Magnetic permeability of wood. Magnetic materials

Determination of the magnetic permeability of a substance. Her role in the description magnetic field

If you conduct an experiment with a solenoid that is connected to a ballistic galvanometer, then when you turn on the current in the solenoid, you can determine the value 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 value $\mu $, which characterizes magnetic properties environment 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 $\overrightarrow(J)$ 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 get:

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

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

Absolute magnetic permeability – this is a proportionality coefficient that takes into account the influence of the environment in which the wires are located.

To get an idea of the magnetic properties of the medium, the magnetic field around a wire with current in a given medium was compared with the magnetic field around the same wire, but located in a vacuum. It was found that in some cases the field is more intense than in a vacuum, in others it is less.

There are:

v Paramagnetic materials and environments in which a stronger MF is obtained (sodium, potassium, aluminum, platinum, manganese, air);

v Diamagnetic materials and environments in which the magnetic field is weaker (silver, mercury, water, glass, copper);

v Ferromagnetic materials in which the strongest magnetic field is created (iron, nickel, cobalt, cast iron and their alloys).

Absolute magnetic permeability for different substances has different sizes.

Magnetic constant – This is the absolute magnetic permeability of vacuum.

Relative magnetic permeability of the medium- a dimensionless quantity showing how many times the absolute magnetic permeability of a substance is greater or less than the magnetic constant:

For diamagnetic substances - , for paramagnetic substances - (for technical calculations of diamagnetic and paramagnetic bodies is taken equal to unity), for ferromagnetic materials - .

MP tension N characterizes the conditions for MF excitation. The intensity in a homogeneous medium does not depend on the magnetic properties of the substance in which the field is created, but takes into account the influence of the current magnitude and the shape of the conductors on the MF intensity at a given point.

MF intensity is a vector quantity. Vector direction N for isotropic media (media with the same magnetic properties in all directions) , coincides with the direction of the magnetic field or vector at a given point.

The magnetic field strength created by various sources is shown in Fig. 13.

Magnetic flux is total number magnetic lines passing through the entire surface under consideration. Magnetic flux F or MI flow through the area S , perpendicular magnetic lines equal to the product of magnetic induction IN by the amount of area that is penetrated by this magnetic flux.

42) When an iron core is introduced into a coil, the magnetic field increases and the core becomes magnetized. This effect was discovered by Ampere. He also discovered that the induction of a magnetic field in a substance can be greater or less than the induction of the field itself. Such substances came to be called magnets.

Magnetics– these are substances that can change the properties of an external magnetic field.

Magnetic permeability substance is determined by the ratio:

B 0 is the induction of the external magnetic field, B is the induction inside the substance.

Depending on the ratio of B and B 0, substances are divided into three types:

1) Diamagnets(m<1), к ним относятся chemical elements: Cu, Ag, Au, Hg. Magnetic permeability m=1-(10 -5 - 10 -6) differs very slightly from unity.

This class of substances was discovered by Faraday. These substances are “pushed out” of the magnetic field. If you hang a diamagnetic rod near the pole of a strong electromagnet, it will be repelled from it. The induction lines of the field and magnet are therefore directed in different directions.

2) Paramagnets have a magnetic permeability m>1, and in this case it also slightly exceeds unity: m=1+(10 -5 - 10 -6). This type of magnetic material includes the chemical elements Na, Mg, K, Al.

The magnetic permeability of paramagnetic materials depends on temperature and decreases as it increases. Without a magnetizing field, paramagnetic materials do not create their own magnetic field. There are no permanent paramagnets in nature.

3) Ferromagnets(m>>1): Fe, Co, Ni, Cd.

These substances can be in a magnetized state without an external field. Existence residual magnetism one of the important properties of ferromagnets. When heated to high temperature the ferromagnetic properties of the substance disappear. The temperature at which these properties disappear is called Curie temperature(for example, for iron T Curie = 1043 K).

At temperatures below the Curie point, a ferromagnet consists of domains. Domains– these are areas of spontaneous spontaneous magnetization (Fig. 9.21). The domain size is approximately 10 -4 -10 -7 m. The existence of magnets is due to the appearance of regions of spontaneous magnetization in matter. An iron magnet can retain its magnetic properties for a long time, since the domains in it are arranged in an orderly manner (one direction predominates). The magnetic properties will disappear if the magnet is hit hard or heated too much. As a result of these influences, the domains become “disordered.”

Fig.9.21. The shape of the domains: a) in the absence of a magnetic field, b) in the presence of an external magnetic field.

