How does magnetism work? Magnetism - from Thales to Maxwell

Even a thousand years before the first observations of electrical phenomena, humanity had already begun to accumulate knowledge about magnetism. And just four hundred years ago, when the development of physics as a science had just begun, researchers separated the magnetic properties of substances from their electrical properties, and only after that began to study them independently. This was the beginning of an experimental and theoretical beginning, which by the middle of the 19th century became the foundation of e dynamic theory of electrical and magnetic phenomena.

It appears that the unusual properties of magnetic iron ore were known as early as the Bronze Age in Mesopotamia. And after the development of iron metallurgy began, people noticed that it attracted iron products. The ancient Greek philosopher and mathematician Thales from the city of Miletus (640−546 BC) also thought about the reasons for this attraction; he explained this attraction by the animation of the mineral.

Greek thinkers imagined how invisible vapors envelop magnetite and iron, how these pairs attract substances to each other. Word "magnet" it could have come from the name of the city of Magnesia-y-Sipila in Asia Minor, not far from which magnetite lay. One of the legends tells that the shepherd Magnis somehow found himself with his sheep next to a rock, which attracted the iron tip of his staff and boots.

The ancient Chinese treatise “Spring and Autumn Records of Master Liu” (240 BC) mentions the property of magnetite to attract iron. A hundred years later, the Chinese noted that magnetite does not attract either copper or ceramics. In the 7th and 8th centuries they noticed that a magnetized iron needle, when suspended freely, turned towards the North Star.

So, by the second half of the 11th century, China began to produce marine compasses, which European sailors mastered only a hundred years after the Chinese. Then the Chinese had already discovered the ability of a magnetized needle to deviate in a direction east of the north, and thus discovered magnetic declination, ahead of European navigators, who came to exactly the same conclusion only in the 15th century.

In Europe, the first to describe the properties of natural magnets was the French philosopher Pierre de Maricourt, who in 1269 served in the army of the Sicilian king Charles of Anjou. During the siege of one of the Italian cities, he sent a friend in Picardy a document that went down in the history of science under the name “Letter on the Magnet,” where he spoke about his experiments with magnetic iron ore.

Maricourt noted that in any piece of magnetite there are two areas that are especially strongly attracted to iron. He noticed this similarity to the poles of the celestial sphere, so he borrowed their names to designate the areas of maximum magnetic force. From there came the tradition of calling the poles of magnets the south and north magnetic poles.

Maricourt wrote that if you break any piece of magnetite into two parts, then each fragment will have its own poles.

Maricourt was the first to connect the effect of repulsion and attraction of magnetic poles with the interaction of opposite (south and north) or like poles. Maricourt is rightfully considered a pioneer of the European experimental scientific school; his notes on magnetism were reproduced in dozens of copies, and with the advent of printing, they were published in the form of a brochure. They were cited by many learned naturalists until the 17th century.

The English naturalist, scientist and doctor William Gilbert was also well acquainted with the work of Marikura. In 1600, he published the work “On the Magnet, Magnetic Bodies and the Great Magnet - the Earth.” In this work, Gilbert provided all the information known at that time about the properties of natural magnetic materials and magnetized iron, and also described his own experiments with a magnetic ball, in which he reproduced a model of terrestrial magnetism.

In particular, he experimentally established that at both poles of the “small Earth” the compass needle turns perpendicular to its surface, at the equator it is set parallel, and at middle latitudes it turns to an intermediate position. In this way, Gilbert managed to simulate the magnetic inclination, which was known in Europe for more than 50 years (in 1544 it was described by Georg Hartmann, a mechanic from Nuremberg).

Gilbert also reproduced the geomagnetic declination, which he attributed not to the perfectly smooth surface of the ball, but on a planetary scale explained this effect by the attraction between continents. He discovered how highly heated iron loses its magnetic properties, and when cooled, it restores them. Finally, Gilbert was the first to clearly distinguish between the attraction of a magnet and the attraction of amber rubbed with wool, which he called electric force. It was a truly innovative work, appreciated by both contemporaries and descendants. Gilbert discovered that it would be correct to think of the Earth as a “large magnet.”

Until the very beginning of the 19th century, the science of magnetism had advanced very little. In 1640, Benedetto Castelli, a student of Galileo, attributed the attraction of magnetite to the many very small magnetic particles it contains.

In 1778, Sebald Brugmans, a native of Holland, noticed how bismuth and antimony repelled the poles of a magnetic needle, the first example of a physical phenomenon that Faraday would later call diamagnetism.

Charles-Augustin Coulomb in 1785, through precise measurements on a torsion balance, proved that the force of interaction between magnetic poles is inversely proportional to the square of the distance between the poles - just as precisely as the force of interaction of electric charges.

Since 1813, the Danish physicist Oersted has been diligently trying to experimentally establish the connection between electricity and magnetism. The researcher used compasses as indicators, but for a long time he could not achieve the goal, because he expected that the magnetic force was parallel to the current, and placed the electric wire at a right angle to the compass needle. The arrow did not react in any way to the occurrence of current.

In the spring of 1820, during one of his lectures, Oersted pulled a wire parallel to the arrow, and it is not clear what led him to this idea. And then the arrow swung. For some reason, Oersted stopped his experiments for several months, after which he returned to them and realized that “the magnetic effect of an electric current is directed along the circles surrounding this current.”

The conclusion was paradoxical, because previously rotating forces had not manifested themselves either in mechanics or anywhere else in physics. Oersted wrote an article where he outlined his conclusions, and never studied electromagnetism again.

In the autumn of the same year, the Frenchman Andre-Marie Ampère began experiments. First of all, repeating and confirming Oersted's results and conclusions, in early October he discovered the attraction of conductors if the currents in them are in the same direction, and repulsion if the currents are opposite.

Ampere also studied the interaction between non-parallel conductors with current, after which he described it with the formula later named Ampere's law. The scientist also showed that coiled wires carrying current rotate under the influence of a magnetic field, as happens with a compass needle.

Finally, he put forward the hypothesis of molecular currents, according to which there are continuous microscopic circular currents parallel to each other inside magnetized materials, which cause the magnetic action of materials.

At the same time, Biot and Savard jointly developed a mathematical formula that allows one to calculate the intensity of a direct current magnetic field.

And so, by the end of 1821, Michael Faraday, already working in London, made a device in which a current-carrying conductor rotated around a magnet, and another magnet rotated around another conductor.

Faraday suggested that both the magnet and the wire are enveloped in concentric lines of force, which determine their mechanical action.

Over time, Faraday became convinced of the physical reality of magnetic force lines. By the end of the 1830s, the scientist was already clearly aware that the energy of both permanent magnets and current-carrying conductors was distributed in the space surrounding them, which was filled with magnetic force lines. In August 1831, the researcher managed to force magnetism to generate electric current.

The device consisted of an iron ring with two opposite windings located on it. The first winding could be connected to an electric battery, and the second was connected to a conductor placed above the needle of a magnetic compass. When direct current flowed through the wire of the first coil, the needle did not change its position, but began to swing at the moments of turning it off and on.

Faraday came to the conclusion that at these moments electrical impulses arose in the wire of the second winding associated with the disappearance or appearance of magnetic lines of force. He made the discovery that The cause of the resulting electromotive force is a change in the magnetic field.

In November 1857, Faraday wrote a letter to Professor Maxwell in Scotland asking him to give mathematical form to the knowledge of electromagnetism. Maxwell complied with the request. Concept of electromagnetic field found place in 1864 in his memoirs.

Maxwell introduced the term “field” to designate the part of space that surrounds and contains bodies that are in a magnetic or electrical state, and he especially emphasized that this space itself can be empty and filled with absolutely any type of matter, and the field will still have place.

In 1873, Maxwell published a Treatise on Electricity and Magnetism, where he presented a system of equations combining electromagnetic phenomena. He gave them the name general equations of the electromagnetic field, and to this day they are called Maxwell's equations. According to Maxwell's theory magnetism is a special kind of interaction between electric currents. This is the foundation on which all theoretical and experimental work related to magnetism is built.

