General information

In a surprising way, the ideas of one person can influence the subsequent development. human society generally. Such a person was Michael Faraday, not too versed in the intricacies of contemporary mathematics, but perfectly understanding physical meaning known by that time information about the nature of electricity and magnetism due to the concept of field interactions put forward by him.

The existence of modern society, based on the use of electricity, magnetism and electrodynamics, we owe to a galaxy of remarkable scientists. Among them, Ampère, Oersted, Henry, Gauss, Weber, Lorentz and, of course, Maxwell should be noted. Ultimately, they brought the science of electricity and magnetism into a single picture, which served as the basis for a whole cohort of inventors who created the prerequisites for the emergence of the modern information society with their creations.

We live surrounded by electric motors and generators: they are our first assistants in production, transport and at home. Any self-respecting person cannot imagine existence without a refrigerator, vacuum cleaner and washing machine. A priority is also a microwave oven, a hair dryer, a coffee grinder, a mixer, a blender and - the ultimate dream - an electric meat grinder and a bread machine. Of course, air conditioning is also a terribly useful thing, but if there are no funds to purchase it, then a simple fan will do.

For some men, the requests are somewhat more modest: the ultimate dream of the most inept man is an electric drill. Some of us, unsuccessfully trying to start the car in forty degrees of frost and hopelessly tormenting the starter (also an electric motor), secretly dream of purchasing a Tesla Motors car with electric motors and batteries in order to forget forever about the problems of gasoline and diesel engines.

Electric motors are everywhere: they take us up in elevators, they transport us in subways, trains, trams, trolleybuses and high-speed trains. They bring us water to the floors of skyscrapers, operate fountains, pump water from mines and wells, roll steel, lift weights, working in various cranes. And they do a lot of other useful things, setting in motion machine tools, tools and mechanisms.

Even exoskeletons for people with disabilities and for the military are made using electric motors, not to mention a whole army of industrial and research robots.

Today, electric motors work in space - just think of the Curiosity rover. They work on land, underground, on water, under water and even in the air - if not today, then tomorrow (article written in November 2015) the Solar Impulse 2 aircraft will finally complete its round-the-world trip, and unmanned aircraft on electric motors, there are simply no numbers. Not without reason, quite serious corporations are now working on mail delivery services using unmanned aerial vehicles.

History reference

Built in 1800 by the Italian physicist Alessandro Volta, the chemical battery, later named after the inventor "voltaic column", truly turned out to be a "horn of plenty" for scientists. It made it possible to set in motion electric charges in conductors, that is, to create electricity. New discoveries using the voltaic column continuously followed one after another in various fields physics and chemistry.

For example, the English scientist Sir Humphrey Davy in 1807, studying the electrolysis of melts of sodium and potassium hydroxides, obtained metallic sodium and potassium. Earlier, in 1801, he also discovered the electric arc, although the Russians consider it to be the discoverer of Vasily Vladimirovich Petrov. Petrov in 1802 described not only the arc itself, but also the possibilities of its practical application for the purposes of melting, welding metals and recovering them from ores, as well as lighting.

But the most important discovery was made by the Danish physicist Hans Christian Oersted: on April 21, 1820, during a demonstration of experiments at a lecture, he noticed the deviation of the magnetic compass needle when turning on and off the electric current flowing through a conductor in the form of a wire. Thus, for the first time, the relationship between electricity and magnetism was confirmed.

The next step was taken by the French physicist André Marie Ampère a few months after becoming acquainted with Oersted's experiment. The course of reasoning of this scientist, set out in the messages sent by him one after another to the French Academy of Sciences, is curious. At first, observing the turn of the compass needle at a conductor with current, Ampère suggested that the Earth's magnetism is also caused by currents flowing around the Earth in the direction from west to east. From this he concluded that the magnetic properties of a body can be explained by the circulation of current within it. Further, Ampère quite boldly concluded that the magnetic properties of any body are determined by closed electric currents inside it, and the magnetic interaction is due not to special magnetic charges, but simply to movement. electric charges, i.e. current.

Amper immediately took over pilot study of this interaction and found that conductors with current flowing in one direction are attracted, and in the opposite direction they are repelled. Mutually perpendicular conductors do not interact with each other.

It is hard to resist citing the law discovered by Ampère in his own formulation:

"The force of interaction of moving charges is proportional to the product of these charges, inversely proportional to the square of the distance between them, as in Coulomb's law, but, moreover, it also depends on the speeds of these charges and the direction of their movement."

So in physics fundamental forces depending on speeds were discovered.

But the real breakthrough in the science of electricity and magnetism was the discovery by Michael Faraday of the phenomenon electromagnetic induction- the occurrence of an electric current in a closed circuit when the magnetic flux passing through it changes. Regardless of Faraday, the phenomenon of electromagnetic induction was also discovered by Joseph Henry in 1832, who incidentally discovered the phenomenon of self-induction.

A public demonstration by Faraday on August 29, 1831 was performed on an installation he invented, consisting of a voltaic pole, a switch, an iron ring, on which two identical coils of copper wire were wound on opposite sides. One of the coils was connected to a battery through a switch, and a galvanometer was connected to the ends of the other. When the current was turned on and off, the galvanometer recorded the appearance of a current of different directions in the second coil.

In Faraday's experiments, an electric current, called the induction current, also appeared when a magnet was inserted into the coil or pulled out of the coil loaded on the measuring circuit. Similarly, the current also appeared when the smaller current-carrying coil was inserted/pulled in/out of the larger coil from the previous experiment. And the direction induction current reversed when inserting/extracting the magnet or small coil with current in accordance with the rule formulated by the Russian scientist Emil Khristianovich Lenz. in 1833.

Based on the experiments performed, Faraday derived a law for electromotive force later named after him.

The ideas and results of Faraday's experiments were rethought and generalized by another great compatriot - the brilliant English physicist and mathematician James Clerk Maxwell - in his four differential equations electrodynamics, later called Maxwell's equations.

It should be noted that three of the four Maxwell equations contain magnetic induction in the form of a vector magnetic field.

Magnetic induction. Definition

Magnetic induction is a vector physical quantity, which is power characteristic magnetic field (its action on charged particles) at a given point in space. It determines how strong F magnetic field acts on a charge q, moving at a speed v. Denoted by a Latin letter AT(pronounced vector B) and the force is calculated using the formula:

F = q [v∙B]

where F is the Lorentz force acting from the side of the magnetic field on the charge q; v- charge movement speed; B- magnetic field induction; [ v × B] - vector product vectors v and B.

Algebraically, the expression can be written as:

F = q∙v∙B sinα

where α - angle between velocity and magnetic induction vectors. vector direction F perpendicular to both of them and directed according to the rule of the left hand.

Magnetic induction is the main fundamental characteristic of a magnetic field, similar to the electric field strength vector.

AT international system SI units, the magnetic induction of the field is measured in teslas (T), in the CGS system - in gauss (Gs)

1 T = 10⁴ Gs

Other quantities of magnetic induction measurement used in various applications, and their conversion from one quantity to another, can be found in the converter of physical quantities.

Measuring instruments for measuring the magnitude of magnetic induction are called teslameters or gaussmeters.

