Magnetic materials: properties and characteristics. Features of various types of magnetism. magnetization processes. Features of strongly magnetic materials. remagnetization losses.

Soft magnetic materials: classification, properties, purpose.

Hard magnetic materials: classification, properties, purpose. Magnetic materials for special purposes: classification, properties, purpose.

Literature

All substances in nature interact with an external magnetic field, but each substance is different.

The magnetic properties of substances depend on the magnetic properties of elementary particles, the structure of atoms and molecules, as well as their groups, but the main determining influence is exerted by electrons and their magnetic moments.

All substances, in relation to the magnetic field, behavior in it, are divided into the following groups:

Diamagnets- materials that do not have a permanent magnetic dipole moment, with a relative magnetic permeability (μ≤1) slightly less than unity. The relative permittivity μ of diamagnets is almost independent of the magnitude of the magnetic field (H) and does not depend on temperature. These include: inert gases (Ne, Ar, Kr, Xe), hydrogen (H 2); copper (Сu), zinc (Zn), silver (Аg), gold (Au), antimony (Sb), etc.

Paramagnets- materials that have permanent dipole moments, but they are randomly located, so the interaction between them is very weak. The relative magnetic permeability of paramagnets is slightly more than unity (μ≥1), weakly dependent on the magnetic field strength and temperature.

Paramagnets include the following materials: oxygen (O 2), aluminum (Al), platinum (Pt), alkali metals, salts of iron, nickel, cobalt, etc.

ferromagnets– materials with permanent magnetic dipole moments, domain structure. In each domain, they are parallel to each other and equally directed, so the interaction between them is very strong. The relative magnetic permeability of ferromagnets is large (μ >> 1), for some alloys it reaches 1500000. It depends on the magnetic field strength and temperature.

These include: iron (Fe), nickel (Ni), cobalt (Co), many alloys, rare earth elements: samarium (Sm), gadolinium (Gd), etc.

Antiferromagnets- materials that have permanent dipole magnetic moments that are antiparallel to each other. Their relative magnetic permeability is slightly more than unity (μ ≥ 1), very weakly dependent on the magnetic field strength and temperature. These include: oxides of cobalt (CoO), manganese (MnO), nickel fluoride (NiF 2), etc.

Ferrimagnets- materials that have antiparallel permanent dipole magnetic moments that do not fully compensate each other. The smaller this compensation, the higher their ferromagnetic properties. The relative magnetic permeability of ferrimagnets can be close to unity (with almost complete compensation of the moments), and can reach tens of thousands (with little compensation).

Ferrites are ferrimagnets, they can be called oxyferrs, since they are oxides of divalent metals with Fe 2 O 3. The general formula of ferrite, where Me is a divalent metal.

The magnetic permeability of ferrites depends on temperature and magnetic field strength, but to a lesser extent than that of ferromagnets.

Ferrites are ceramic ferromagnetic materials with low electrical conductivity, as a result of which they can be classified as electronic semiconductors with high magnetic (μ ≈ 10 4) and high dielectric (ε ≈ 10 3) permeability.

Dia-, para- and antiferromagnets can be combined into a group of weakly magnetic substances, and ferro- and ferrimagnets into a group of strongly magnetic substances.

For technical applications in the field of radio electronics, highly magnetic substances are of the greatest interest. (Fig. 6.1)

Rice. 6.1. Structural diagram of magnetic materials

The magnetic properties of materials are determined by internal hidden forms of movement of electric charges, which are elementary circular currents. The circular current is characterized by a magnetic moment and can be replaced by an equivalent magnetic dipole. Magnetic dipoles are formed mainly by the spin rotation of electrons, while the orbital rotation of electrons takes a weak part in this process, as well as nuclear rotation.

In most materials, the spin moments of electrons cancel each other out. Therefore, ferromagnetism is not observed in all substances of the periodic table.

Conditions required for a material to be ferromagnetic:

1. Existence of elementary circular currents in atoms.

2. The presence of uncompensated spin moments, electrons.

3. The ratio between the diameter of the electron orbit (D), which has an uncompensated spin moment, and the crystal lattice constant of the substance (a) must be

. (6.1)

4. The presence of a domain structure, i.e. such crystalline regions in which the dipole magnetic moments are parallel oriented.