After Ampere conjectured that no “magnetic charges” exist and that the magnetization of bodies is explained by molecular circular currents (§§ 57 and 61), almost a hundred years passed when, finally, this assumption was fully convincingly proven by direct experiments. The question of the nature of magnetism was resolved by experiments in the field of so-called magneto-mechanical phenomena. Methods for carrying out and calculating these experiments were developed on the basis of ideas about the structure of atoms developed by Rutherford in 1911 and Bohr in 1913 (however, some experiments similar in concept were carried out before, in particular by Maxwell, but without success).

When Rutherford studied the phenomena of radioactivity, it was found that electrons in atoms rotate in closed orbits around positively charged atomic nuclei; Bohr showed in a theoretical analysis of the spectra that only some of these orbits are stable; finally, following this (in 1925, also based on the analysis of spectra), the rotation of electrons around its axis was discovered, as if analogous to the daily rotation of the Earth; the combination of these data led to a clear understanding of the nature of ampere circular currents. It became obvious that the main elements of magnetism in substances are: either the rotation of electrons around nuclei, or the rotation of electrons around their axis, or both of these rotations simultaneously.

When staged in 1914-1915. The first successful magnetomechanical experiments, which are explained below, initially assumed that the magnetic properties of substances are completely determined by the orbital motion of electrons around nuclei. However, the quantitative results of the experiments mentioned above showed that the properties of ferromagnetic and paramagnetic substances are determined not by the movement of electrons in orbits, but by the rotation of electrons around their axis.

To understand the intent of magnetomechanical experiments and correctly evaluate the conclusions to which these experiments led, it is necessary to calculate the ratio of the magnetic moment of the circular current created by the movement of the electron to the mechanical angular momentum of the electron.

The magnitude of any current, as is known, is determined by the amount of electricity passing through the cross section per unit time; It is obvious that the magnitude of the current equivalent to the orbital rotation of the electron is equal to the product of the electron charge and the number of revolutions per unit time, where is the speed of the electron and the radius of the orbit. The indicated product expresses the value of the equivalent current in electrostatic units. To obtain the magnitude of the current in electromagnetic units, the indicated product must be divided by the speed of light (p. 296); Thus,

A circular current produces the same magnetic field as a magnetic sheet with a torque equal to the product of the current and the area flowing around it [formula (17)]:

Thus, we see that the movement of an electron around the nucleus imparts to the atom a magnetic moment equal to

Comparing this magnetic moment with the mechanical angular momentum of the electron:

we find that the ratio of the magnetic moment to the mechanical impulse does not depend on either the speed of the electron or the radius of the orbit

Indeed, a more complete theory shows that equation (33) is valid not only for circular orbits, but also for elliptical orbits of the electron.

The rotation of an electron around its axis imparts a certain magnetic moment to the electron itself. The rotation of an electron around its axis is called spin (from the English word “spin”, meaning rotation around an axis). If we assume that the electron has a spherical shape and that the charge of the electron is distributed with uniform density over the spherical surface, then calculations show that the ratio of the spin magnetic moment of the electron to the mechanical momentum of the electron's rotation around its axis is twice as large as the similar ratio for orbital motion:

The above considerations about the proportionality of the magnetic moment and rotational momentum indicate that, under certain conditions, magnetic phenomena may be associated with gyroscopic effects. Maxwell tried to experimentally discover this connection between magnetic phenomena and gyroscopic effects, but only to Einstein and de Haas (1915), A.F. Ioffe and P.L. Kapitsa (1917) and Barnet (1914 and 1922). .) for the first time it was possible to carry out successful experiments. Einstein and de Haas established that an iron rod suspended in a solenoid as a core, when magnetized by a current passed through the solenoid, acquires a rotational impulse (Fig. 256). To obtain a noticeable effect, Einstein and de Haas took advantage of the phenomenon of resonance, performing periodic magnetization reversal with an alternating current with a frequency coinciding with the frequency of the natural torsional vibrations of the rod.

Rice. 256. Scheme of the experiment of Einstein and de Haas, a - mirror, O - light source.

The Einstein and de Haas effect is explained as follows. When magnetized, the axes of elementary magnets - “electron tops” - are oriented in the direction of the magnetic field; the geometric sum of the rotational impulses of the “electronic tops” becomes different from zero, and since at the beginning of the experiment the rotational impulse of the iron rod (considered as a mechanical system of atoms) was equal to zero, then according to the law of conservation of rotational impulse

(vol. I, § 38) due to magnetization, the rod as a whole must acquire a rotation impulse equal in magnitude, but opposite in direction to the geometric sum of the rotation impulses of the “electronic tops”.

Barnet performed the opposite experiment of Einstein and de Haas, namely, Barnet caused the magnetization of an iron rod, causing it to rotate rapidly; magnetization occurred in the direction opposite to the axis of rotation. Just as, due to the daily rotation of the Earth, the axis of the gyrocompass takes a position parallel to the earth’s axis (vol. I, § 38), in the same way, in Barnet’s experiment, the axes of “electronic tops” take a position parallel to the axis of rotation of the iron rod (due to the fact that If the electron charge is negative, the direction of magnetization will be opposite to the axis of rotation of the rod).

In the experiments of A.F. Ioffe and P.L. Kapitsa (1917), a magnetized iron rod suspended on a thread was subjected to rapid heating above the Curie point. In this case, the ordered arrangement of “elementary tops”, the axes of which, due to magnetization, were oriented along the field parallel to the axis of the rod, was lost and replaced by a chaotic distribution of the direction of the axes, so that the total magnetic and mechanical moments of the “elementary tops” turned out to be close to zero (Fig. 257). Due to the law of conservation of angular momentum, the iron rod acquired a rotational momentum when demagnetized.

Rice. 257. Diagram explaining the idea of ​​the Ioffe-Kapitsa experiment. a - the iron rod is magnetized; b - the rod is demagnetized by heating above the Curie point.

Measurements of the magnetic moment and rotational momentum in the experiments of Einstein and de Haas, in the experiments of Barnet and in the experiments of Ioffe and Kapitza, which were repeatedly repeated by many scientists, showed that the ratio of these quantities is determined by formula (34), and not by formula (33). This indicates that the main element of magnetism in iron (and in ferromagnetic bodies in general) is the spin-axial rotation of electrons, and not the orbital motion of electrons around the positive nuclei of atoms.

However, the orbital motion of electrons also affects the magnetic properties of substances: the magnetic moment of atoms, ions and molecules is a geometric sum of spin and orbital magnetic moments (however, the structure of atoms is such that spin moments again play a decisive role in this sum).

When the total magnetic moment of a particle is zero, the substance turns out to be diamagnetic. Formally, diamagnetic substances are characterized by a magnetic permeability less than one; therefore, negative magnetic susceptibility means that diamagnetic substances are magnetized in the direction opposite to the strength of the magnetizing field.

The electron theory explains diamagnetism by the influence of the magnetic field on the orbital motion of electrons around nuclei. This movement of the electron, as already explained, is equivalent to a current. When a magnetic field begins to act on an atom and its intensity increases from zero to a certain value, “an additional current is induced,” which, according to Lenz’s law (§ 71), has such a direction that the magnetic moment created by this “additional current” is always directed opposite to the one that increased from zero to field. If the magnetizing field is perpendicular to the orbital plane, then it simply changes the speed of the electron in its orbit, and this changed speed value is maintained as long as the atom is in the magnetic field; if the field is not perpendicular to the orbital plane, then precessional motion of the orbital axis around the direction of the field arises and is established (similar to the precession of the axis of a top around the vertical passing through the fulcrum of the top) (Vol. I, § 38).

Calculations lead to the following formula for the magnetic susceptibility of diamagnetic substances:

here is the charge and mass of the electron, the number of electrons in an atom, the number of atoms per unit volume of matter, the average radius of electron orbits.

Thus, the diamagnetic effect is a common property of all substances; however, this effect is small, and therefore it can only be observed if there is no strong paramagnetic effect opposite it.

The theory of paramagnetism was developed by Langevin in 1905 and developed on the basis of modern concepts by Fleck, Stoner and others (in 1927 and in subsequent years). Depending on the structure of the atom, the magnetic moments created by individual intra-atomic electrons can either cancel each other out, so that the atom as a whole turns out to be non-magnetic (such substances exhibit diamagnetic properties), or the resulting magnetic moment of the atom turns out to be non-zero. In this last case, as quantum mechanics shows, the magnetic moment of the atom (more precisely, its electron shell) is naturally expressed (Vol. III, §§ 59, 67-70) through a kind of “atom of magnetism” According to quantum

In mechanics, this “atom of magnetism” is the magnetic moment created by the rotation of an electron around the nucleus - the Bohr magneton, equal to

(here the charge of the electron, Planck’s constant, c is the speed of light, the mass of the electron).