Magnetic field induction. Physics of phenomena

Depending on the reaction to an external magnetic field, all substances are divided into three groups:

• Diamagnets
• Paramagnets
• ferromagnets

The terms diamagnetism and paramagnetism were introduced by Faraday in 1845. For quantification these reactions introduced the concept of magnetic permeability. In the SI system introduced absolute magnetic permeability, measured in H/m, and relative dimensionless magnetic permeability, equal to the ratio of the permeability of a given medium to the vacuum permeability. For diamagnets, the relative magnetic permeability is somewhat less than unity, for paramagnets it is somewhat greater than unity. In ferromagnets, the magnetic permeability is much greater than unity and is non-linear.

Phenomenon diamagnetism It consists in the ability of a substance to counteract the influence of an external magnetic field due to magnetization against its direction. That is, diamagnets are repelled by a magnetic field. In this case, the atoms, molecules or ions of the diamagnet acquire a magnetic moment directed against the external field.

Phenomenon paramagnetism is the ability of a substance to become magnetized when exposed to an external magnetic field. Unlike diamagnets, paramagnets are pulled in by a magnetic field. In this case, the atoms, molecules or ions of the paramagnet acquire a magnetic moment in the direction coinciding with the direction of the external magnetic field. When the field is removed, paramagnets do not retain magnetization.

Phenomenon ferromagnetism is the ability of a substance to spontaneously magnetize in the absence of an external magnetic field or to be magnetized under the influence of an external magnetic field and retain magnetization when the field is removed. In this case, most of the magnetic moments of atoms, molecules or ions are parallel to each other. This order is maintained down to temperatures below a certain critical temperature, called the Curie point. At temperatures above the Curie point for a given substance, ferromagnets turn into paramagnets.

The magnetic permeability of superconductors is zero.

The absolute magnetic permeability of air is approximately equal to the magnetic permeability of vacuum and in technical calculations is taken equal to 4π 10 ⁻⁷ H/m

Peculiarities of the Behavior of the Magnetic Field in Diamagnets

As mentioned above, diamagnetic materials create an induced magnetic field directed against an external magnetic field. Diamagnetism is a quantum mechanical effect inherent in all substances. In paramagnets and ferromagnets, it is leveled due to other, stronger effects.

Diamagnets include, for example, substances such as inert gases, nitrogen, hydrogen, silicon, phosphorus and pyrolytic carbon; some metals - bismuth, zinc, copper, gold, silver. Many other inorganic and organic compounds are also diamagnetic, including water.

In an inhomogeneous magnetic field, diamagnets are shifted to a region of a weaker field. Magnetic lines of force as if pushed out of the body by diamagnetic materials. The phenomenon of diamagnetic levitation is based on this property. In a sufficiently strong magnetic field created by modern magnets, it is possible to levitate not only various diamagnets, but also small living beings, consisting mainly of water.

Scientists from the University of Niemingen, the Netherlands, succeeded in hanging a frog in the air in a field with a magnetic induction of about 16 T, and researchers from a NASA laboratory using a superconductor magnet - levitation of a mouse, which, as a biological object, is much closer to a person than a frog .

All conductors exhibit diamagnetism when exposed to an alternating magnetic field.

The essence of the phenomenon is that under the action of an alternating magnetic field, eddy currents - Foucault currents - directed against the action of an external magnetic field are induced in the conductors.

Features of the behavior of a magnetic field in paramagnets

The interaction of a magnetic field with paramagnets is completely different. Because the atoms, molecules, or ions of paramagnetic materials have their own magnetic moment, they align in the direction of the external magnetic field. This creates a resulting magnetic field that is greater than the original field.

Paramagnets include aluminum, platinum, alkali and alkaline earth metals lithium, cesium, sodium, magnesium, tungsten, as well as alloys of these metals. Oxygen, nitric oxide, manganese oxide, ferric chloride and many other chemical compounds are also paramagnetic.

Paramagnets are weakly magnetic substances, their magnetic permeability is slightly more than unity. In an inhomogeneous magnetic field, paramagnets are drawn into the region of a stronger field. In the absence of a magnetic field, paramagnets do not retain magnetization, since due to thermal motion, the intrinsic magnetic moments of their atoms, molecules, or ions are randomly directed.

Features of the behavior of a magnetic field in ferromagnets

Due to their inherent property of being spontaneously magnetized, ferromagnets form natural magnets, which have been known to mankind since ancient times. Magical properties were attributed to magnets, they were used in various religious rituals and even in the construction of buildings. The first prototype of the compass, invented by the Chinese in the second or first centuries BC, was used by inquisitive ancestors to build houses according to the rules of Feng Shui. The use of the compass as a means of navigation began as early as the 11th century to travel across the desert along the Great Silk Road. Later, the use of the compass in maritime affairs played a significant role in the development of navigation, the discovery of new lands and the development of new sea trade routes.

Ferromagnetism is a manifestation of the quantum mechanical properties of electrons that have spin, i.e. own dipole magnetic moment. Simply put, electrons behave like tiny magnets. For each completed electron shell an atom can only have a pair of electrons with opposite spins, i.e. the magnetic field of such electrons is directed in opposite directions. Because of this, atoms with a paired number of electrons have a total magnetic moment equal to zero, therefore, only atoms with an unfilled outer shell and having an unpaired number of electrons are ferromagnets.

Ferromagnets include metals of transition groups (iron, copper, nickel) and rare earth metals (gadolinium, terbium, dysprosium, holmium and erbium), as well as alloys of these metals. Alloys of the above elements with non-ferromagnetic materials are also ferromagnets; alloys and compounds of chromium and manganese with non-ferromagnetic elements, as well as some of the metals of the actinide group.

Ferromagnets have a magnetic permeability value much greater than unity; the dependence of their magnetization under the action of an external magnetic field is non-linear and they are characterized by the manifestation of hysteresis - if the action of the magnetic field is removed, ferromagnets remain magnetized. To remove this residual magnetization, it is necessary to apply a reverse field.

A graph of the dependence of the magnetic permeability μ on the strength of the magnetic field H in a ferromagnet, called the Stoletov curve, shows that at zero magnetic field strength H = 0, the magnetic permeability has a small value μ₀; then, as the intensity increases, the magnetic permeability rapidly increases to a maximum μ max , then slowly drops to zero.

The pioneer in the study of the properties of ferromagnets was the Russian physicist and chemist Alexander Stoletov. Now the curve of dependence of magnetic permeability on the strength of the magnetic field bears his name.

Modern ferromagnetic materials are widely used in science and technology: many technologies and devices are based on their use and on the use of the phenomenon of magnetic induction. For example, in computer technology: the first generations of computers had memory on ferrite cores, information was stored on magnetic tapes, floppy disks and hard drives. However, the latter are still used in computers and are produced in hundreds of millions of pieces a year.

The use of magnetic induction in electrical engineering and electronics

AT modern world There are many examples of the use of magnetic field induction, primarily in power electrical engineering: in electricity generators, voltage transformers, in various electromagnetic drives of various devices, tools and mechanisms, in measuring technology and in science, in various physical installations for conducting experiments, as well as in means of electrical protection and emergency shutdown.