5. The temperature of the material (substance) must be below the Curie point, since at a higher temperature the domain structure disappears, the material passes from the ferromagnetic state to the paramagnetic state.

A characteristic property of the ferromagnetic state of matter is the presence of spontaneous magnetization without the application of an external magnetic field. However, the magnetic flux of such a body will be equal to zero, since the direction of the magnetic moments of individual domains is different (a domain structure with a closed magnetic circuit).

The degree of magnetization of a substance is characterized by the magnitude of magnetization, or the intensity of magnetization (J), which is defined as the limit of the ratio of the resulting magnetic moment Σm, related to the volume of the substance (V), when the volume tends to zero

. (6.2)

If we place the substance in an external magnetic field with strength H, then the ratio between J and H will be

J = 4 πχH, (6.3)

where χ (kappa) is called magnetic viscosity.

The relative magnetic permeability μ depends on χ:

μ = 1 +4 πχ . (6.4)

The intensity of the magnetization can be determined by knowing μ

μ = 1+. (6.5)

In general, the magnetic field in a ferromagnet is created as the sum of two components: external, created by the strength of the external magnetic field H, and internal, created by the magnetization (J).

The total magnetic field is characterized by magnetic induction B:

B = μ 0 (H + J), (6.6)

where μ 0 – magnetic constant (magnetic permeability of vacuum)

μ 0 = 4 π ∙10 -7 , g/m. (6.7)

Expressing the value of J in terms of χ and then μ, we get:

B = μ 0 H(1 + 4 πχ ) orB = μ 0 μH. (6.8)

Absolute value of magnetic permeability

μ abs = μ 0 ∙ μ . (6.9)

The final formula for magnetic induction B

B = μ abs H. (6.10)

The process of magnetization of a ferromagnetic material under the influence of an external magnetic field is as follows:

the growth of domains whose magnetic moments are close in direction to the external field, and the decrease in other domains;

orientation of the magnetic moments of all domains in the direction of the external field.

The magnetization process is characterized for each ferromagnet by its main magnetization curve B \u003d f (H).

The magnetic permeability μ also changes during the magnetization process.

This is shown in fig. 6.2.

Rice. 6.2. Curves of magnetization (B = f(H)) and magnetic permeability (μ = f(H))

The magnetic permeability μ at a strength H close to zero is called initial (section 1), and when the material passes to saturation, it will take on a maximum value (2), with a further increase in H, the magnetic permeability μ decreases (sections 3 and 4).

During cyclic magnetization of a ferromagnet, the magnetization and demagnetization curves form a hysteresis loop. The hysteresis loop obtained under the condition of saturation of the material is called the limiting one. From the hysteresis loop, obtained, for example, on the oscilloscope screen, you can get quite complete information about the main magnetic parameters of the material (Fig. 6.3).

Rice. 6.3. Hysteresis loop

The main parameters are:

1) residual induction, after the removal of the field strength - Br;

2) coercive force Hc - the tension that must be applied to the sample in order to remove the residual induction;

3) maximum induction B max , which is achieved when the sample is fully saturated;

4) specific hysteresis losses for one cycle of magnetization reversal, which are characterized by the area covered by the hysteresis loop.

The remaining magnetic parameters of the material, as well as losses due to magnetization reversal (hysteresis), eddy currents, energy in the gap (for a permanent magnet) can be calculated using the formulas that were given above and will be given later.

Losses in ferromagneticmaterials - these are the energy costs that go to the remagnetization of ferromagnets, to the occurrence of eddy currents in an alternating magnetic field, to the magnetic viscosity of the material - they create the so-called losses, which can be divided into the following types:

a) hysteresis losses Рg, proportional to the area of ​​the hysteresis loop

Rg = η∙f∙
∙ V, W (6.11)

where η is the hysteresis coefficient for a given material;

f is the field frequency, Hz;

AT max– maximum induction, T;

V is the sample volume, m3;

n≈ 1.6...2 - the value of the exponent;

b) eddy current losses

Rv.t. = ξ∙f 2 ∙B max ∙ V, W (6.12)

where ξ is a coefficient depending on the specific electrical resistance of the material and on the shape of the sample;

c) post-effect losses Pp.s. according to the formula

Rp.s. \u003d P - Rg - Pv.t. (6.13)

Eddy current losses can be reduced by increasing the electrical resistance of the ferromagnet. To do this, the magnetic circuit, for example, for transformers, is recruited from separate thin ferromagnetic plates isolated from each other.