Every electron has exactly the same magnetic moment, regardless of its movement around the nucleus, but due to its structure or, as they conventionally say, due to its rotation around an axis. The magnetic moment of the spin is equal to the Bohr magneton, while the mechanical moment of the spin [in accordance with formulas (33) and (34)] is equal to half the orbital moment of the electron.

Some atomic nuclei also have magnetic moments, but thousands of times smaller than the magnetic moments inherent in the electron shells of atoms § 115). The magnetic moments of nuclei are expressed through the nuclear magneton, the value of which is determined by the same formula as the value of the Bohr magneton, if in this formula the mass of the electron is replaced by the mass of the proton.

According to Langevin's theory, when a paramagnetic substance is magnetized, the molecules are oriented by their magnetic moments in the direction of the field lines, but the molecular thermal

movement to one degree or another upsets this orientation. The molecular picture of magnetization of a paramagnetic substance is similar to the polarization of a dielectric (§ 22), if, of course, we imagine that hard electric dipoles are replaced by elementary magnets, and the electric field is replaced by a magnetic field. The degree of orientation of elementary magnets in the direction of the magnetizing field can be judged by the value of the average projection of the magnetic moment onto the direction of the field (calculated per molecule). With a random arrangement of the axes of elementary magnets, when all elementary magnets are oriented in the direction of the field,

Langevin showed that at temperature and at the intensity of the internal magnetic field in the morning, similar to the formula for in § 22), the ratio is expressed by the following function:

For small values, as already mentioned in § 22, the above Langevin function (36) takes on the value y, so in this case

Obviously, magnetization is equal to the product of the value and the number of molecules per unit volume:

Thus, at a constant density of a substance, magnetization is inversely proportional to the absolute temperature. This fact was empirically established by Curie in 1895.

For most paramagnetic substances, it is small in comparison with unity, therefore, by substituting in the formula and replacing through, the value in comparison with unity can be neglected; then we get:

where denotes the specific magnetic susceptibility (i.e., susceptibility per unit mass). This formula is called Curie's law. For many paramagnets, the following, more complex form of Curie’s law [formula (31)] is more accurate:

The value for some paramagnetic substances is positive, for others it is negative.

When magnetized, a paramagnetic substance is drawn into the space between the poles of the magnet. Therefore, during magnetization, a paramagnetic substance can produce work, whereas work must be expended on demagnetization. In this regard, as was theoretically predicted by Debye, paramagnetic substances during rapid adiabatic demagnetization should experience some cooling (especially in the region of very low temperatures, where the magnetic susceptibility of the paramagnetic increases greatly with decreasing temperature). Experiments carried out since 1933 in a number of laboratories confirmed the conclusions of the theory and served as the basis for the development of a magnetic method for deep cooling of bodies. The paramagnetic substance is cooled by conventional methods in a magnetic field to the temperature of liquid helium, after which the substance is quickly removed from the magnetic field, which causes an even greater decrease in temperature in this substance. This method produces temperatures that differ from absolute zero by thousandths of a degree.

A characteristic feature of ferromagnetic substances is that in relatively weak fields they are magnetized almost to complete saturation. Therefore, in ferromagnets there are some forces that, overcoming the influence of thermal motion, promote the ordered orientation of elementary magnetic moments. The assumption about the existence of an internal field of forces promoting the magnetization of ferromagnets was first expressed by the Russian scientist B. L. Rosing in 1892 and substantiated by P. Weiss in 1907.

In ferromagnetic substances, the elementary magnets are electrons rotating around their axis - spins. In development of Weiss's ideas, it is assumed that the spins, being located at the nodes of the crystal lattice and interacting with each other, create an internal field, which in separate small areas of the ferromagnetic crystal (these areas are called domains) turns all the spins in one direction, so that each such area (domain) turns out to be spontaneously (spontaneously) magnetized to saturation. However, adjacent areas of the crystal in the absence of an external magnetic field have different directions

magnetization. Calculations show that, for example, in iron crystals, “spontaneous” magnetization can occur in the direction of any edge of the cubic crystal cell.

A weak external magnetic field causes all spins in the domain to turn in the direction of that edge of the cubic cell that makes the smallest angle with the direction of the magnetizing field.

Rice. 258. Orientation of spins in domains during magnetization of a ferromagnet.

A stronger field causes the spins to rotate again closer to the direction of the field. Magnetic saturation is achieved when the magnetic moments of all spontaneously magnetized microcrystalline areas are oriented in the direction of the field. When magnetized, it is not the domains that rotate, but all the spins in them; all the backs in any microcrystalline turn at the same time, like soldiers in formation; this rotation of spins occurs first in some domains, then in others. Thus, the process of magnetization of a ferromagnetic substance is stepwise (Fig. 258).

Experimentally, stepwise magnetization was first discovered by Barkhausen (1919). The simplest experiment suitable for demonstrating this phenomenon is as follows: an iron rod inserted into a coil connected to a telephone is gradually magnetized by slowly turning a horseshoe magnet suspended above the coil (Fig. 259); At the same time, a characteristic rustling sound is heard in the phone, which breaks up into separate beats if the magnetizing field is changed slowly enough (by hundredths of an oersted per sec.).

Rice. 259. Barkhausen's experiment.

It turned out that the Barkhausen effect is exceptionally strong when magnetizing a thin nickel wire, which was previously curled into a curl by pulling it through a block, and then inserted into a capillary, which forcibly holds it in a straightened state. The intermittent nature of magnetization affects the magnetization diagram in the form of tiny stepped steps (Fig. 260).

Areas of spontaneous magnetization - domains - were experimentally discovered and studied by N. S. Akulov, who used for this purpose the powder magnetic flaw detection method he developed. Since domains are similar to small magnets, the field at the boundary between them is not uniform.

Rice. 260. Stepped nature of magnetization curves. Areas marked with circles are shown on an enlarged scale.

To reveal the outlines of domains, a sample of a demagnetized ferromagnetic substance is placed under a microscope and the surface of the sample is coated with a liquid with the finest iron dust suspended in it. Iron dust, collecting near the boundaries of domains, clearly marks their contours (Fig. 261),

Rice. 261. Domains in pure iron (a), in silicon iron (b) and in cobalt (c).

In the picture of the origin of ferromagnetic properties explained above, one important part remained unclear for some time, namely the nature of the forces that form the internal field that causes the ordered orientation of spins inside domains. In 1927, the Soviet physicist Ya. G. Dorfman carried out an experiment that showed that the internal field forces in ferromagnets are not

are forces of magnetic interaction, but have a different origin. By isolating a narrow beam from a stream of fast-moving electrons (“beta rays” emitted by radioactive substances), Dorfman forced these electrons to pass through a thin ferromagnetic film of nickel; A photographic plate was placed behind the nickel film, which made it possible, after development, to determine where the electrons met with it, so that it was possible to measure with great accuracy the angle at which the electrons were deflected when passing through the magnetized nickel film (Fig. 262). Calculations show that if the internal field in a ferromagnet were of the nature of ordinary magnetic interactions, then the trace of the electron beam would shift on the photographic plate in the Dorfman installation by almost 2 cm; in reality the displacement turned out to be negligible.

Rice. 262. Diagram explaining the idea of ​​Dorfman's experiment.

Theoretical research by prof. Frenkel (1928) and later Bloch, Stoner and Slater showed that the ordered orientation of spins in domains is caused by a special kind of forces, the existence of which was revealed by quantum mechanics and which manifest themselves in the chemical interaction of atoms (in a covalent bond; Vol. I, § 130 ). These forces, according to the method of calculating and interpreting them accepted in quantum mechanics, are called exchange forces. Calculations have shown that the energy of exchange interaction between iron atoms in a single crystal is hundreds of times higher than the energy of magnetic interaction. This is consistent with the measurements that were made by Ya. G. Dorfman in the experiments mentioned above.