Electric motors, generators and transformers

In 1824, the English physicist and mathematician Peter Barlow described the unipolar motor he invented, which became the prototype of modern electric motors. direct current. The invention is also valuable because it was made long before the discovery of the phenomenon of electromagnetic induction.

Nowadays, almost all electric motors use the Ampere force, which acts on a current-carrying circuit in a magnetic field, causing it to move.

In order to demonstrate the phenomenon of magnetic induction, Faraday created an experimental setup in 1831, an important part of which was a device now known as a toroidal transformer. The principle of operation of the Faraday transformer is still used in all modern voltage and current transformers, regardless of power, design and scope.

In addition, Faraday scientifically substantiated and experimentally proved the possibility of converting mechanical motion into electricity using the unipolar DC generator he invented, which became the prototype of all DC generators.

First generator alternating current was created by the French inventor Hippolyte Pixie in 1832. Later, at the suggestion of Ampere, it was supplemented by a switching device, which made it possible to obtain a pulsating direct current.

Almost all electric power generators using the principle of magnetic induction are based on the occurrence of an electromotive force in a closed circuit, which is in a changing magnetic field. In this case, either the magnetic rotor rotates relative to the fixed stator coils in alternating current generators, or the rotor windings rotate relative to the fixed stator magnets (yoke) in DC generators.

The most powerful generator in the world, built in 2013 for the Taishan nuclear power plant by the Chinese company DongFang Electric, can generate a power of 1,750 MW.

In addition to conventional type generators and electric motors associated with the conversion mechanical energy in electrical energy and vice versa, there are so-called magnetohydrodynamic generators and engines operating on a different principle.

Relays and electromagnets

The electromagnet, invented by the American scientist J. Henry, became the first electric actuator and the forerunner of the familiar electric bell. Later, on its basis, Henry created an electromagnetic relay, which became the first automatic switching device with a binary state.

Shure dynamic microphone used in a video studio site

When transmitting a telegraph signal over long distances, relays were used as DC amplifiers, switching the connection of external batteries of intermediate stations for further signal transmission.

Dynamic heads and microphones

In modern audio technology, electromagnetic speakers are widely used, the sound in which appears due to the interaction of a moving coil attached to a cone, through which an audio frequency current flows, with a magnetic field in the gap of a fixed permanent magnet. As a result, the coil together with the diffuser move and create sound waves.

Dynamic microphones use the same design as the dynamic head, but in a microphone, on the contrary, a moving coil with a mini-diffuser in the gap of a fixed permanent magnet oscillates under the influence of an acoustic signal and generates an electrical sound frequency signal.

Measuring instruments and sensors

Despite the abundance of modern digital measuring instruments, in measurement technology, devices of magnetoelectric, electromagnetic, electrodynamic, ferrodynamic and induction types are still used.

All systems of the above types use the principle of interaction of magnetic fields or a permanent magnet with the field of a coil with current, or a ferromagnetic core with fields of coils with current, or magnetic fields of coils with current.

Due to the relative inertia of such measurement systems, they are applicable for measuring the average values ​​of variables.

General information

Surprisingly, the ideas of one person can influence the subsequent development of human society as a whole. Such a person was Michael Faraday, who was not too versed in the intricacies of contemporary mathematics, but who perfectly understood the physical meaning of the information about the nature of electricity and magnetism known by that time thanks to the concept of field interactions he put forward.

The existence of modern society, based on the use of electricity, magnetism and electrodynamics, we owe to a galaxy of remarkable scientists. Among them, Ampère, Oersted, Henry, Gauss, Weber, Lorentz and, of course, Maxwell should be noted. Ultimately, they brought the science of electricity and magnetism into a single picture, which served as the basis for a whole cohort of inventors who created the prerequisites for the emergence of the modern information society with their creations.

We live surrounded by electric motors and generators: they are our first assistants in production, transport and at home. Any self-respecting person cannot imagine existence without a refrigerator, vacuum cleaner and washing machine. A priority is also a microwave oven, a hair dryer, a coffee grinder, a mixer, a blender and - the ultimate dream - an electric meat grinder and a bread machine. Of course, air conditioning is also a terribly useful thing, but if there are no funds to purchase it, then a simple fan will do.

For some men, the requests are somewhat more modest: the ultimate dream of the most inept man is an electric drill. Some of us, unsuccessfully trying to start the car in forty degrees of frost and hopelessly tormenting the starter (also an electric motor), secretly dream of purchasing a Tesla Motors car with electric motors and batteries in order to forget forever about the problems of gasoline and diesel engines.

Electric motors are everywhere: they take us up in elevators, they transport us in subways, trains, trams, trolleybuses and high-speed trains. They bring us water to the floors of skyscrapers, operate fountains, pump water from mines and wells, roll steel, lift weights, working in various cranes. And they do a lot of other useful things, setting in motion machine tools, tools and mechanisms.

Even exoskeletons for people with disabilities and for the military are made using electric motors, not to mention a whole army of industrial and research robots.

Today, electric motors work in space - just think of the Curiosity rover. They work on land, underground, on water, under water and even in the air - if not today, then tomorrow (article written in November 2015) the Solar Impulse 2 aircraft will finally complete its round-the-world trip, and unmanned aerial vehicles on electric motors there are simply no numbers. Not without reason, quite serious corporations are now working on mail delivery services using unmanned aerial vehicles.

History reference

Built in 1800 by the Italian physicist Alessandro Volta, the chemical battery, later named after the inventor "voltaic column", truly turned out to be a "horn of plenty" for scientists. It allowed to set in motion electric charges in conductors, that is, to create an electric current. New discoveries using the voltaic column followed one after another in various fields of physics and chemistry.

For example, the English scientist Sir Humphrey Davy in 1807, studying the electrolysis of melts of sodium and potassium hydroxides, obtained metallic sodium and potassium. Earlier, in 1801, he also discovered the electric arc, although the Russians consider it to be the discoverer of Vasily Vladimirovich Petrov. Petrov in 1802 described not only the arc itself, but also the possibilities of its practical application for the purposes of melting, welding metals and recovering them from ores, as well as lighting.

But the most important discovery was made by the Danish physicist Hans Christian Oersted: on April 21, 1820, during a demonstration of experiments at a lecture, he noticed the deviation of the magnetic compass needle when turning on and off the electric current flowing through a conductor in the form of a wire. Thus, for the first time, the relationship between electricity and magnetism was confirmed.

The next step was taken by the French physicist André Marie Ampère a few months after becoming acquainted with Oersted's experiment. The course of reasoning of this scientist, set out in the messages sent by him one after another to the French Academy of Sciences, is curious. At first, observing the turn of the compass needle at a conductor with current, Ampère suggested that the Earth's magnetism is also caused by currents flowing around the Earth in the direction from west to east. From this he concluded that the magnetic properties of a body can be explained by the circulation of current within it. Further, Ampère quite boldly concluded that the magnetic properties of any body are determined by closed electric currents inside it, and the magnetic interaction is due not to special magnetic charges, but simply to the movement of electric charges, i.e. current.