In practice, it is sometimes used ferromagnets with an open magnetic circuit, i.e. having, for example, an air gap with high magnetic resistance. In a body with an air gap, free poles arise, creating a demagnetizing field directed towards the external magnetizing field. There is a decrease in induction the greater, the wider the air gap. This is manifested in electric machines, magnetic lifting devices, etc.

The energy in the gap (W L), for example, a permanent magnet, is expressed by the formula

, J/m 3 , (6.14)

where AT L and H L are the actual induction and the field strength for a given length of the air gap.

By changing the applied tension to the ferromagnet, it is possible to obtain the maximum energy in a given gap.

To find W max, a diagram is used in which, according to the demagnetization curve for a magnetic material located in the second quadrant (section of the hysteresis loop), an energy curve in the gap is plotted, given by different values ​​of B (or H). The dependence of W L on B L and H L is shown in fig. 6.4.

Rice. 6.4. Energy in the air gap of a ferromagnet

To determine the field strength H, at which there will be a maximum energy in the magnet gap, it is necessary to draw a tangent to the maximum energy (at point A), and draw a horizontal line from it until it intersects with the hysteresis loop in the second quadrant. Then lower the perpendicular to the intersection with the coordinate H. The point H L 2 will determine the desired magnetic field strength.

According to the main magnetic parameters, ferromagnetic materials can be classify into the following groups;

Magnetically soft - materials with low coercive force Hc (up to 100 A/m), high magnetic permeability and low hysteresis losses. They are used as DC magnetic circuits (cores of transformers, measuring instruments, inductors, etc.)

Tosoft magnetic materials relate:

technically pure iron, carbonyl iron;

electrical steel;

permalloys;

alsifera;

ferrites (copper-manganese);

thermomagnetic alloys (Ni-Cr-Fe), etc.

2. Magnetically hard - materials with a large coercive force (Hc > 100 A/m) (see Fig. 4.5, G).

Hard magnetic materials are used to make permanent magnets, which use the magnetic energy in the air gap between the magnet poles.

To hard magnetic materials relate:

Cast alni alloys (Al-Ni-Fe);

Alnico (Al-Ni-Co-Fe);

Magnico;

Alloy steels hardened to martensite, etc.

Of particular interest are alloys based on rare earth materials (YCo, CeCo, SmCo, etc.), which have a high value of H c and w max .

3. Ferrites - materials that are double iron oxides with oxides of divalent metals (MeO∙Fe 2 O 3). Ferrites can be magnetically soft and magnetically hard, depending on their crystal structure, for example, the type of spinel - (MgAl 3 O 4), gausmagnet (Mn 3 O 4), garnet Ga 3 Al 2 (SiO 4) 3, etc. Their electrical resistivity is high (from 10 -1 to 10 10 Ohm∙m), therefore, eddy current losses, especially at high frequencies, are small.

4. Magnetodielectrics - materials consisting of a ferromagnetic powder with a dielectric binder. The powder is usually taken on the basis of a magnetically soft material - carbonyl iron, alsifer, and a material with low dielectric losses - polystyrene, bakelite, etc., serves as a binder dielectric.

Questions for self-examination:

Classification of substances according to magnetic properties.

Features of strongly magnetic substances (domains, anisotropy, magnetization curve, magnetostriction, magnetic permeability, hysteresis, etc.)

Factors affecting magnetic properties

Losses in magnetic materials

Classification of highly magnetic materials

Low frequency soft magnetic materials

High frequency soft magnetic materials

Hard magnetic materials

Magnetic materials for special purposes

Applications

Conductor materials Table A.1

conductor		Ohm∙mm 2 /m	specific resistance-		heat transfer water content W/m∙deg	especially copper,	Work function of an electron	Board temperature,
pure metals
Aluminum
Molybdenum
Tungsten
poly-crystal
Manganin			(5…30)∙10 -6
Constantan			(5…20)∙10 -6
Nickel silver
Thermocouples
Copper-constantan				Tism up to 350 °С
Chromel-alumel				Tism up to 1000 °С
Platinum-platinum-rhodium				Tism up to 1600 °С