Nevertheless, practically the most important properties of ferromagnets are determined not so much by the exchange interaction, but mainly by the magnetic interaction. The fact is that although the existence of regions of “spontaneous” magnetization (domains) in ferromagnets is caused by exchange forces (the ordered orientation of the spins corresponds to the minimum energy of exchange interaction, i.e., is the most stable), the predominant directions of magnetization of the domains are determined by the symmetry of the crystal lattice and correspond to minimum energy of magnetic interaction. And the process of technical magnetization, as explained above (Fig. 258), consists in flipping all the spins inside individual domains, first in the direction of the crystallographic axis of easy magnetization, which makes the smallest angle with the direction of the field, and then in turning the spins in the direction of the field. The energy expenditure required to carry out such a stepwise overturning of spins in turn in all

domains and their rotation along the field, as well as a number of quantities that depend on the specified energy costs (values ​​that determine magnetization, magnetostriction and other phenomena), are most successfully calculated by methods developed by N. S. Akulov (since 1928) and E E. Kondorsky (since 1937).

Rice. 263. Comparison of theoretical magnetization curves with experimental data (they are shown in circles) for an iron single crystal.

From Fig. 263, which we present as one of the examples, one can see that the theoretical curves obtained from the equations of N. S. Akulov are in good agreement with the experimental data; the diagram on the right represents the magnetization of an iron single crystal in the direction of the spatial diagonal of the cubic lattice, the diagram on the left represents the same in the direction of the diagonal of the cube face,

Charged bodies are capable of creating another type of field in addition to the electric one. If the charges move, then a special type of matter is created in the space around them, called magnetic field. Consequently, electric current, which is the ordered movement of charges, also creates a magnetic field. Like the electric field, the magnetic field is not limited in space, propagates very quickly, but still with a finite speed. It can only be detected by its effect on moving charged bodies (and, as a consequence, currents).

To describe the magnetic field, it is necessary to introduce a force characteristic of the field, similar to the intensity vector E electric field. Such a characteristic is the vector B magnetic induction. In the SI system of units, the unit of magnetic induction is 1 Tesla (T). If in a magnetic field with induction B place a conductor length l with current I, then a force called Ampere force, which is calculated by the formula:

Where: IN– magnetic field induction, I– current strength in the conductor, l– its length. The Ampere force is directed perpendicular to the magnetic induction vector and the direction of the current flowing through the conductor.

To determine the direction of the Ampere force is usually used "Left hand" rule: if you position your left hand so that the induction lines enter the palm, and the outstretched fingers are directed along the current, then the abducted thumb will indicate the direction of the Ampere force acting on the conductor (see figure).

If the angle α between the directions of the magnetic induction vector and the current in the conductor is different from 90°, then to determine the direction of the Ampere force it is necessary to take the component of the magnetic field, which is perpendicular to the direction of the current. It is necessary to solve the problems of this topic in the same way as in dynamics or statics, i.e. by describing the forces along the coordinate axes or adding the forces according to the rules of vector addition.

Moment of forces acting on the frame with current

Let the frame with current be in a magnetic field, and the plane of the frame is perpendicular to the field. The Ampere forces will compress the frame, and their resultant will be equal to zero. If you change the direction of the current, then the Ampere forces will change their direction, and the frame will not compress, but stretch. If the lines of magnetic induction lie in the plane of the frame, then a rotational moment of Ampere forces occurs. Rotational moment of Ampere forces is equal to:

Where: S- frame area, α - the angle between the normal to the frame and the magnetic induction vector (the normal is a vector perpendicular to the plane of the frame), N– number of turns, B– magnetic field induction, I– current strength in the frame.

Lorentz force

Ampere force acting on a segment of conductor of length Δ l with current strength I, located in a magnetic field B can be expressed in terms of forces acting on individual charge carriers. These forces are called Lorentz forces. Lorentz force acting on a particle with a charge q in a magnetic field B, moving at speed v, is calculated using the following formula:

Corner α in this expression is equal to the angle between the speed and the magnetic induction vector. The direction of the Lorentz force acting on positively a charged particle, as well as the direction of the Ampere force, can be found using the left-hand rule or the gimlet rule (like the Ampere force). The magnetic induction vector needs to be mentally inserted into the palm of your left hand, four closed fingers should be directed according to the speed of movement of the charged particle, and the bent thumb will show the direction of the Lorentz force. If the particle has negative charge, then the direction of the Lorentz force, found by the left-hand rule, will need to be replaced with the opposite one.

The Lorentz force is directed perpendicular to the velocity and magnetic field induction vectors. When a charged particle moves in a magnetic field The Lorentz force does no work. Therefore, the magnitude of the velocity vector does not change when the particle moves. If a charged particle moves in a uniform magnetic field under the influence of the Lorentz force, and its speed lies in a plane perpendicular to the magnetic field induction vector, then the particle will move in a circle, the radius of which can be calculated using the following formula:

The Lorentz force in this case plays the role of a centripetal force. The period of revolution of a particle in a uniform magnetic field is equal to:

The last expression shows that for charged particles of a given mass m the period of revolution (and therefore both the frequency and angular velocity) does not depend on the speed (and therefore on the kinetic energy) and the radius of the trajectory R.

Magnetic field theory

If two parallel wires carry current in the same direction, they attract each other; if in opposite directions, then they repel. The laws of this phenomenon were experimentally established by Ampere. The interaction of currents is caused by their magnetic fields: the magnetic field of one current acts as an Ampere force on another current and vice versa. Experiments have shown that the modulus of force acting on a segment of length Δ l each of the conductors is directly proportional to the current strength I 1 and I 2 in conductors, cut length Δ l and inversely proportional to the distance R between them:

Where: μ 0 is a constant value called magnetic constant. The introduction of the magnetic constant into the SI simplifies the writing of a number of formulas. Its numerical value is:

μ 0 = 4π ·10 –7 H/A 2 ≈ 1.26·10 –6 H/A 2 .

Comparing the expression just given for the force of interaction of two conductors with current and the expression for the Ampere force, it is not difficult to obtain an expression for induction of the magnetic field created by each of the straight conductors carrying current at a distance R from him:

Where: μ – magnetic permeability of the substance (more on this below). If the current flows in a circular turn, then center of the turn magnetic field induction determined by the formula:

Power lines The magnetic field is called the line along the tangent to which the magnetic arrows are located. Magnetic needle called a long and thin magnet, its poles are pointlike. A magnetic needle suspended on a thread always turns in one direction. Moreover, one end of it is directed towards the north, the other - to the south. Hence the name of the poles: north ( N) and southern ( S). Magnets always have two poles: north (indicated in blue or the letter N) and southern (in red or letter S). Magnets interact in the same way as charges: like poles repel, and unlike poles attract. It is impossible to obtain a magnet with one pole. Even if the magnet is broken, each part will have two different poles.

Magnetic induction vector

Magnetic induction vector- vector physical quantity, which is a characteristic of a magnetic field, numerically equal to the force acting on a current element of 1 A and a length of 1 m, if the direction of the field line is perpendicular to the conductor. Designated IN, unit of measurement - 1 Tesla. 1 T is a very large value, therefore, in real magnetic fields, magnetic induction is measured in mT.

The magnetic induction vector is directed tangentially to the lines of force, i.e. coincides with the direction of the north pole of a magnetic needle placed in a given magnetic field. The direction of the magnetic induction vector does not coincide with the direction of the force acting on the conductor, therefore the magnetic field lines, strictly speaking, are not force lines.

Magnetic field line of permanent magnets directed in relation to the magnets themselves as shown in the figure:

In case magnetic field of electric current to determine the direction of the field lines, use the rule "Right hand": if you take the conductor in your right hand so that the thumb is directed along the current, then the four fingers clasping the conductor show the direction of the lines of force around the conductor:

In the case of direct current, magnetic induction lines are circles whose planes are perpendicular to the current. The magnetic induction vectors are directed tangentially to the circle.

Solenoid- a conductor wound on a cylindrical surface through which electric current flows I similar to the field of a direct permanent magnet. Inside the solenoid length l and number of turns N a uniform magnetic field with induction is created (its direction is also determined by the right-hand rule):

Magnetic field lines look like closed lines- This is a common property of all magnetic lines. Such a field is called a vortex field. In the case of permanent magnets, the lines do not end at the surface, but penetrate into the magnet and are closed internally. This difference between electric and magnetic fields is explained by the fact that, unlike electric, magnetic charges do not exist.