Ampère immediately took up an experimental study of this interaction and found that conductors with current flowing in one direction attract, and repel in the opposite direction. Mutually perpendicular conductors do not interact with each other.

It is hard to resist citing the law discovered by Ampère in his own formulation:

"The force of interaction of moving charges is proportional to the product of these charges, inversely proportional to the square of the distance between them, as in Coulomb's law, but, moreover, it also depends on the speeds of these charges and the direction of their movement."

So in physics fundamental forces depending on speeds were discovered.

But a real breakthrough in the science of electricity and magnetism was the discovery by Michael Faraday of the phenomenon of electromagnetic induction - the occurrence of an electric current in a closed circuit when the magnetic flux passing through it changes. Regardless of Faraday, the phenomenon of electromagnetic induction was also discovered by Joseph Henry in 1832, who incidentally discovered the phenomenon of self-induction.

A public demonstration by Faraday on August 29, 1831 was performed on an installation he invented, consisting of a voltaic pole, a switch, an iron ring, on which two identical coils of copper wire were wound on opposite sides. One of the coils was connected to a battery through a switch, and a galvanometer was connected to the ends of the other. When the current was turned on and off, the galvanometer recorded the appearance of a current of different directions in the second coil.

In Faraday's experiments, an electric current, called the induction current, also appeared when a magnet was inserted into the coil or pulled out of the coil loaded on the measuring circuit. Similarly, the current also appeared when the smaller current-carrying coil was inserted/pulled in/out of the larger coil from the previous experiment. Moreover, the direction of the induction current changed to the opposite when a magnet or a small coil with a current was inserted/extracted in accordance with the rule formulated by the Russian scientist Emil Khristianovich Lenz. in 1833.

Based on the experiments performed, Faraday derived the law for the electromotive force, later named after him.

The ideas and results of Faraday's experiments were rethought and generalized by another great compatriot - the brilliant English physicist and mathematician James Clerk Maxwell - in his four differential equations of electrodynamics, later called Maxwell's equations.

It should be noted that in three of the four Maxwell equations, magnetic induction appears in the form of a magnetic field vector.

Magnetic induction. Definition

Magnetic induction is a vector physical quantity, which is a force characteristic of a magnetic field (its action on charged particles) at a given point in space. It determines how strong F magnetic field acts on a charge q, moving at a speed v. Denoted by a Latin letter AT(pronounced vector B) and the force is calculated using the formula:

F = q [v∙B]

where F is the Lorentz force acting from the side of the magnetic field on the charge q; v- charge movement speed; B- magnetic field induction; [ v × B] - cross product of vectors v and B.

Algebraically, the expression can be written as:

F = q∙v∙B sinα

where α - angle between velocity and magnetic induction vectors. vector direction F perpendicular to both of them and directed according to the rule of the left hand.

Magnetic induction is the main fundamental characteristic of a magnetic field, similar to the electric field strength vector.

In the International System of Units SI, the magnetic induction of the field is measured in teslas (T), in the CGS system - in gauss (Gs)

1 T = 10⁴ Gs

Other quantities of magnetic induction measurement used in various applications, and their conversion from one quantity to another, can be found in the converter of physical quantities.

Measuring instruments for measuring the magnitude of magnetic induction are called teslameters or gaussmeters.

Magnetic field induction. Physics of phenomena

Depending on the reaction to an external magnetic field, all substances are divided into three groups:

• Diamagnets
• Paramagnets
• ferromagnets

The terms diamagnetism and paramagnetism were introduced by Faraday in 1845. To quantify these reactions, the concept of magnetic permeability has been introduced. In the SI system introduced absolute magnetic permeability, measured in H/m, and relative dimensionless magnetic permeability, equal to the ratio of the permeability of a given medium to the vacuum permeability. For diamagnets, the relative magnetic permeability is somewhat less than unity, for paramagnets it is somewhat greater than unity. In ferromagnets, the magnetic permeability is much greater than unity and is non-linear.

Phenomenon diamagnetism It consists in the ability of a substance to counteract the influence of an external magnetic field due to magnetization against its direction. That is, diamagnets are repelled by a magnetic field. In this case, the atoms, molecules or ions of the diamagnet acquire a magnetic moment directed against the external field.

Phenomenon paramagnetism is the ability of a substance to become magnetized when exposed to an external magnetic field. Unlike diamagnets, paramagnets are pulled in by a magnetic field. In this case, the atoms, molecules or ions of the paramagnet acquire a magnetic moment in the direction coinciding with the direction of the external magnetic field. When the field is removed, paramagnets do not retain magnetization.

Phenomenon ferromagnetism is the ability of a substance to spontaneously magnetize in the absence of an external magnetic field or to be magnetized under the influence of an external magnetic field and retain magnetization when the field is removed. In this case, most of the magnetic moments of atoms, molecules or ions are parallel to each other. This order is maintained down to temperatures below a certain critical temperature, called the Curie point. At temperatures above the Curie point for a given substance, ferromagnets turn into paramagnets.

The magnetic permeability of superconductors is zero.

The absolute magnetic permeability of air is approximately equal to the magnetic permeability of vacuum and in technical calculations is taken equal to 4π 10 ⁻⁷ H/m

Peculiarities of the Behavior of the Magnetic Field in Diamagnets

As mentioned above, diamagnetic materials create an induced magnetic field directed against an external magnetic field. Diamagnetism is a quantum mechanical effect inherent in all substances. In paramagnets and ferromagnets, it is leveled due to other, stronger effects.

Diamagnets include, for example, substances such as inert gases, nitrogen, hydrogen, silicon, phosphorus and pyrolytic carbon; some metals - bismuth, zinc, copper, gold, silver. Many other inorganic and organic compounds are also diamagnetic, including water.

In an inhomogeneous magnetic field, diamagnets are shifted to a region of a weaker field. Magnetic lines of force are, as it were, pushed out of the body by diamagnetic materials. The phenomenon of diamagnetic levitation is based on this property. In a sufficiently strong magnetic field created by modern magnets, it is possible to levitate not only various diamagnets, but also small living beings, consisting mainly of water.

Scientists from the University of Niemingen, the Netherlands, succeeded in hanging a frog in the air in a field with a magnetic induction of about 16 T, and researchers from a NASA laboratory using a superconductor magnet - levitation of a mouse, which, as a biological object, is much closer to a person than a frog .

All conductors exhibit diamagnetism when exposed to an alternating magnetic field.

The essence of the phenomenon is that under the action of an alternating magnetic field, eddy currents - Foucault currents - directed against the action of an external magnetic field are induced in the conductors.

Features of the behavior of a magnetic field in paramagnets

The interaction of a magnetic field with paramagnets is completely different. Because the atoms, molecules, or ions of paramagnetic materials have their own magnetic moment, they align in the direction of the external magnetic field. This creates a resulting magnetic field that is greater than the original field.

Paramagnets include aluminum, platinum, alkali and alkaline earth metals lithium, cesium, sodium, magnesium, tungsten, as well as alloys of these metals. Oxygen, nitric oxide, manganese oxide, ferric chloride and many other chemical compounds are also paramagnetic.