Semiconductor materials Table A.2

	Name semiconductor kovy material			own carriers	Mobility carriers u,
Inorganic Crystal. elementary (atomic)
	Germanium
Crystal. connections
	Silicon carbide						sublimation
	Antimony indium
	gallium arsenide
	gallium phosphide
	indium arsenide
	Bismuth telluride
	lead sulfide
glassy
	Chalcogenides	As 2 Te 2 Se, As 2 Se 3 Al 2 Se 3
organic
	Anthracene
	Naphthalene
	Dyes and pigments Copper phthalocyanine
	Molecular complexes Iodine pyrene
	Polymers Polyacrylonitrile

Dielectric materials Table A.3

State of aggregation	Mother's name alov (dielectrics)	Dielectric constant, relative E	volume- resistance , Ohm m	dielectric loss angle	Strength (electrical) E pr, MV / m	Specific heat density λ, W/m ºK
	SF6
liquid-bones	Transformer oil
Solid materials	Organic a) Paraffin Holovax
	b) Bakel resin Rosin Polyvinyl- Polystyrene Polyethylene Polymethyl methacrylate Epoxy resin
	Compound
	d) Phenol-layer (FAS)
	e) Varnish fabric
	Electro-cardboard (EVT)
	g) Butadiene rubber
	Rubber insulating
	h) Fluoro-plast-4 ftoroplast-3
	Inorganic a) Electrical glass.
	b) Steatite (ceramic) electrical engineering porcelain
	c) Muscovite mica Mikalex
	d) Ferro-ceramics VK-1 Piezoquartz
	e) Fluoride insulation (AlF 3)
	f) Asbestos
	Element Organ. a) Silicon org. resin
	b) Silicon organ. rubber

Magnetic materials Table A.4

Name of magnetic material	Chemical composition or brand	Relative magnetic permeability, μ		Magnetic induction B, T		Coer-citive- force Ns, A/m	Specific email resistance ρ, μOhm∙m	Energy in the gap , J / m 3
		initial, μ n	maxi-small, μ max	remaining accurate, V	maxi-small, V max
Magnetically soft
Electrical tech. steel
Permalloy low nickel
Permalloy high nickel
supermalloy
Alcifer
Ferrites
Nickel-zinc ferrite
Ferrite manganese-zinc
Magnetic hard
barium
barium
Magnetodielectrics
Based on carbonyl iron

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Absolute magnetic permeability - this is a proportionality factor 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, we compared the magnetic field around the wire with current in the given medium with the magnetic field around the same wire, but in vacuum. It was found that in some cases the field is more intense than in vacuum, in others it is less.

Distinguish:

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

v Diamagnetic materials and media 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 a different value.

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

MP tension N characterizes the conditions for excitation of the MF. 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 magnitude of the current and the shape of the conductors on the intensity of the magnetic field at a given point.

MP tension is a vector quantity. vector direction H 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 intensity of the magnetic field created by various sources is shown in fig. thirteen.

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

42) When an iron core is introduced into the coil, the magnetic field increases and the core becomes magnetized. This effect was discovered by Ampère. 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 became known as magnets.

Magnetics are substances capable of changing the properties of an external magnetic field.

Magnetic permeability substances is determined by the ratio:

B 0 - induction of the external magnetic field, B - 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 химические элементы: Cu, Ag, Au, Hg. Магнитная проницаемость m=1-(10 -5 - 10 -6) очень незначительно отличается от единицы.

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, then it will repel from it. The lines of induction of the field and the magnet, therefore, are directed in different directions.

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

The magnetic permeability of paramagnets depends on temperature and decreases with its increase. Without a magnetizing field, paramagnets 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 a high temperature, the ferromagnetic properties of a 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 size of the domain is approximately 10 -4 -10 -7 m. The occurrence of regions of spontaneous magnetization in the substance is due to the existence of magnets. An iron magnet can retain its magnetic properties for a long time, since the domains in it line up in an orderly manner (one direction prevails). The magnetic properties will disappear if the magnet is hit hard or heated strongly. As a result of these influences, the domains are "disordered".