Magnetic properties of matter

All substances have magnetic properties. The magnetic properties of a substance are characterized relative magnetic permeability μ , for which the following is true:

This formula expresses the correspondence of the magnetic field induction vector in a vacuum and in a given environment. Unlike electric interaction, during magnetic interaction in a medium one can observe both an increase and a weakening of the interaction compared to a vacuum, which has a magnetic permeability μ = 1. U diamagnetic materials magnetic permeability μ slightly less than one. Examples: water, nitrogen, silver, copper, gold. These substances somewhat weaken the magnetic field. Paramagnets- oxygen, platinum, magnesium - somewhat enhance the field, having μ a little more than one. U ferromagnets- iron, nickel, cobalt - μ >> 1. For example, for iron μ ≈ 25000.

Magnetic flux. Electromagnetic induction

Phenomenon electromagnetic induction was discovered by the outstanding English physicist M. Faraday in 1831. It consists in the occurrence of an electric current in a closed conducting circuit when the magnetic flux penetrating the circuit changes over time. Magnetic flux Φ across the square S contour is called the value:

Where: B– module of the magnetic induction vector, α – angle between the magnetic induction vector B and normal (perpendicular) to the plane of the contour, S– contour area, N– number of turns in the circuit. The SI unit of magnetic flux is called Weber (Wb).

Faraday experimentally established that when the magnetic flux changes in a conducting circuit, induced emf ε ind, equal to the rate of change of magnetic flux through a surface bounded by a contour, taken with a minus sign:

A change in the magnetic flux passing through a closed loop can occur for two possible reasons.

1. The magnetic flux changes due to the movement of the circuit or its parts in a time-constant magnetic field. This is the case when conductors, and with them free charge carriers, move in a magnetic field. The occurrence of induced emf is explained by the action of the Lorentz force on free charges in moving conductors. The Lorentz force plays the role of an external force in this case.
2. The second reason for the change in the magnetic flux penetrating the circuit is the change in time of the magnetic field when the circuit is stationary.

When solving problems, it is important to immediately determine why the magnetic flux changes. Three options are possible:

1. The magnetic field changes.
2. The contour area changes.
3. The orientation of the frame relative to the field changes.

In this case, when solving problems, the EMF is usually calculated modulo. Let us also pay attention to one particular case in which the phenomenon of electromagnetic induction occurs. So, the maximum value of the induced emf in a circuit consisting of N turns, area S, rotating with angular velocity ω in a magnetic field with induction IN:

Movement of a conductor in a magnetic field

When moving a conductor with a length l in a magnetic field B at speed v a potential difference arises at its ends, caused by the action of the Lorentz force on free electrons in the conductor. This potential difference (strictly speaking, emf) is found using the formula:

Where: α - the angle that is measured between the direction of speed and the vector of magnetic induction. No EMF occurs in the stationary parts of the circuit.

If the rod is long L rotates in a magnetic field IN around one of its ends with angular velocity ω , then a potential difference (EMF) will arise at its ends, which can be calculated using the formula:

Inductance. Self-induction. Magnetic field energy

Self-induction is an important special case of electromagnetic induction, when a changing magnetic flux, causing an induced emf, is created by a current in the circuit itself. If the current in the circuit under consideration changes for some reason, then the magnetic field of this current also changes, and, consequently, the own magnetic flux penetrating the circuit. A self-inductive emf arises in the circuit, which, according to Lenz’s rule, prevents a change in the current in the circuit. Self magnetic flux Φ , penetrating a circuit or coil with current, is proportional to the current strength I:

Proportionality factor L in this formula is called the self-induction coefficient or inductance coils. The SI unit of inductance is called Henry (H).

Remember: the inductance of the circuit does not depend on either the magnetic flux or the current strength in it, but is determined only by the shape and size of the circuit, as well as the properties of the environment. Therefore, when the current in the circuit changes, the inductance remains unchanged. The inductance of the coil can be calculated using the formula:

Where: n- concentration of turns per unit length of the coil:

Self-induced emf, arising in a coil with a constant inductance value, according to Faraday’s formula is equal to:

So the self-induction EMF is directly proportional to the inductance of the coil and the rate of change of current in it.

A magnetic field has energy. Just as there is a reserve of electrical energy in a charged capacitor, there is a reserve of magnetic energy in the coil through the turns of which current flows. Energy W m magnetic field of a coil with inductance L, created by current I, can be calculated using one of the formulas (they follow from each other, taking into account the formula Φ = LI):

By correlating the formula for the energy of the magnetic field of the coil with its geometric dimensions, we can obtain a formula for volumetric magnetic field energy density(or energy per unit volume):

Lenz's rule

Inertia- a phenomenon that occurs both in mechanics (when accelerating a car, we lean back, counteracting the increase in speed, and when braking, we lean forward, counteracting the decrease in speed), and in molecular physics (when a liquid is heated, the rate of evaporation increases, the fastest molecules leave the liquid, reducing the speed heating) and so on. In electromagnetism, inertia manifests itself in opposition to changes in the magnetic flux passing through a circuit. If the magnetic flux increases, then the induced current arising in the circuit is directed so as to prevent the magnetic flux from increasing, and if the magnetic flux decreases, then the induced current arising in the circuit is directed so as to prevent the magnetic flux from decreasing.

On this site. To do this, you need nothing at all, namely: devote three to four hours every day to preparing for the CT in physics and mathematics, studying theory and solving problems. The fact is that the CT is an exam where it is not enough just to know physics or mathematics, you also need to be able to quickly and without failures solve a large number of problems on different topics and of varying complexity. The latter can only be learned by solving thousands of problems.

Successful, diligent and responsible implementation of these three points will allow you to show an excellent result at the CT, the maximum of what you are capable of.

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The elementary magnet is the electron; to be more precise, it is not the electron itself, but its rotation - the rotation of the very wheel in the form of which we imagine the electron. If in electricity it functions as an energy carrier, like atoms and air molecules in pneumatics, then in magnetism its role is different: it is an element that regulates relative position and rotation. To understand what has been said, let us allow ourselves one more figurative comparison: if in electricity an electron is like a soldier in battle, then in magnetism it is like a soldier in the ranks.

An electron has all the attributes of a magnet: active poles and active side; thanks to them, it is aligned appropriately in relation to other electrons. The poles of the magnet (in this case, the ends of the electron) received geographical names: north and south. This did not happen by chance; observing the behavior of magnetic needles, people noted their orientation to the North and South Poles of the Earth. Understanding that the Earth itself is a magnet, and looking mentally from space at its North Pole, we will note the counterclockwise rotation (the Sun rises in the East and sets in the West); hence the north pole of the magnet. When looking at the South Pole, we will find the direction of rotation of the Earth, naturally, clockwise; by analogy, the corresponding end of the magnet is called the south pole. Fortunately, these directions of rotation, consistent with the names of the poles, turned out to be what they should be in electromagnetic phenomena, and we will show this below.

In the meantime, before our eyes is an electron; and it is located so that its axis of rotation is vertical, and the direction of rotation, if you look at it from above, is counterclockwise; therefore, its north pole will be at the top and the south pole at the bottom - a familiar geographical arrangement. The side of the electron closest to us shifts to the right. Let us agree to continue to imagine the location of an electron and any magnet in space in exactly this way.

If several electrons are nearby and if nothing interferes, then they, like us alreadythey said they would line up coaxially withone direction of rotation, forming a cord rotating around its axis; this is also a magnet, only in it the magnetic poles will appear, of course, only on the outermost electrons, and these manifestations will remain unchanged: no matter how longthere was no cord, its poles will always influence the environment unchanged. Now we can say that known from electrophysics a magnetic field line is electrons coaxially located and rotating in the same direction; Synonyms for magnetic field line are magnetic cord and electron cord.

The body of an atom, which is a rotating torus shell, is by definition also a magnetic cord, only this cord is closed and therefore has no poles. However, the torn atom becomes an ordinary magnetic cord; ordinary - in magnetic manifestations, but unusual in the strength of these manifestations: the body of the atom is denser and more durable.

The unidirectional rotation of cords in a magnetic beam is unnatural and can only be maintained under a certain external influence; Atoms and the etheric wind can have such an effect.