Paramagnets are weakly magnetic substances, their magnetic permeability is slightly more than unity. In an inhomogeneous magnetic field, paramagnets are drawn into the region of a stronger field. In the absence of a magnetic field, paramagnets do not retain magnetization, since due to thermal motion, the intrinsic magnetic moments of their atoms, molecules, or ions are randomly directed.

Features of the behavior of a magnetic field in ferromagnets

Due to their inherent property of being spontaneously magnetized, ferromagnets form natural magnets, which have been known to mankind since ancient times. Magical properties were attributed to magnets, they were used in various religious rituals and even in the construction of buildings. The first prototype of the compass, invented by the Chinese in the second or first centuries BC, was used by inquisitive ancestors to build houses according to the rules of Feng Shui. The use of the compass as a means of navigation began as early as the 11th century to travel across the desert along the Great Silk Road. Later, the use of the compass in maritime affairs played a significant role in the development of navigation, the discovery of new lands and the development of new sea trade routes.

Ferromagnetism is a manifestation of the quantum mechanical properties of electrons that have spin, i.e. own dipole magnetic moment. Simply put, electrons behave like tiny magnets. Each filled electron shell of an atom can contain only a pair of electrons with opposite spins, i.e. the magnetic field of such electrons is directed in opposite directions. Because of this, atoms with a paired number of electrons have a total magnetic moment equal to zero, therefore, only atoms with an unfilled outer shell and having an unpaired number of electrons are ferromagnets.

Ferromagnets include metals of transition groups (iron, copper, nickel) and rare earth metals (gadolinium, terbium, dysprosium, holmium and erbium), as well as alloys of these metals. Alloys of the above elements with non-ferromagnetic materials are also ferromagnets; alloys and compounds of chromium and manganese with non-ferromagnetic elements, as well as some of the metals of the actinide group.

Ferromagnets have a magnetic permeability value much greater than unity; the dependence of their magnetization under the action of an external magnetic field is non-linear and they are characterized by the manifestation of hysteresis - if the action of the magnetic field is removed, ferromagnets remain magnetized. To remove this residual magnetization, it is necessary to apply a reverse field.

A graph of the dependence of the magnetic permeability μ on the strength of the magnetic field H in a ferromagnet, called the Stoletov curve, shows that at zero magnetic field strength H = 0, the magnetic permeability has a small value μ₀; then, as the intensity increases, the magnetic permeability rapidly increases to a maximum μ max , then slowly drops to zero.

The pioneer in the study of the properties of ferromagnets was the Russian physicist and chemist Alexander Stoletov. Now the curve of dependence of magnetic permeability on the strength of the magnetic field bears his name.

Modern ferromagnetic materials are widely used in science and technology: many technologies and devices are based on their use and on the use of the phenomenon of magnetic induction. For example, in computer technology: the first generations of computers had memory on ferrite cores, information was stored on magnetic tapes, floppy disks and hard drives. However, the latter are still used in computers and are produced in hundreds of millions of pieces a year.

The use of magnetic induction in electrical engineering and electronics

In the modern world, there are many examples of the use of magnetic field induction, primarily in power electrical engineering: in electricity generators, voltage transformers, in various electromagnetic drives of various devices, tools and mechanisms, in measuring technology and in science, in various physical installations for experiments. , as well as in the means of electrical protection and emergency shutdown.

Electric motors, generators and transformers

In 1824, the English physicist and mathematician Peter Barlow described the unipolar motor he invented, which became the prototype of modern DC electric motors. The invention is also valuable because it was made long before the discovery of the phenomenon of electromagnetic induction.

Nowadays, almost all electric motors use the Ampere force, which acts on a current-carrying circuit in a magnetic field, causing it to move.

In order to demonstrate the phenomenon of magnetic induction, Faraday created an experimental setup in 1831, an important part of which was a device now known as a toroidal transformer. The principle of operation of the Faraday transformer is still used in all modern voltage and current transformers, regardless of power, design and scope.

In addition, Faraday scientifically substantiated and experimentally proved the possibility of converting mechanical motion into electricity using the unipolar DC generator he invented, which became the prototype of all DC generators.

The first alternating current generator was created by the French inventor Hippolyte Pixie in 1832. Later, at the suggestion of Ampere, it was supplemented by a switching device, which made it possible to obtain a pulsating direct current.

Almost all electric power generators using the principle of magnetic induction are based on the occurrence of an electromotive force in a closed circuit, which is in a changing magnetic field. In this case, either the magnetic rotor rotates relative to the fixed stator coils in alternating current generators, or the rotor windings rotate relative to the fixed stator magnets (yoke) in DC generators.

The most powerful generator in the world, built in 2013 for the Taishan nuclear power plant by the Chinese company DongFang Electric, can generate a power of 1,750 MW.

In addition to generators and electric motors of the traditional type, associated with the conversion of mechanical energy into electrical energy and vice versa, there are so-called magnetohydrodynamic generators and motors operating on a different principle.

Relays and electromagnets

The electromagnet, invented by the American scientist J. Henry, became the first electric actuator and the forerunner of the familiar electric bell. Later, on its basis, Henry created an electromagnetic relay, which became the first automatic switching device with a binary state.

Shure dynamic microphone used in a video studio site

When transmitting a telegraph signal over long distances, relays were used as DC amplifiers, switching the connection of external batteries of intermediate stations for further signal transmission.

Dynamic heads and microphones

In modern audio technology, electromagnetic speakers are widely used, the sound in which appears due to the interaction of a moving coil attached to a cone, through which an audio frequency current flows, with a magnetic field in the gap of a fixed permanent magnet. As a result, the coil together with the diffuser move and create sound waves.

Dynamic microphones use the same design as the dynamic head, but in a microphone, on the contrary, a moving coil with a mini-diffuser in the gap of a fixed permanent magnet oscillates under the influence of an acoustic signal and generates an electrical sound frequency signal.

Measuring instruments and sensors

Despite the abundance of modern digital measuring instruments, devices of magnetoelectric, electromagnetic, electrodynamic, ferrodynamic and induction types are still used in measurement technology.

All systems of the above types use the principle of interaction of magnetic fields or a permanent magnet with the field of a coil with current, or a ferromagnetic core with fields of coils with current, or magnetic fields of coils with current.

Due to the relative inertia of such measurement systems, they are applicable for measuring the average values ​​of variables.

General information

Surprisingly, the ideas of one person can influence the subsequent development of human society as a whole. Such a person was Michael Faraday, who was not too versed in the intricacies of contemporary mathematics, but who perfectly understood the physical meaning of the information about the nature of electricity and magnetism known by that time thanks to the concept of field interactions he put forward.

The existence of modern society, based on the use of electricity, magnetism and electrodynamics, we owe to a galaxy of remarkable scientists. Among them, Ampère, Oersted, Henry, Gauss, Weber, Lorentz and, of course, Maxwell should be noted. Ultimately, they brought the science of electricity and magnetism into a single picture, which served as the basis for a whole cohort of inventors who created the prerequisites for the emergence of the modern information society with their creations.