Fig.9.21. Domain shape: 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 magnets. The domain is well illustrated in Fig. 9.21, which shows that the current in the domain moves along a broken closed loop. Closed currents of electrons lead to the appearance of a magnetic field perpendicular to the plane of the electron orbit. In the absence of an external magnetic field, the magnetic field of the domains is chaotically directed. This magnetic field changes direction under the action of an external magnetic field. Magnetics, 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 diamagnets, the magnetic field of a larger number of domains is directed in the direction opposite to the action of the external magnetic field, and in paramagnets, on the contrary, in the direction 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 a value 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.

Curve of magnetization. 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 the phenomenon of delay in the change in magnetic induction in a ferromagnet relative to the change in the strength of an external magnetic field is called.

Figure 9.22 shows the dependence of the magnetic field in the 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 up to the value . A decrease in the external magnetic field to zero leads to a decrease in the magnetic field in the substance (at the point with) up to In ost(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 value of the induction of the external magnetic field, necessary for the complete demagnetization of the substance (point d in Fig. 9.21) is called coercive force. The zero value of the sample magnetization is obtained by changing the direction of the external magnetic field to the 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 matter 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 the magnetic induction in the same direction, we achieve complete demagnetization of the substance at the point , and further, we find ourselves again at the point . Thus, we obtain a closed function that describes the cycle of complete remagnetization. Such a dependence for the cycle of complete magnetization reversal of the induction of the magnetic field of the sample on the magnitude of the external magnetic field 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.

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

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

Summarizing the result of the 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. Therefore, an induction emf occurs in the circuit.

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

Magnetic permeability. Magnetic properties of substances

Magnetic properties of substances

Just as the electrical properties of a substance are characterized by the permittivity, the magnetic properties of a substance are characterized by magnetic permeability.

Due to the fact that all substances in a magnetic field create their own magnetic field, the magnetic induction vector in a homogeneous medium differs from the vector at the same point in space in the absence of a medium, i.e., in vacuum.

The relation is called magnetic permeability of the medium.

So, in a homogeneous medium, the magnetic induction is equal to:

The value of m for iron is very large. This can be verified by experience. If an iron core is inserted into a long coil, then the magnetic induction, according to formula (12.1), will increase m times. Consequently, the flux of magnetic induction will increase by the same amount. When the circuit that feeds the magnetizing coil with direct current is opened, an induction current appears in the second, small coil wound over the main one, which is recorded by a galvanometer (Fig. 12.1).

If an iron core is inserted into the coil, then the deviation of the galvanometer needle when the circuit is opened will be m times greater. Measurements show that the magnetic flux when an iron core is introduced into the coil can increase thousands of times. Therefore, the magnetic permeability of iron is enormous.

There are three main classes of substances with sharply different magnetic properties: ferromagnets, paramagnets and diamagnets.

ferromagnets

Substances in which, like iron, m >> 1, are called ferromagnets. In addition to iron, cobalt and nickel, as well as a number of rare earth elements and many alloys, are ferromagnets. The most important property of ferromagnets is the existence of residual magnetism. A ferromagnetic substance can be in a magnetized state without an external magnetizing field.

An iron object (for example, a rod) is known to be drawn into a magnetic field, that is, it moves to an area where the magnetic induction is greater. Accordingly, it is attracted to a magnet or an electromagnet. This happens because the elementary currents in iron are oriented in such a way that the direction of the magnetic induction of their field coincides with the direction of the induction of the magnetizing field. As a result, the iron rod turns into a magnet, the nearest pole of which is opposite to the pole of the electromagnet. Opposite poles of magnets are attracted (Fig. 12.2).

Rice. 12.2

STOP! Decide for yourself: A1-A3, B1, B3.

Paramagnets

There are substances that behave like iron, that is, they are drawn into a magnetic field. These substances are called paramagnetic. These include some metals (aluminum, sodium, potassium, manganese, platinum, etc.), oxygen and many other elements, as well as various electrolyte solutions.

Since paramagnets are drawn into the field, the lines of induction of their own magnetic field created by them and the magnetizing field are directed in the same way, so the field is amplified. Thus, they have m > 1. But m differs from unity very slightly, only by a value of the order of 10 -5 ... 10 -6 . Therefore, powerful magnetic fields are required to observe paramagnetic phenomena.