The atoms of some chemicals, such as iron, nickel and cobalt, are designed in such a way that the electrons attached to them are arranged in magnetic cords. If, at the moment of solidification of these substances, their atoms are arranged so that all their magnetic cords form one magnetic beam, then the resulting solid body will turn out to be a magnet. In the future, the atoms of such a natural magnet will hold the resulting magnetic beam and counteract the desire of its individual magnetic cords to change their direction of rotation to the opposite. The action of the magnetic beam also extends to the spaces adjacent to the magnet, that is, beyond its boundaries: the free electrons located there will naturally line up in lines, as if building up the magnetic cords of a solid body; True, the cords can no longer be located close to each other in free space - colliding shells will interfere - and the magnetic beam emerging from the solid body will fan out.

Another factor that holds the magnetic beam is the different speed of the etheric wind; This phenomenon is of great importance in electromagnetism, and therefore we will consider it in more detail. Let's imagine a certain magnetic cord located across the etheric flow. If the speed of the ether in the cross section of the flow is the same, then such a wind can only bend or deflect the cord, but cannot affect the direction of its rotation. It’s another matter if the speed of the ether in the cross section of the flow turns out to be different: on one side of the cord it is greater, and on the other - less; such a difference in blowing speedether will either promote the rotation of the magnetic cord or hinder it. With assistance, the cord will feel safe, but with resistance, sooner or later it will be forced to change the direction of its rotation.

The ethereal wind at different speeds has exactly the same effect on the magnetic beam. If the ethereal flow piercing it has a high speed on one side, and it decreases as it moves to the other, then all the magnetic cords of the beam will be forced to rotate in the same direction, despite their reluctance to do so. Moreover, the ethereal wind at different speeds not only orients the magnetic cords, but also contributes to their formation: electrons that find themselves in the field of action of an ethereal flow at such speeds will align with one directionrotations, that is, they will be combined into cords.

Electric field strength

Electric field strength is a vector characteristic of the field, a force acting on a unit electric charge at rest in a given reference frame.

Tension is determined by the formula:

$E↖(→)=(F↖(→))/(q)$

where $E↖(→)$ is the field strength; $F↖(→)$ is the force acting on the charge $q$ placed at a given point in the field. The direction of the vector $E↖(→)$ coincides with the direction of the force acting on the positive charge and is opposite to the direction of the force acting on the negative charge.

The SI unit of voltage is volt per meter (V/m).

Field strength of a point charge. According to Coulomb's law, a point charge $q_0$ acts on another charge $q$ with a force equal to

$F=k(|q_0||q|)/(r^2)$

The modulus of the field strength of a point charge $q_0$ at a distance $r$ from it is equal to

$E=(F)/(q)=k(|q_0|)/(r^2)$

The intensity vector at any point of the electric field is directed along the straight line connecting this point and the charge.

Electric field lines

The electric field in space is usually represented by lines of force. The concept of lines of force was introduced by M. Faraday while studying magnetism. This concept was then developed by J. Maxwell in his research on electromagnetism.

A line of force, or an electric field strength line, is a line whose tangent at each point coincides with the direction of the force acting on a positive point charge located at that point in the field.

Tension lines of a positively charged ball;

Tension lines of two oppositely charged balls;

Tension lines of two similarly charged balls

Tension lines of two plates charged with charges of different signs, but equal in absolute value.

The tension lines in the last figure are almost parallel in the space between the plates, and their density is the same. This suggests that the field in this region of space is uniform. An electric field is called homogeneous if its strength is the same at all points in space.

In an electrostatic field, the lines of force are not closed; they always begin on positive charges and end on negative charges. They do not intersect anywhere; the intersection of the field lines would indicate the uncertainty of the direction of the field strength at the intersection point. The density of field lines is greater near charged bodies, where the field strength is greater.

Field of a charged ball. The field strength of a charged conducting ball at a distance from the center of the ball exceeding its radius $r≥R$ is determined by the same formula as the fields of a point charge. This is evidenced by the distribution of field lines, similar to the distribution of intensity lines of a point charge.

The charge of the ball is distributed evenly over its surface. Inside the conducting ball, the field strength is zero.

Magnetic field. Magnet interaction

The phenomenon of interaction between permanent magnets (the establishment of a magnetic needle along the Earth’s magnetic meridian, the attraction of unlike poles, the repulsion of like poles) has been known since ancient times and was systematically studied by W. Gilbert (the results were published in 1600 in his treatise “On the Magnet, Magnetic Bodies and the Great Magnet - Earth").

Natural (natural) magnets

The magnetic properties of some natural minerals were known already in ancient times. Thus, there is written evidence from more than 2000 years ago about the use of natural permanent magnets as compasses in China. The attraction and repulsion of magnets and the magnetization of iron filings by them is mentioned in the works of ancient Greek and Roman scientists (for example, in the poem “On the Nature of Things” by Lucretius Cara).

Natural magnets are pieces of magnetic iron ore (magnetite), consisting of $FeO$ (31%) and $Fe_2O$ (69%). If such a piece of mineral is brought close to small iron objects - nails, sawdust, a thin blade, etc., they will be attracted to it.

Artificial permanent magnets

Permanent magnet- this is a product made of a material that is an autonomous (independent, isolated) source of a constant magnetic field.

Artificial permanent magnets are made from special alloys, which include iron, nickel, cobalt, etc. These metals acquire magnetic properties (magnetize) if they are brought close to permanent magnets. Therefore, in order to make permanent magnets from them, they are specially kept in strong magnetic fields, after which they themselves become sources of a constant magnetic field and are able to retain magnetic properties for a long time.

The figure shows an arc and strip magnets.

In Fig. pictures of the magnetic fields of these magnets are given, obtained by the method that M. Faraday first used in his research: with the help of iron filings scattered on a sheet of paper on which the magnet lies. Each magnet has two poles - these are the places of greatest concentration of magnetic field lines (they are also called magnetic field lines, or lines of magnetic induction field). These are the places that iron filings are most attracted to. One of the poles is usually called northern(($N$), other - southern($S$). If you bring two magnets close to each other with like poles, you can see that they repel, and if they have opposite poles, they attract.

In Fig. it is clearly seen that the magnetic lines of the magnet are closed lines. The magnetic field lines of two magnets facing each other with like and unlike poles are shown. The central part of these paintings resembles patterns of electric fields of two charges (opposite and like). However, a significant difference between electric and magnetic fields is that electric field lines begin and end at charges. Magnetic charges do not exist in nature. The magnetic field lines leave the north pole of the magnet and enter the south; they continue in the body of the magnet, i.e., as mentioned above, they are closed lines. Fields whose field lines are closed are called vortex. A magnetic field is a vortex field (this is its difference from an electric one).

Application of magnets

The most ancient magnetic device is the well-known compass. In modern technology, magnets are used very widely: in electric motors, in radio engineering, in electrical measuring equipment, etc.

Earth's magnetic field

The globe is a magnet. Like any magnet, it has its own magnetic field and its own magnetic poles. That is why the compass needle is oriented in a certain direction. It is clear where exactly the north pole of the magnetic needle should point, because opposite poles attract. Therefore, the north pole of the magnetic needle points to the south magnetic pole of the Earth. This pole is located in the north of the globe, somewhat away from the north geographic pole (on Prince of Wales Island - about $75°$ north latitude and $99°$ west longitude, at a distance of approximately $2100$ km from the north geographic pole).

When approaching the north geographic pole, the lines of force of the Earth's magnetic field increasingly tilt toward the horizon at a greater angle, and in the area of ​​the south magnetic pole they become vertical.

The Earth's north magnetic pole is located near the south geographic pole, namely at $66.5°$ south latitude and $140°$ east longitude. This is where the magnetic field lines emerge from the Earth.

In other words, the Earth's magnetic poles do not coincide with its geographic poles. Therefore, the direction of the magnetic needle does not coincide with the direction of the geographic meridian, and the magnetic needle of the compass only approximately shows the direction to the north.

The compass needle can also be influenced by some natural phenomena, for example, magnetic storms, which are temporary changes in the Earth's magnetic field associated with solar activity. Solar activity is accompanied by the emission of streams of charged particles, in particular electrons and protons, from the surface of the Sun. These streams, moving at high speed, create their own magnetic field that interacts with the Earth's magnetic field.