We live surrounded by electric motors and generators: they are our first assistants in production, transport and at home. Any self-respecting person cannot imagine existence without a refrigerator, vacuum cleaner and washing machine. A priority is also a microwave oven, a hair dryer, a coffee grinder, a mixer, a blender and - the ultimate dream - an electric meat grinder and a bread machine. Of course, air conditioning is also a terribly useful thing, but if there are no funds to purchase it, then a simple fan will do.

For some men, the requests are somewhat more modest: the ultimate dream of the most inept man is an electric drill. Some of us, unsuccessfully trying to start the car in forty degrees of frost and hopelessly tormenting the starter (also an electric motor), secretly dream of purchasing a Tesla Motors car with electric motors and batteries in order to forget forever about the problems of gasoline and diesel engines.

Electric motors are everywhere: they take us up in elevators, they transport us in subways, trains, trams, trolleybuses and high-speed trains. They bring us water to the floors of skyscrapers, operate fountains, pump water from mines and wells, roll steel, lift weights, working in various cranes. And they do a lot of other useful things, setting in motion machine tools, tools and mechanisms.

Even exoskeletons for people with disabilities and for the military are made using electric motors, not to mention a whole army of industrial and research robots.

Today, electric motors work in space - just think of the Curiosity rover. They work on land, underground, on water, under water and even in the air - if not today, then tomorrow (article written in November 2015) the Solar Impulse 2 aircraft will finally complete its round-the-world trip, and unmanned aerial vehicles on electric motors there are simply no numbers. Not without reason, quite serious corporations are now working on mail delivery services using unmanned aerial vehicles.

History reference

Built in 1800 by the Italian physicist Alessandro Volta, the chemical battery, later named after the inventor "voltaic column", truly turned out to be a "horn of plenty" for scientists. It allowed to set in motion electric charges in conductors, that is, to create an electric current. New discoveries using the voltaic column followed one after another in various fields of physics and chemistry.

For example, the English scientist Sir Humphrey Davy in 1807, studying the electrolysis of melts of sodium and potassium hydroxides, obtained metallic sodium and potassium. Earlier, in 1801, he also discovered the electric arc, although the Russians consider it to be the discoverer of Vasily Vladimirovich Petrov. Petrov in 1802 described not only the arc itself, but also the possibilities of its practical application for the purposes of melting, welding metals and recovering them from ores, as well as lighting.

But the most important discovery was made by the Danish physicist Hans Christian Oersted: on April 21, 1820, during a demonstration of experiments at a lecture, he noticed the deviation of the magnetic compass needle when turning on and off the electric current flowing through a conductor in the form of a wire. Thus, for the first time, the relationship between electricity and magnetism was confirmed.

The next step was taken by the French physicist André Marie Ampère a few months after becoming acquainted with Oersted's experiment. The course of reasoning of this scientist, set out in the messages sent by him one after another to the French Academy of Sciences, is curious. At first, observing the turn of the compass needle at a conductor with current, Ampère suggested that the Earth's magnetism is also caused by currents flowing around the Earth in the direction from west to east. From this he concluded that the magnetic properties of a body can be explained by the circulation of current within it. Further, Ampère quite boldly concluded that the magnetic properties of any body are determined by closed electric currents inside it, and the magnetic interaction is due not to special magnetic charges, but simply to the movement of electric charges, i.e. current.

Ampère immediately took up an experimental study of this interaction and found that conductors with current flowing in one direction attract, and repel in the opposite direction. Mutually perpendicular conductors do not interact with each other.

It is hard to resist citing the law discovered by Ampère in his own formulation:

"The force of interaction of moving charges is proportional to the product of these charges, inversely proportional to the square of the distance between them, as in Coulomb's law, but, moreover, it also depends on the speeds of these charges and the direction of their movement."

So in physics fundamental forces depending on speeds were discovered.

But a real breakthrough in the science of electricity and magnetism was the discovery by Michael Faraday of the phenomenon of electromagnetic induction - the occurrence of an electric current in a closed circuit when the magnetic flux passing through it changes. Regardless of Faraday, the phenomenon of electromagnetic induction was also discovered by Joseph Henry in 1832, who incidentally discovered the phenomenon of self-induction.

A public demonstration by Faraday on August 29, 1831 was performed on an installation he invented, consisting of a voltaic pole, a switch, an iron ring, on which two identical coils of copper wire were wound on opposite sides. One of the coils was connected to a battery through a switch, and a galvanometer was connected to the ends of the other. When the current was turned on and off, the galvanometer recorded the appearance of a current of different directions in the second coil.

In Faraday's experiments, an electric current, called the induction current, also appeared when a magnet was inserted into the coil or pulled out of the coil loaded on the measuring circuit. Similarly, the current also appeared when the smaller current-carrying coil was inserted/pulled in/out of the larger coil from the previous experiment. Moreover, the direction of the induction current changed to the opposite when a magnet or a small coil with a current was inserted/extracted in accordance with the rule formulated by the Russian scientist Emil Khristianovich Lenz. in 1833.

Based on the experiments performed, Faraday derived the law for the electromotive force, later named after him.

The ideas and results of Faraday's experiments were rethought and generalized by another great compatriot - the brilliant English physicist and mathematician James Clerk Maxwell - in his four differential equations of electrodynamics, later called Maxwell's equations.

It should be noted that in three of the four Maxwell equations, magnetic induction appears in the form of a magnetic field vector.

Magnetic induction. Definition

Magnetic induction is a vector physical quantity, which is a force characteristic of a magnetic field (its action on charged particles) at a given point in space. It determines how strong F magnetic field acts on a charge q, moving at a speed v. Denoted by a Latin letter AT(pronounced vector B) and the force is calculated using the formula:

F = q [v∙B]

where F is the Lorentz force acting from the side of the magnetic field on the charge q; v- charge movement speed; B- magnetic field induction; [ v × B] - cross product of vectors v and B.

Algebraically, the expression can be written as:

F = q∙v∙B sinα

where α - angle between velocity and magnetic induction vectors. vector direction F perpendicular to both of them and directed according to the rule of the left hand.

Magnetic induction is the main fundamental characteristic of a magnetic field, similar to the electric field strength vector.

In the International System of Units SI, the magnetic induction of the field is measured in teslas (T), in the CGS system - in gauss (Gs)

1 T = 10⁴ Gs

Other quantities of magnetic induction measurement used in various applications, and their conversion from one quantity to another, can be found in the converter of physical quantities.

Measuring instruments for measuring the magnitude of magnetic induction are called teslameters or gaussmeters.

Magnetic field induction. Physics of phenomena

Depending on the reaction to an external magnetic field, all substances are divided into three groups:

• Diamagnets
• Paramagnets
• ferromagnets

The terms diamagnetism and paramagnetism were introduced by Faraday in 1845. To quantify these reactions, the concept of magnetic permeability has been introduced. In the SI system introduced absolute magnetic permeability, measured in H/m, and relative dimensionless magnetic permeability, equal to the ratio of the permeability of a given medium to the vacuum permeability. For diamagnets, the relative magnetic permeability is somewhat less than unity, for paramagnets it is somewhat greater than unity. In ferromagnets, the magnetic permeability is much greater than unity and is non-linear.