Diamagnets

A special class of substances are diamagnets discovered by Faraday. They are pushed out of the magnetic field. If you hang a diamagnetic rod near the pole of a strong electromagnet, then it will repel from it. Consequently, the lines of induction of the field created by him are directed opposite to the lines of induction of the magnetizing field, that is, the field is weakened (Fig. 12.3). Accordingly, for diamagnets m< 1, причем отличается от единицы на вели­чину порядка 10 –6 . Магнитные свойства у диамагнетиков вы­ражены слабее, чем у парамагнетиков.

If in the experiments described above, instead of an iron core, cores of other materials are taken, 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 of these materials is introduced into the coil, the increase in the 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 ​​are combined into one group of ferromagnetic materials.

However, all other "non-magnetic" materials also have some effect on the magnetic flux, although this effect is much less than that of ferromagnetic materials. With very careful measurements, this change can be detected and the magnetic permeability of various materials can be determined. However, it must be borne in mind that in the experiment described above, we compared the magnetic flux in the coil, the cavity of which is filled with iron, with the flux in the coil, inside which there is air. While we were talking about such strongly 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 comparisons with a coil with no air inside (vacuum). Thus, for the 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 a unit (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 the fact that some substances have a magnetic permeability greater than one, while others have it less than one, is especially remarkable, that is, 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 Table. 7, the difference in permeability from unity is small for both paramagnetic and diamagnetic substances.

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

Table 7. 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, as well as the influence of ferromagnetic substances, by the fact that a flux emanating from elementary ampere currents is added to the magnetic flux created by the current in the coil winding. 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 action 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.

The decrease in the magnetic flux when the coil is filled 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 elementary currents arise in diamagnetic substances under the action of an external magnetic field, 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. Elementary currents in them are directed opposite to the current in the solenoid

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

If you conduct an experiment with a solenoid that is connected to a ballistic galvanometer, then when the current is turned on in the solenoid, you can determine the value of the magnetic flux Ф, which will be proportional to the rejection of the galvanometer needle. We will conduct the experiment twice, and we will 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 found 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 flux is obtained when the entire solenoid is filled with iron, that is, the winding is tightly wound around the iron core. You can 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 the magnetic flux when the core is introduced into the solenoid is explained by the fact that the magnetic flux created by a combination of oriented ampere molecular currents was added to the magnetic flux, which creates a current in the solenoid winding. Under the influence of a magnetic field, molecular currents are oriented, and their total magnetic moment ceases to be equal to zero, an additional magnetic field arises.

Definition

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

This is a dimensionless characteristic of matter. An increase in flux Ф by $\mu $ times (1) means that the magnetic induction $\overrightarrow(B)$ in the core is as many times greater than in vacuum at the same current in the solenoid. Therefore, it can be written 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, such an auxiliary vector quantity as the magnetic field strength ($\overrightarrow(H)$) is used, which is related to $\overrightarrow(B)$ by the following relationship:

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

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

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

where $\mu$=1. In the presence of 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 have obtained that the strength of the magnetic field 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 matter

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 the magnetic susceptibility, a dimensionless quantity. For non-ferromagnetic substances and in small fields, $\varkappa $ does not depend on the intensity, it 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

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

Substitute in (8) the expression for the magnetization vector (7), we get:

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

We express 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 both greater than unity and 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 I=2A if it is immersed in liquid oxygen. The magnetic susceptibility of liquid oxygen is $\varkappa =3.4\cdot (10)^(-3).$

As a basis for solving the problem, we take an expression that reflects the relationship between the 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.

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

where $\ \overrightarrow(r)$ is the radius vector drawn from the current element to the point under consideration, $\overrightarrow(dl)$ is the conductor element with current (the direction is given by the current direction), $\vartheta$ 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 coil (R), therefore we have:

The resulting vector of the magnetic field strength 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 wick, directed along the normal of the coil. Then, according to the principle of superposition, the total strength of the magnetic field can be obtained by going to the integral:

We substitute (1.3) into (1.4), we get:

We 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 do the calculations:

Answer: $J=3,4\cdot (10)^(-2)\frac(A)(m).$

Example 2

Task: Calculate the proportion of the total magnetic field in a tungsten rod, which 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 is accounted for by molecular currents, can be found as:

where $J$ is the 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 bar is calculated according to the formula:

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

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

Let's do the calculations:

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

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