On the globe (except for short-term changes in the magnetic field) there are areas in which there is a constant deviation of the direction of the magnetic needle from the direction of the Earth's magnetic line. These are the areas magnetic anomaly(from the Greek anomalia - deviation, abnormality). One of the largest such areas is the Kursk magnetic anomaly. The anomalies are caused by huge deposits of iron ore at a relatively shallow depth.

The Earth's magnetic field reliably protects the Earth's surface from cosmic radiation, the effect of which on living organisms is destructive.

Flights of interplanetary space stations and ships have made it possible to establish that the Moon and the planet Venus have no magnetic field, while the planet Mars has a very weak one.

Experiments by Oerstedai ​​Ampere. Magnetic field induction

In 1820, the Danish scientist G. H. Oersted discovered that a magnetic needle placed near a conductor through which current flows rotates, tending to be perpendicular to the conductor.

The diagram of G. H. Oersted's experiment is shown in the figure. The conductor included in the current source circuit is located above the magnetic needle parallel to its axis. When the circuit is closed, the magnetic needle deviates from its original position. When the circuit is opened, the magnetic needle returns to its original position. It follows that the current-carrying conductor and the magnetic needle interact with each other. Based on this experiment, we can conclude that there is a magnetic field associated with the flow of current in a conductor and the vortex nature of this field. The described experiment and its results were Oersted's most important scientific achievement.

In the same year, the French physicist Ampere, who was interested in Oersted's experiments, discovered the interaction of two straight conductors with current. It turned out that if the currents in the conductors flow in one direction, i.e., they are parallel, then the conductors attract, if in opposite directions (i.e., they are antiparallel), then they repel.

Interactions between current-carrying conductors, i.e., interactions between moving electric charges, are called magnetic, and the forces with which current-carrying conductors act on each other are called magnetic forces.

According to the theory of short-range action, which M. Faraday adhered to, the current in one of the conductors cannot directly affect the current in the other conductor. Similar to the case with stationary electric charges around which there is an electric field, it was concluded that in the space surrounding the currents, there is a magnetic field, which acts with some force on another current-carrying conductor placed in this field, or on a permanent magnet. In turn, the magnetic field created by the second current-carrying conductor acts on the current in the first conductor.

Just as an electric field is detected by its effect on a test charge introduced into this field, a magnetic field can be detected by the orienting effect of a magnetic field on a frame with a current of small (compared to the distances at which the magnetic field changes noticeably) dimensions.

The wires supplying current to the frame should be intertwined (or placed close to each other), then the resulting force exerted by the magnetic field on these wires will be zero. The forces acting on such a current-carrying frame will rotate it so that its plane becomes perpendicular to the magnetic field induction lines. In the example, the frame will rotate so that the current-carrying conductor is in the plane of the frame. When the direction of current in the conductor changes, the frame will rotate $180°$. In the field between the poles of a permanent magnet, the frame will turn with a plane perpendicular to the magnetic field lines of the magnet.

Magnetic induction

Magnetic induction ($B↖(→)$) is a vector physical quantity that characterizes the magnetic field.

The direction of the magnetic induction vector $B↖(→)$ is taken to be:

1) the direction from the south pole $S$ to the north pole $N$ of a magnetic needle freely established in a magnetic field, or

2) the direction of the positive normal to a closed circuit with current on a flexible suspension, freely installed in a magnetic field. The normal directed towards the movement of the tip of the gimlet (with a right-hand thread), the handle of which is rotated in the direction of the current in the frame, is considered positive.

It is clear that directions 1) and 2) coincide, which was established by Ampere’s experiments.

As for the magnitude of magnetic induction (i.e., its modulus) $B$, which could characterize the strength of the field, experiments have established that the maximum force $F$ with which the field acts on a current-carrying conductor (placed perpendicular to the induction lines magnetic field), depends on the current $I$ in the conductor and on its length $∆l$ (proportional to them). However, the force acting on a current element (of unit length and current strength) depends only on the field itself, i.e. the ratio $(F)/(I∆l)$ for a given field is a constant value (similar to the ratio of force to charge for electric field). This value is determined as magnetic induction.

The magnetic field induction at a given point is equal to the ratio of the maximum force acting on a current-carrying conductor to the length of the conductor and the current strength in the conductor placed at this point.

The greater the magnetic induction at a given point in the field, the greater the force the field at that point will act on a magnetic needle or a moving electric charge.

The SI unit of magnetic induction is tesla(Tl), named after the Serbian electrical engineer Nikola Tesla. As can be seen from the formula, $1$ T $=l(H)/(A m)$

If there are several different sources of magnetic field, the induction vectors of which at a given point in space are equal to $(В_1)↖(→), (В_2)↖(→), (В_3)↖(→),...$, then, according to the principle of field superposition, the magnetic field induction at this point is equal to the sum of the magnetic field induction vectors created every source.

$В↖(→)=(В_1)↖(→)+(В_2)↖(→)+(В_3)↖(→)+...$

Magnetic induction lines

To visually represent the magnetic field, M. Faraday introduced the concept magnetic lines of force, which he repeatedly demonstrated in his experiments. A picture of the field lines can easily be obtained using iron filings sprinkled on cardboard. The figure shows: lines of magnetic induction of direct current, solenoid, circular current, direct magnet.

Magnetic induction lines, or magnetic lines of force, or just magnetic lines are called lines whose tangents at any point coincide with the direction of the magnetic induction vector $B↖(→)$ at this point in the field.

If, instead of iron filings, small magnetic needles are placed around a long straight conductor carrying current, then you can see not only the configuration of the field lines (concentric circles), but also the direction of the field lines (the north pole of the magnetic needle indicates the direction of the induction vector at a given point).

The direction of the forward current magnetic field can be determined by right gimlet rule.

If you rotate the handle of the gimlet so that the translational movement of the tip of the gimlet indicates the direction of the current, then the direction of rotation of the handle of the gimlet will indicate the direction of the magnetic field lines of the current.

The direction of the forward current magnetic field can also be determined using first rule of the right hand.

If you grasp the conductor with your right hand, pointing the bent thumb in the direction of the current, then the tips of the remaining fingers at each point will show the direction of the induction vector at this point.

Vortex field

Magnetic induction lines are closed, which indicates that there are no magnetic charges in nature. Fields whose field lines are closed are called vortex fields. That is, the magnetic field is a vortex field. This differs from the electric field created by charges.

Solenoid

A solenoid is a coil of wire carrying current.

The solenoid is characterized by the number of turns per unit length $n$, length $l$ and diameter $d$. The thickness of the wire in the solenoid and the pitch of the helix (helical line) are small compared to its diameter $d$ and length $l$. The term “solenoid” is also used in a broader sense - this is the name given to coils with an arbitrary cross-section (square solenoid, rectangular solenoid), and not necessarily cylindrical in shape (toroidal solenoid). There is a long solenoid ($l>>d$) and a short one ($l

The solenoid was invented in 1820 by A. Ampere to enhance the magnetic action of current discovered by X. Oersted and used by D. Arago in experiments on the magnetization of steel rods. The magnetic properties of a solenoid were experimentally studied by Ampere in 1822 (at the same time he introduced the term “solenoid”). The equivalence of the solenoid to permanent natural magnets was established, which was a confirmation of Ampere’s electrodynamic theory, which explained magnetism by the interaction of ring molecular currents hidden in bodies.

The magnetic field lines of the solenoid are shown in the figure. The direction of these lines is determined using second rule of the right hand.

If you clasp the solenoid with the palm of your right hand, directing four fingers along the current in the turns, then the extended thumb will indicate the direction of the magnetic lines inside the solenoid.

Comparing the magnetic field of a solenoid with the field of a permanent magnet, you can see that they are very similar. Like a magnet, a solenoid has two poles - north ($N$) and south ($S$). The North Pole is the one from which magnetic lines emerge; the south pole is the one they enter. The north pole of the solenoid is always located on the side that the thumb of the palm points to when it is positioned in accordance with the second rule of the right hand.

A solenoid in the form of a coil with a large number of turns is used as a magnet.

Studies of the magnetic field of a solenoid show that the magnetic effect of a solenoid increases with increasing current and the number of turns in the solenoid. In addition, the magnetic action of a solenoid or current-carrying coil is enhanced by introducing an iron rod into it, which is called core

Electromagnets

A solenoid with an iron core inside is called electromagnet.