Phenomenon diamagnetism It consists in the ability of a substance to counteract the influence of an external magnetic field due to magnetization against its direction. That is, diamagnets are repelled by a magnetic field. In this case, the atoms, molecules or ions of the diamagnet acquire a magnetic moment directed against the external field.

Phenomenon paramagnetism is the ability of a substance to become magnetized when exposed to an external magnetic field. Unlike diamagnets, paramagnets are pulled in by a magnetic field. In this case, the atoms, molecules or ions of the paramagnet acquire a magnetic moment in the direction coinciding with the direction of the external magnetic field. When the field is removed, paramagnets do not retain magnetization.

Phenomenon ferromagnetism is the ability of a substance to spontaneously magnetize in the absence of an external magnetic field or to be magnetized under the influence of an external magnetic field and retain magnetization when the field is removed. In this case, most of the magnetic moments of atoms, molecules or ions are parallel to each other. This order is maintained down to temperatures below a certain critical temperature, called the Curie point. At temperatures above the Curie point for a given substance, ferromagnets turn into paramagnets.

The magnetic permeability of superconductors is zero.

The absolute magnetic permeability of air is approximately equal to the magnetic permeability of vacuum and in technical calculations is taken equal to 4π 10 ⁻⁷ H/m

Peculiarities of the Behavior of the Magnetic Field in Diamagnets

As mentioned above, diamagnetic materials create an induced magnetic field directed against an external magnetic field. Diamagnetism is a quantum mechanical effect inherent in all substances. In paramagnets and ferromagnets, it is leveled due to other, stronger effects.

Diamagnets include, for example, substances such as inert gases, nitrogen, hydrogen, silicon, phosphorus and pyrolytic carbon; some metals - bismuth, zinc, copper, gold, silver. Many other inorganic and organic compounds are also diamagnetic, including water.

In an inhomogeneous magnetic field, diamagnets are shifted to a region of a weaker field. Magnetic lines of force are, as it were, pushed out of the body by diamagnetic materials. The phenomenon of diamagnetic levitation is based on this property. In a sufficiently strong magnetic field created by modern magnets, it is possible to levitate not only various diamagnets, but also small living beings, consisting mainly of water.

Scientists from the University of Niemingen, the Netherlands, succeeded in hanging a frog in the air in a field with a magnetic induction of about 16 T, and researchers from a NASA laboratory using a superconductor magnet - levitation of a mouse, which, as a biological object, is much closer to a person than a frog .

All conductors exhibit diamagnetism when exposed to an alternating magnetic field.

The essence of the phenomenon is that under the action of an alternating magnetic field, eddy currents - Foucault currents - directed against the action of an external magnetic field are induced in the conductors.

Features of the behavior of a magnetic field in paramagnets

The interaction of a magnetic field with paramagnets is completely different. Because the atoms, molecules, or ions of paramagnetic materials have their own magnetic moment, they align in the direction of the external magnetic field. This creates a resulting magnetic field that is greater than the original field.

Paramagnets include aluminum, platinum, alkali and alkaline earth metals lithium, cesium, sodium, magnesium, tungsten, as well as alloys of these metals. Oxygen, nitric oxide, manganese oxide, ferric chloride and many other chemical compounds are also paramagnetic.

Paramagnets are weakly magnetic substances, their magnetic permeability is slightly more than unity. In an inhomogeneous magnetic field, paramagnets are drawn into the region of a stronger field. In the absence of a magnetic field, paramagnets do not retain magnetization, since due to thermal motion, the intrinsic magnetic moments of their atoms, molecules, or ions are randomly directed.

Features of the behavior of a magnetic field in ferromagnets

Due to their inherent property of being spontaneously magnetized, ferromagnets form natural magnets, which have been known to mankind since ancient times. Magical properties were attributed to magnets, they were used in various religious rituals and even in the construction of buildings. The first prototype of the compass, invented by the Chinese in the second or first centuries BC, was used by inquisitive ancestors to build houses according to the rules of Feng Shui. The use of the compass as a means of navigation began as early as the 11th century to travel across the desert along the Great Silk Road. Later, the use of the compass in maritime affairs played a significant role in the development of navigation, the discovery of new lands and the development of new sea trade routes.

Ferromagnetism is a manifestation of the quantum mechanical properties of electrons that have spin, i.e. own dipole magnetic moment. Simply put, electrons behave like tiny magnets. Each filled electron shell of an atom can contain only a pair of electrons with opposite spins, i.e. the magnetic field of such electrons is directed in opposite directions. Because of this, atoms with a paired number of electrons have a total magnetic moment equal to zero, therefore, only atoms with an unfilled outer shell and having an unpaired number of electrons are ferromagnets.

Ferromagnets include metals of transition groups (iron, copper, nickel) and rare earth metals (gadolinium, terbium, dysprosium, holmium and erbium), as well as alloys of these metals. Alloys of the above elements with non-ferromagnetic materials are also ferromagnets; alloys and compounds of chromium and manganese with non-ferromagnetic elements, as well as some of the metals of the actinide group.

Ferromagnets have a magnetic permeability value much greater than unity; the dependence of their magnetization under the action of an external magnetic field is non-linear and they are characterized by the manifestation of hysteresis - if the action of the magnetic field is removed, ferromagnets remain magnetized. To remove this residual magnetization, it is necessary to apply a reverse field.

A graph of the dependence of the magnetic permeability μ on the strength of the magnetic field H in a ferromagnet, called the Stoletov curve, shows that at zero magnetic field strength H = 0, the magnetic permeability has a small value μ₀; then, as the intensity increases, the magnetic permeability rapidly increases to a maximum μ max , then slowly drops to zero.

The pioneer in the study of the properties of ferromagnets was the Russian physicist and chemist Alexander Stoletov. Now the curve of dependence of magnetic permeability on the strength of the magnetic field bears his name.

Modern ferromagnetic materials are widely used in science and technology: many technologies and devices are based on their use and on the use of the phenomenon of magnetic induction. For example, in computer technology: the first generations of computers had memory on ferrite cores, information was stored on magnetic tapes, floppy disks and hard drives. However, the latter are still used in computers and are produced in hundreds of millions of pieces a year.

The use of magnetic induction in electrical engineering and electronics

In the modern world, there are many examples of the use of magnetic field induction, primarily in power electrical engineering: in electricity generators, voltage transformers, in various electromagnetic drives of various devices, tools and mechanisms, in measuring technology and in science, in various physical installations for experiments. , as well as in the means of electrical protection and emergency shutdown.

Electric motors, generators and transformers

In 1824, the English physicist and mathematician Peter Barlow described the unipolar motor he invented, which became the prototype of modern DC electric motors. The invention is also valuable because it was made long before the discovery of the phenomenon of electromagnetic induction.

Nowadays, almost all electric motors use the Ampere force, which acts on a current-carrying circuit in a magnetic field, causing it to move.

In order to demonstrate the phenomenon of magnetic induction, Faraday created an experimental setup in 1831, an important part of which was a device now known as a toroidal transformer. The principle of operation of the Faraday transformer is still used in all modern voltage and current transformers, regardless of power, design and scope.

In addition, Faraday scientifically substantiated and experimentally proved the possibility of converting mechanical motion into electricity using the unipolar DC generator he invented, which became the prototype of all DC generators.