Domains can be represented as closed currents in microvolumes of magnetic materials. The domain is well illustrated in Fig. 9.21, from which it can be seen that the current in the domain moves along a broken closed loop. Closed electron currents lead to the appearance of a magnetic field perpendicular to the electron orbital plane. In the absence of an external magnetic field, the magnetic field of the domains is directed chaotically. This magnetic field changes direction under the influence of an external magnetic field. Magnets, as already noted, are divided into groups depending on how the magnetic field of the domain reacts to the action of an external magnetic field. In diamagnetic materials, the magnetic field more domains is directed in the direction opposite to the action of the external magnetic field, and in paramagnetic materials, on the contrary, in the direction of the action of the external magnetic field. However, the number of domains whose magnetic fields are directed in opposite directions differs by a very small amount. Therefore, the magnetic permeability m in dia- and paramagnets differs from unity by an amount of the order of 10 -5 - 10 -6. In ferromagnets, the number of domains with a magnetic field in the direction of the external field is many times greater than the number of domains with the opposite direction of the magnetic field.

Magnetization curve. Hysteresis loop. The phenomenon of magnetization is due to the existence of residual magnetism under the action of an external magnetic field on a substance.

Magnetic hysteresis is the phenomenon of delay in changes in magnetic induction in a ferromagnet relative to changes in the strength of the external magnetic field.

Figure 9.22 shows the dependence of the magnetic field in a substance on the external magnetic field B=B(B 0). Moreover, along the Ox axis they put external field, along the Oy axis – the magnetization of the substance. An increase in the external magnetic field leads to an increase in the magnetic field in the substance along the line to a value. Reducing the external magnetic field to zero leads to a decrease in the magnetic field in the substance (at the point With) to the value To the east(residual magnetization, the value of which is greater than zero). This effect is a consequence of the delay in the magnetization of the sample.

The induction value of the external magnetic field required for complete demagnetization of the substance (point d in Fig. 9.21) is called coercive force. The zero value of sample magnetization is obtained by changing the direction of the external magnetic field to a value. Continuing to increase the external magnetic field in the opposite direction to the maximum value, we bring it to the value. Then, we change the direction of the magnetic field, increasing it back to the value. In this case, our substance remains magnetized. Only the magnitude of the magnetic field induction has the opposite direction compared to the value at the point. Continuing to increase the value of magnetic induction in the same direction, we achieve complete demagnetization of the substance at point , and then we find ourselves again at point . Thus, we obtain a closed function that describes the cycle of complete magnetization reversal. Such a dependence of the magnetic field induction of a sample on the magnitude of the external magnetic field during a cycle of complete magnetization reversal is called hysteresis loop. The shape of the hysteresis loop is one of the main characteristics of any ferromagnetic substance. However, it is impossible to get to the point in this way.

Nowadays, it is quite easy to obtain strong magnetic fields. A large number of installations and devices operate on permanent magnets. They achieve fields of 1 – 2 T at room temperature. In small volumes, physicists have learned to obtain constant magnetic fields of up to 4 Tesla, using special alloys for this purpose. At low temperatures, on the order of the temperature of liquid helium, magnetic fields above 10 Tesla are obtained.

43) Law of electromagnetic induction (Faraday-Maxwell law). Lenz's rules

Summarizing the results of his experiments, Faraday formulated the law of electromagnetic induction. He showed that with any change in the magnetic flux in a closed conducting circuit, an induction current is excited. Consequently, an induced emf occurs in the circuit.

The induced emf is directly proportional to the rate of change of magnetic flux over time. The mathematical notation of this law was drawn up by Maxwell and therefore it is called the Faraday-Maxwell law (the law of electromagnetic induction).

There are microscopic circular currents ( molecular currents). This idea was later confirmed, after the discovery of the electron and the structure of the atom: these currents are created by the movement of electrons around the nucleus and, since they are oriented in the same way, in total they form a field inside and around the magnet.

On the image A the planes in which elementary electric currents are located are randomly oriented due to the chaotic thermal motion of atoms, and the substance does not exhibit magnetic properties. In a magnetized state (under the influence, for example, of an external magnetic field) (Figure b) these planes are oriented in the same way, and their actions are summed up.

Magnetic permeability.

The reaction of the medium to the influence of an external magnetic field with induction B0 (field in a vacuum) is determined by the magnetic susceptibility μ :

Where IN— magnetic field induction in a substance. Magnetic permeability is similar to dielectric constant ɛ .

Based on their magnetic properties, substances are divided into diamagnetic materials, paramagnets And ferromagnets. For diamagnetic materials the coefficient μ , which characterizes the magnetic properties of the medium, is less than unity (for example, for bismuth μ = 0.999824); in paramagnetic materials μ > 1 (for platinum μ - 1.00036); in ferromagnets μ ≫ 1 (iron, nickel, cobalt).

