically soft and are used in various electrical devices - relays, transformers, magnetic circuits, etc.

Literature

1. Aksenovich L. A. Physics in high school: Theory. Assignments. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P.330-335.
2. Zhilko, V.V. Physics: textbook. allowance for 11th grade. general education school from Russian language training / V.V. Zhilko, A.V. Lavrinenko, L. G. Markovich. - Mn.: Nar. Asveta, 2002. - pp. 291-297.
3. Slobodyanyuk A.I. Physics 10. §13 Interaction of a magnetic field with matter

Notes

1. We consider the direction of the magnetic field induction vector only in the middle of the circuit.