The first alternating current generator was created by the French inventor Hippolyte Pixie in 1832. Later, at the suggestion of Ampere, it was supplemented by a switching device, which made it possible to obtain a pulsating direct current.

Almost all electric power generators using the principle of magnetic induction are based on the occurrence of an electromotive force in a closed circuit, which is in a changing magnetic field. In this case, either the magnetic rotor rotates relative to the fixed stator coils in alternating current generators, or the rotor windings rotate relative to the fixed stator magnets (yoke) in DC generators.

The most powerful generator in the world, built in 2013 for the Taishan nuclear power plant by the Chinese company DongFang Electric, can generate a power of 1,750 MW.

In addition to generators and electric motors of the traditional type, associated with the conversion of mechanical energy into electrical energy and vice versa, there are so-called magnetohydrodynamic generators and motors operating on a different principle.

Relays and electromagnets

The electromagnet, invented by the American scientist J. Henry, became the first electric actuator and the forerunner of the familiar electric bell. Later, on its basis, Henry created an electromagnetic relay, which became the first automatic switching device with a binary state.

Shure dynamic microphone used in a video studio site

When transmitting a telegraph signal over long distances, relays were used as DC amplifiers, switching the connection of external batteries of intermediate stations for further signal transmission.

Dynamic heads and microphones

In modern audio technology, electromagnetic speakers are widely used, the sound in which appears due to the interaction of a moving coil attached to a cone, through which an audio frequency current flows, with a magnetic field in the gap of a fixed permanent magnet. As a result, the coil together with the diffuser move and create sound waves.

Dynamic microphones use the same design as the dynamic head, but in a microphone, on the contrary, a moving coil with a mini-diffuser in the gap of a fixed permanent magnet oscillates under the influence of an acoustic signal and generates an electrical sound frequency signal.

Measuring instruments and sensors

Despite the abundance of modern digital measuring instruments, devices of magnetoelectric, electromagnetic, electrodynamic, ferrodynamic and induction types are still used in measurement technology.

All systems of the above types use the principle of interaction of magnetic fields or a permanent magnet with the field of a coil with current, or a ferromagnetic core with fields of coils with current, or magnetic fields of coils with current.

Due to the relative inertia of such measurement systems, they are applicable for measuring the average values ​​of variables.

The strength of the magnetic field is not the main quantity characterizing the magnetic field, although the definition of the strength is valid for the calculation of coils without a magnetic circuit.

For a coil with a magnetic circuit, the main quantity characterizing the magnetic field is the magnetic induction B. This is a vector quantity, i.e. it (like tension) is given by a numerical value and direction in space. Magnetic induction is determined by the force acting on a moving charged particle. When depicting a picture of a magnetic field using magnetic lines, they are drawn thicker in that part of the field where there is more induction.

The unit of measurement for magnetic induction is tesla (T). Previously, another unit of measurement of magnetic induction was used - gauss (Gs).

These units are related by the ratio: 1Tl = 10000Gs.

The product of the magnetic induction B and the area S perpendicular to the magnetic induction vector ( magnetic lines), is called the magnetic flux F. Thus, the magnetic flux:

The unit of magnetic flux is weber(Wb). With the same magnetic field strength H, different magnetic inductions B are obtained in different materials. The ratio B / H is called the absolute magnetic permeability of the material μ a, i.e.

The absolute magnetic permeability of the material μ a is equal to the product of the magnetic constant (magnetic permeability of the vacuum) μ 0 and the relative magnetic permeability μ r:

raoorropor

M magnetic constant

H/m (henry per meter, henry is the unit of measure for inductance).

The value of μ r shows how many times μ a of the material is greater than the magnetic constant μ 0 .

In a material whose magnetic permeability is equal to μ r,

and in a vacuum (practically in air)

where V is expressed in teslas and H in A/m.

When measuring the magnetic induction in gauss, and the magnetic field strength in A / cm, for the magnetic induction in air we get:

For ferromagnetic materials, the relative magnetic permeability μ r is many times greater than 1, it changes with the change in induction B. The relationship between B and H for ferromagnetic materials is often plotted as magnetization curves.

In practical problems (magnetic circuits of electrical machines and devices) for calculating the traction force, EMF, attraction force, etc. it is required to determine the magnetic flux F or induction B. The value of these quantities is determined from the magnetization curves if the magnetic field strength H is known, which, in turn, is set by the magnetic voltage or MMF.

H magnetic field strength of the coil

H = 500 A/m. What will be the magnetic induction if a magnetic circuit made of transformer steel is inserted into the coil (in the figure), the relative magnetic permeability of which is μ r \u003d 2400.

B \u003d μ a * H \u003d μ o * μ r * H \u003d 4 * π * 10 -7 * 2400 * 500 \u003d 1.5 T

For transformer steel containing 4% Si, the magnetic induction B at a coil magnetic field strength of 500 A/m is 1.19 T (see the magnetization curves in the figure). Determine the absolute magnetic permeability of the transformer steel at the operating point μ a and the relative magnetic permeability μ r . Recall that the value of μ r shows how many times μ a of the material is greater than the magnetic permeability

μ o \u003d 4 * π * 10 -7.

Absolute magnetic permeability

μ a = V/N = 1.19/500

μ a \u003d μ r * μ o \u003d 4 * π * 10 -7 * μ r.

μ r \u003d μ a / μ o \u003d B / H \u003d 1.19 / (500 * 4 * π * 10 -7) \u003d 1893.9

According to the given experimental dependences B and H for various materials to determine the coefficients of second-order polynomials, in the best way (by the minimum sum of squared errors) providing their analytical description (mathematical model).

Sheet steel

Transformer steel (4% Si)

cast steel

To evaluate the polynomial coefficients

B \u003d a * H 2 + b * H + C

Let's write down the vector

H = '. size A = 10.1

Then we create matrix A:

A = [H^2 H ones(V(1),1)]

And we form a vector B:

B = '.

Let's estimate the coefficients

Using the file sah575.m. It estimates the coefficients of the square polynomial for sheet steel

a1 = [-0.0206 0.2952 0.3429],

for transformer steel

a2 = [-0.0246 0.3239 0.2000]

and for sheet steel

a3 = [-0.0277 0.2566 0.0150].

It is necessary to perform calculations for each type of material in the direct calculation mode.

/here is the file sah 375.m/

What will be the magnetic flux Ф in the magnetic circuit (see problem 1.), If the cross section of the magnetic circuit S = 4 cm²?

The magnetic flux, measured in webers (Wb), is

F \u003d B * S \u003d 1.5 * 4 * 10 -4 \u003d 0.0006 Wb

(Tl = Wb/m²)

Number of coil turns w=500 . In a magnetic core made of transformer steel with a length l=25 cm it is necessary to provide magnetic induction B=1.19 T What m.f.s. and current is needed for this?

According to the magnetization curve of transformer steel (see Fig.) we find that in order to create B = 1.19 T, it is required to create a magnetic field strength H = 500 A/m. With a length of the magnetic circuit (with a coil) l = 25 cm = 0.25 m, the required m.f.s. calculated by the formula