Magnetics

All substances in a magnetic field are magnetized (an internal magnetic field appears in them). Depending on the size and direction internal field substances are divided into:

1) diamagnetic materials,

2) paramagnetic materials,

3) ferromagnets.

The magnetization of a substance is characterized by magnetic permeability,

Magnetic induction in matter,

Magnetic induction in a vacuum.

Any atom can be characterized by a magnetic moment .

The current strength in the circuit, - the area of ​​the circuit, - the normal vector to the surface of the circuit.

The microcurrent of an atom is created by the movement of negative electrons in orbit and around own axis, as well as rotation of the positive nucleus around its own axis.

1. Diamagnets.

When not external field, in atoms diamagnetic materials the currents of electrons and nuclei are compensated. The total microcurrent of an atom and its magnetic moment are equal to zero.

In an external magnetic field, nonzero elementary currents are induced (induced) in atoms. The magnetic moments of the atoms are oriented in the opposite direction.

A small field of its own is created, directed opposite to the external one, weakening it.

In diamagnetic materials.

Because< , то для диамагнетиков 1.

2. Paramagnets

IN paramagnets microcurrents of atoms and their magnetic moments are not equal to zero.

Without an external field, these microcurrents are located chaotically.

In an external magnetic field, microcurrents of paramagnetic atoms are oriented along the field, enhancing it.

In a paramagnetic material, magnetic induction = + slightly exceeds .

For paramagnets, 1. For dia- and paramagnets, we can assume 1.

Table 1. Magnetic permeability of para- and diamagnetic materials.

The magnetization of paramagnetic materials depends on temperature, because The thermal movement of atoms prevents the ordered arrangement of microcurrents.

Most substances in nature are paramagnetic.

The intrinsic magnetic field in dia- and paramagnets is insignificant and is destroyed if the substance is removed from the external field (the atoms return to their original state, the substance is demagnetized).

3. Ferromagnets

Magnetic permeability ferromagnets reaches hundreds of thousands and depends on the magnitude of the magnetizing field ( highly magnetic substances).

Ferromagnets: iron, steel, nickel, cobalt, their alloys and compounds.

In ferromagnets, there are regions of spontaneous magnetization (“domains”) in which all atomic microcurrents are oriented in the same way. The domain size reaches 0.1 mm.

In the absence of an external field, the magnetic moments of individual domains are randomly oriented and compensated. In an external field, those domains in which microcurrents enhance the external field increase their size at the expense of neighboring ones. The resulting magnetic field = + in ferromagnets is much stronger compared to para- and diamagnetic materials.

Domains containing billions of atoms have inertia and do not quickly return to their original disordered state. Therefore, if a ferromagnet is removed from the external field, then its own field remains for a long time.

The magnet demagnetizes during long-term storage (over time, the domains return to a chaotic state).

Another method of demagnetization is heating. For each ferromagnet there is a temperature (it is called the “Curie point”) at which the bonds between atoms in the domains are destroyed. In this case, the ferromagnet turns into a paramagnet and demagnetization occurs. For example, the Curie point for iron is 770°C.

The magnetic field of the coil is determined by the current and the strength of this field, and the field induction. Those. The field induction in a vacuum is proportional to the magnitude of the current. If a magnetic field is created in a certain environment or substance, then the field affects the substance, and it, in turn, changes the magnetic field in a certain way.

A substance located in an external magnetic field is magnetized and an additional internal magnetic field appears in it. It is associated with the movement of electrons along intra-atomic orbits, as well as around their own axis. The movement of electrons and atomic nuclei can be considered as elementary circular currents.

Magnetic properties elementary circular current are characterized by a magnetic moment.

In the absence of an external magnetic field, the elementary currents inside the substance are oriented randomly (chaotically) and, therefore, the total or total magnetic moment equal to zero and in the surrounding space the magnetic field of elementary internal currents is not detected.

The influence of an external magnetic field on elementary currents in matter is that the orientation of the axes of rotation of charged particles changes so that their magnetic moments are directed in one direction. (towards the external magnetic field). The intensity and nature of magnetization of different substances in the same external magnetic field differ significantly. The quantity characterizing the properties of the medium and the influence of the medium on the magnetic field density is called absolute magnetic permeability or magnetic permeability of the medium (μ With ) . This is the relation = . Measured [ μ With ]=Gn/m.

The absolute magnetic permeability of a vacuum is called the magnetic constant μ O =4π 10 -7 H/m.

The ratio of absolute magnetic permeability to magnetic constant is called relative magnetic permeabilityμ c /μ 0 =μ. Those. relative magnetic permeability is a value that shows how many times the absolute magnetic permeability of the medium is greater or less than the absolute permeability of vacuum. μ is a dimensionless quantity that varies over a wide range. This value forms the basis for dividing all materials and media into three groups.

Diamagnets . These substances have μ< 1. К ним относятся - медь, серебро, цинк, ртуть, свинец, сера, хлор, вода и др. Например, у меди μ Cu = 0,999995. Эти вещества слабо взаимодействуют с магнитом.