Electromagnets can contain not one, but several coils (windings) and have cores of different shapes.

Such an electromagnet was first constructed by the English inventor W. Sturgeon in 1825. With a mass of $0.2$ kg, W. Sturgeon’s electromagnet held a load weighing $36$ N. In the same year, J. Joule increased the lifting force of the electromagnet to $200$ N, and six years later American scientist J. Henry built an electromagnet weighing $300$ kg, capable of holding a load weighing $1$ t!

Modern electromagnets can lift loads weighing several tens of tons. They are used in factories when moving heavy iron and steel products. Electromagnets are also used in agriculture to clean the grains of a number of plants from weeds and in other industries.

Ampere power

A straight section of conductor $∆l$, through which current $I$ flows, is acted upon by a force $F$ in a magnetic field with induction $B$.

To calculate this force, use the expression:

$F=B|I|∆lsinα$

where $α$ is the angle between the vector $B↖(→)$ and the direction of the section of conductor with current (current element); The direction of the current element is taken to be the direction in which the current flows through the conductor. The force $F$ is called Ampere force in honor of the French physicist A. M. Ampere, who was the first to discover the effect of a magnetic field on a current-carrying conductor. (In fact, Ampere established a law for the force of interaction between two elements of current-carrying conductors. He was a proponent of the theory of long-range action and did not use the concept of field.

However, according to tradition and in memory of the scientist’s merits, the expression for the force acting on a current-carrying conductor from a magnetic field is also called Ampere’s law.)

The direction of Ampere's force is determined using the left-hand rule.

If you position the palm of your left hand so that the magnetic field lines enter it perpendicularly, and the four extended fingers indicate the direction of the current in the conductor, then the outstretched thumb will indicate the direction of the force acting on the current-carrying conductor. Thus, the Ampere force is always perpendicular to both the magnetic field induction vector and the direction of the current in the conductor, i.e., perpendicular to the plane in which these two vectors lie.

The consequence of the Ampere force is the rotation of the current-carrying frame in a constant magnetic field. This finds practical application in many devices, e.g. electrical measuring instruments- galvanometers, ammeters, where a movable frame with current rotates in the field of a permanent magnet and by the angle of deflection of a pointer fixedly connected to the frame, one can judge the amount of current flowing in the circuit.

Thanks to the rotating effect of the magnetic field on the current-carrying frame, it also became possible to create and use electric motors- machines in which electrical energy is converted into mechanical energy.

Lorentz force

The Lorentz force is a force acting on a moving point electric charge in an external magnetic field.

Dutch physicist H. A. Lorenz at the end of the 19th century. established that the force exerted by a magnetic field on a moving charged particle is always perpendicular to the direction of motion of the particle and the lines of force of the magnetic field in which this particle moves.

The direction of the Lorentz force can be determined using the left-hand rule.

If you position the palm of your left hand so that the four extended fingers indicate the direction of movement of the charge, and the vector of the magnetic induction field enters the palm, then the extended thumb will indicate the direction of the Lorentz force acting on the positive charge.

If the charge of the particle is negative, then the Lorentz force will be directed in the opposite direction.

The modulus of the Lorentz force is easily determined from Ampere's law and is:

where $q$ is the charge of the particle, $υ$ is the speed of its movement, $α$ is the angle between the velocity and magnetic field induction vectors.

If, in addition to the magnetic field, there is also an electric field that acts on the charge with a force $(F_(el))↖(→)=qE↖(→)$, then the total force acting on the charge is equal to:

$F↖(→)=(F_(el))↖(→)+(F_l)↖(→)$

Often this total force is called the Lorentz force, and the force expressed by the formula $F=|q|υBsinα$ is called magnetic part of the Lorentz force.

Since the Lorentz force is perpendicular to the direction of motion of the particle, it cannot change its speed (it does no work), but can only change the direction of its motion, i.e., bend the trajectory.

This curvature of the trajectory of electrons in a TV picture tube is easy to observe if you bring a permanent magnet to its screen: the image will be distorted.

Motion of a charged particle in a uniform magnetic field. Let a charged particle fly with a speed $υ$ into a uniform magnetic field perpendicular to the tension lines. The force exerted by the magnetic field on the particle will cause it to rotate uniformly in a circle of radius r, which is easy to find using Newton’s second law, the expression for centripetal acceleration and the formula $F=|q|υBsinα$:

$(mυ^2)/(r)=|q|υB$

From here we get

$r=(mυ)/(|q|B)$

where $m$ is the particle mass.

Application of the Lorentz force. The action of a magnetic field on moving charges is used, for example, in mass spectrographs, which make it possible to separate charged particles by their specific charges, i.e., by the ratio of the charge of a particle to its mass, and from the results obtained to accurately determine the masses of the particles.

The vacuum chamber of the device is placed in a field (the induction vector $B↖(→)$ is perpendicular to the figure). Charged particles (electrons or ions) accelerated by the electric field, having described an arc, fall on the photographic plate, where they leave a trace that allows the radius of the trajectory $r$ to be measured with great accuracy. This radius determines the specific charge of the ion. Knowing the charge of an ion, it is easy to calculate its mass.

Magnetic properties of substances

In order to explain the existence of the magnetic field of permanent magnets, Ampere suggested that microscopic circular currents exist in a substance with magnetic properties (they were called molecular). This idea was subsequently, after the discovery of the electron and the structure of the atom, brilliantly confirmed: these currents are created by the movement of electrons around the nucleus and, being oriented in the same way, in total create a field around and inside the magnet.

In Fig. 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), these planes are oriented identically, and their actions add up.

Magnetic permeability. The reaction of the medium to the influence of an external magnetic field with induction $B_0$ (field in a vacuum) is determined by the magnetic susceptibility $μ$:

where $B$ is the magnetic field induction in the substance. Magnetic permeability is similar to dielectric constant $ε$.

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

Diamagnets are repelled by a magnet, paramagnetic materials are attracted. By these signs they can be distinguished from each other. For most substances, the magnetic permeability practically does not differ from unity, only 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.

The Curie temperature ($T_c$) is the temperature above which ferromagnetic materials lose their magnetic properties. It is different for each ferromagnet. For example, for iron $Т_с = 753°$С, for nickel $Т_с = 365°$С, for cobalt $Т_с = 1000°$ С. There are ferromagnetic alloys with $Т_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 very 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 made from 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.

Lenz's rule

Lenz's rule (Lenz's law) was established by E. H. Lenz in 1834. It refines the law of electromagnetic induction, discovered in 1831 by M. Faraday. Lenz's rule determines the direction of the induced current in a closed loop as it moves in an external magnetic field.

The direction of the induction current is always such that the forces it experiences from the magnetic field counteract the movement of the circuit, and the magnetic flux $Ф_1$ created by this current tends to compensate for changes in the external magnetic flux $Ф_e$.

Lenz's law is an expression of the law of conservation of energy for electromagnetic phenomena. Indeed, when a closed loop moves in a magnetic field due to external forces, it is necessary to perform some work against the forces arising as a result of the interaction of the induced current with the magnetic field and directed in the direction opposite to the movement.

Lenz's rule is illustrated in the figure. If a permanent magnet is moved into a coil closed to a galvanometer, the induced current in the coil will have a direction that will create a magnetic field with vector $B"$ directed opposite to the induction vector of the magnet's field $B$, i.e. it will push the magnet out of the coil or prevent its movement. When a magnet is pulled out of the coil, on the contrary, the field created by the induction current will attract the coil, i.e., again prevent its movement.

To apply Lenz's rule in order to determine the direction of the induced current $I_e$ in the circuit, you must follow these recommendations.

1. Set the direction of the magnetic induction lines $B↖(→)$ of the external magnetic field.
2. Find out whether the flux of magnetic induction of this field through the surface bounded by the contour ($∆Ф > 0$) increases or decreases ($∆Ф
3. Set the direction of the magnetic induction lines $В"↖(→)$ of the magnetic field of the induced current $I_i$. These lines should be directed, according to Lenz's rule, opposite to the lines $В↖(→)$, if $∆Ф > 0$, and have the same direction as them if $∆Ф
4. Knowing the direction of the magnetic induction lines $B"↖(→)$, determine the direction of the induction current $I_i$ using gimlet rule.