Diamagnets are repelled by a magnet, paramagnetic materials are attracted to it. By these features they can be distinguished from each other. For many substances, the magnetic permeability is almost the same as unity, but for ferromagnets it greatly exceeds it, reaching several tens of thousands of units.

Ferromagnets.

Ferromagnets exhibit the strongest magnetic properties. The magnetic fields created by ferromagnets are much stronger than the external magnetizing field. True, the magnetic fields of ferromagnets are not created as a result of the rotation of electrons around the nuclei - orbital magnetic moment, and due to the electron’s own rotation - its own magnetic moment, called spin.

Curie temperature ( TWith) is the temperature above which ferromagnetic materials lose their magnetic properties. It is different for each ferromagnet. For example, for iron T s= 753 °C, for nickel T s= 365 °C, for cobalt T s= 1000 °C. There are ferromagnetic alloys in which T s < 100 °С.

The first detailed studies of the magnetic properties of ferromagnets were carried out by the outstanding Russian physicist A. G. Stoletov (1839-1896).

Ferromagnets are used quite widely: as permanent magnets (in electrical measuring instruments, loudspeakers, telephones, etc.), steel cores in transformers, generators, electric motors (to enhance the magnetic field and save electricity). Magnetic tapes, which are made of ferromagnetic materials, record sound and images for tape recorders and video recorders. Information is recorded on thin magnetic films for storage devices in electronic computers.

Called magnetic permeability . Absolute magneticpermeability environment is the ratio of B to H. According to International system units it is measured in units called 1 henry per meter.

Numeric value it is expressed by the ratio of its value to the value of the magnetic permeability of the vacuum and is denoted by µ. This value is called relative magneticpermeability(or simply magnetic permeability) of the medium. As a relative quantity, it does not have a unit of measurement.

Consequently, the relative magnetic permeability µ is a value showing how many times the field induction of a given medium is less (or greater) than the induction of a vacuum magnetic field.

When a substance is exposed to an external magnetic field, it becomes magnetized. How does this happen? According to Ampere's hypothesis, microscopic electric currents constantly circulate in every substance, caused by the movement of electrons in their orbits and the presence of their own. Under normal conditions, this movement is disordered, and the fields “quench” (compensate) each other. When a body is placed in an external field, the currents are ordered, and the body becomes magnetized (i.e., having its own field).

The magnetic permeability of all substances is different. Based on its size, substances can be divided into three large groups.

U diamagnetic materials the value of magnetic permeability µ is slightly less than unity. For example, bismuth has µ = 0.9998. Diamagnets include zinc, lead, quartz, copper, glass, hydrogen, benzene, and water.

Magnetic permeability paramagnetic slightly more than one (for aluminum µ = 1.000023). Examples of paramagnetic materials are nickel, oxygen, tungsten, hard rubber, platinum, nitrogen, air.

Finally, the third group includes a number of substances (mainly metals and alloys), whose magnetic permeability significantly (several orders of magnitude) exceeds unity. These substances are ferromagnets. This mainly includes nickel, iron, cobalt and their alloys. For steel µ = 8∙10^3, for a nickel-iron alloy µ=2.5∙10^5. Ferromagnets have properties that distinguish them from other substances. Firstly, they have residual magnetism. Secondly, their magnetic permeability depends on the magnitude of the external field induction. Thirdly, for each of them there is a certain temperature threshold, called Curie point, at which it loses its ferromagnetic properties and becomes paramagnetic. For nickel the Curie point is 360°C, for iron - 770°C.

The properties of ferromagnets are determined not only by magnetic permeability, but also by the value of I, called magnetization of this substance. This is a complex nonlinear function of magnetic induction; the increase in magnetization is described by a line called magnetization curve. In this case, having reached a certain point, the magnetization practically stops growing (the magnetic saturation). The lag of the magnetization value of a ferromagnet from the growing value of the external field induction is called magnetic hysteresis. In this case, there is a dependence of the magnetic characteristics of a ferromagnet not only on its current state, but also on its previous magnetization. The graphical representation of the curve of this dependence is called hysteresis loop.

Due to their properties, ferromagnets are widely used in technology. They are used in the rotors of generators and electric motors, in the manufacture of transformer cores and in the production of parts for electronic computers. Ferromagnets are used in tape recorders, telephones, magnetic tapes and other media.

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);

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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 the 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 amplifies 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.

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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).

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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 use 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).

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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 :

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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 current through the solenoid opposite direction, 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 .

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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 hysteresis phenomenon . 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 values of coercive force; 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

Aksenovich L. A. Physics in high school: Theory. Tasks. 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.
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.
Slobodyanyuk A.I. Physics 10. §13 Interaction of a magnetic field with matter