Paramagnets . These substances have μ > 1. These include aluminum, magnesium, tin, platinum, manganese, oxygen, air, etc. Air = 1.0000031. . These substances, like diamagnetic materials, interact weakly with a magnet.

For technical calculations, μ of diamagnetic and paramagnetic bodies is taken equal to unity.

Ferromagnets . This is a special group of substances that play a huge role in electrical engineering. These substances have μ >> 1. These include iron, steel, cast iron, nickel, cobalt, gadolinium and metal alloys. These substances are strongly attracted to a magnet. For these substances, μ = 600-10,000. For some alloys, μ reaches record values ​​of up to 100,000. It should be noted that μ for ferromagnetic materials is not constant and depends on the magnetic field strength, type of material and temperature.

The large value of µ in ferromagnets is explained by the fact that they contain regions of spontaneous magnetization (domains), within which the elementary magnetic moments are directed in the same way. When folded, they form common magnetic moments of the domains.

In the absence of a magnetic field, the magnetic moments of the domains are randomly oriented and the total magnetic moment of the body or substance is zero. Under the influence of an external field, the magnetic moments of the domains are oriented in one direction and form a common magnetic moment of the body, directed in the same direction as the external magnetic field.

This important feature are used in practice by using ferromagnetic cores in coils, which makes it possible to sharply increase magnetic induction and magnetic flux at the same values ​​of currents and number of turns or, in other words, to concentrate the magnetic field in a relatively small volume.

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

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

For isotropic substances the ratio:

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

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

See also

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Excerpt characterizing Magnetic permeability

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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. Tensions in homogeneous environment does not depend on the magnetic properties of the substance in which the field is created, but takes into account the influence of the magnitude of the current and the shape of the conductors on the intensity of the magnetic field at a given point.

MP tension – vector quantity. Vector direction N For isotropic media(media with identical magnetic properties in all directions) , coincides with the direction of the magnetic field or vector at a given point.

The strength of the magnetic field created various sources, shown in Fig. 13.

Magnetic flux- This 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 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 important properties 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 directed to the side, opposite action 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 magnetic fields which are sent to opposite sides, 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, the external field is plotted along the Ox axis, and the magnetization of the substance is plotted along the Oy axis. 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 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 until maximum value, 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 opposite direction compared to the value at 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 get closed function, which 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. Large quantity installations and devices operate on permanent magnets. They achieve radiation levels 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 electromagnetic induction(Faraday-Maxwell z.). Lenz's rules

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

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

Of course, a field with induction was created in the iron instead of which it would have been in the air. Therefore, we can say that compared to air, iron is 2400 times more “permeable” to a magnetic field.

The relative magnetic permeability of iron can be called the ratio magnetic induction in iron and in air

if a magnetic field is observed inside identical ring coils, one of which is wound on iron ring, and the other does not contain any ferromagnetic bodies.

In this case, of course, the values ​​of induction and Вв are determined at the same value of the specific total current.

Magnetic permeability of the same ferromagnetic material at different meanings induction is different. In fact, imagine the magnetic characteristic shown in Fig. 3.4, in the form of a table: the first line contains the values ​​of the specific total current, the second - the values ​​of the magnetic induction observed in the iron (closed ring inside the coil), the third - the values ​​of the magnetic induction in the same ring coil without ferromagnetic bodies, increased by 10 000 times.

The first row of the table corresponds to the experiments based on which the magnetic characteristic in Fig. 3.4. The second line is calculated using the formula

The relative magnetic permeability values ​​for different inductions are calculated using the formula

As can be seen from the table, the magnetic permeability first increases and then decreases. The results obtained can be depicted by the graph shown in Fig. 3.5.

Rice. 3.5. Relative magnetic permeability pure iron depending on the specific total current

The first studies of the magnetic properties of materials on closed ring samples and the establishment of the nature and change in permeability with the field belong to Moscow University professor A. G. Stoletov. He emphasized that for developing electrical engineering, knowing the magnetic properties of steel is as important as knowing the properties of steam for builders of steam engines.

The decrease in relative magnetic permeability with increasing induction represents the second characteristic feature ferromagnetic bodies. At first they are easily magnetized; magnetic induction reaches large values at sufficiently weak magnetizing currents. However, a further increase in magnetic induction requires an increasingly significant increase in current - it is very difficult to create an induction above approximately 2.0-2.2 Tesla in iron. This is indicated by the flat course of the magnetic characteristic shown in Fig. 3.4, in the region of large inductions.

To increase the induction from 1.65 to it is necessary to increase the specific total current from 100 to 1000 A. But in order to increase the induction further, it is necessary to increase the magnetizing current to 2000 A/cm (see Table 3.1). When order is inducted, magnetic saturation occurs, as they say.

Example 1. In a ring coil with a number of turns at medium length steel core 25 cm current flows I = 1 A. Magnetic flux in a steel core having cross section turns out to be equal