Practical application of Faraday's law of electromagnetic induction. Practical application of electromagnetic induction

Essay

in the discipline "Physics"

Topic: “Discovery of the phenomenon of electromagnetic induction”

Completed:

Student of group 13103/1

Saint Petersburg

2. Faraday's experiments. 3

3. Practical application of the phenomenon of electromagnetic induction. 9

4. List of used literature... 12

Electromagnetic induction is the phenomenon of the occurrence of electric current in a closed circuit when the magnetic flux passing through it changes. Electromagnetic induction was discovered by Michael Faraday on August 29, 1831. He discovered that the electromotive force arising in a closed conducting circuit is proportional to the rate of change of the magnetic flux through the surface bounded by this circuit. The magnitude of the electromotive force (EMF) does not depend on what is causing the flux change - a change in the magnetic field itself or the movement of the circuit (or part of it) in the magnetic field. The electric current caused by this emf is called induced current.

In 1820, Hans Christian Oersted showed that an electric current flowing through a circuit causes a magnetic needle to deflect. If electric current generates magnetism, then the appearance of electric current must be associated with magnetism. This idea captured the English scientist M. Faraday. “Convert magnetism into electricity,” he wrote in his diary in 1822.

Michael Faraday

Michael Faraday (1791-1867) was born in London, in one of its poorest parts. His father was a blacksmith, and his mother was the daughter of a tenant farmer. When Faraday reached school age, he was sent to primary school. The course Faraday took here was very narrow and was limited only to learning to read, write and begin to count.

A few steps from the house in which the Faraday family lived, there was a bookshop, which was also a bookbinding establishment. This is where Faraday ended up, having completed his primary school course, when the question arose about choosing a profession for him. Michael was only 13 years old at this time. Already in his youth, when Faraday was just beginning his self-education, he sought to rely exclusively on facts and verify the messages of others with his own experiences.

These aspirations dominated him all his life as the main features of his scientific activity. Faraday began to carry out physical and chemical experiments as a boy at his first acquaintance with physics and chemistry. One day Michael attended one of the lectures of Humphry Davy, the great English physicist. Faraday made a detailed note of the lecture, bound it and sent it to Davy. He was so impressed that he invited Faraday to work with him as a secretary. Soon Davy went on a trip to Europe and took Faraday with him. Over the course of two years, they visited the largest European universities.

Returning to London in 1815, Faraday began working as an assistant in one of the laboratories of the Royal Institution in London. At that time it was one of the best physics laboratories in the world. From 1816 to 1818 Faraday published a number of small notes and short memoirs on chemistry. Faraday's first work on physics dates back to 1818.

Based on the experiences of his predecessors and combining several of his own experiences, by September 1821 Michael published “The History of the Advances of Electromagnetism.” Already at this time, he formed a completely correct concept of the essence of the phenomenon of deflection of a magnetic needle under the influence of current.

Having achieved this success, Faraday left his studies in the field of electricity for ten years, devoting himself to the study of a number of subjects of a different kind. In 1823, Faraday made one of the most important discoveries in the field of physics - he was the first to liquefy gas, and at the same time established a simple but effective method for converting gases into liquid. In 1824, Faraday made several discoveries in the field of physics. Among other things, he established the fact that light affects the color of glass, changing it. The following year, Faraday again turned from physics to chemistry, and the result of his work in this area was the discovery of gasoline and sulfur-naphthalene acid.

In 1831, Faraday published a treatise “On a Special Kind of Optical Illusion,” which served as the basis for an excellent and curious optical projectile called the “chromotrope.” In the same year, another treatise by the scientist, “On Vibrating Plates,” was published. Many of these works could in themselves immortalize the name of their author. But the most important of Faraday's scientific works are his studies in the field of electromagnetism and electrical induction.

Faraday's experiments

Obsessed with ideas about the inextricable connection and interaction of the forces of nature, Faraday tried to prove that just as Ampere could create magnets with the help of electricity, so it was possible to create electricity with the help of magnets.

His logic was simple: mechanical work easily turns into heat; on the contrary, heat can be converted into mechanical work (say, in a steam engine). In general, among the forces of nature, the following relationship most often occurs: if A gives birth to B, then B gives birth to A.

If Ampere obtained magnets with the help of electricity, then, apparently, it is possible to “obtain electricity from ordinary magnetism.” Arago and Ampère set themselves the same task in Paris, and Colladon in Geneva.

Strictly speaking, an important branch of physics that treats the phenomena of electromagnetism and inductive electricity, and which is currently of such enormous importance for technology, was created by Faraday out of nothing. By the time Faraday finally devoted himself to research in the field of electricity, it was established that under ordinary conditions the presence of an electrified body is sufficient for its influence to excite electricity in any other body. At the same time, it was known that a wire through which current passes and which also represents an electrified body does not have any effect on other wires placed nearby.

What caused this exception? This is the question that interested Faraday and the solution of which led him to the most important discoveries in the field of induction electricity. Faraday carried out many experiments and kept pedantic notes. He devotes a paragraph to each small study in his laboratory notes (published in London in full in 1931 under the title “Faraday’s Diary”). Faraday’s ability to work is evidenced by the fact that the last paragraph of the “Diary” is marked with the number 16041. Faraday’s brilliant skill as an experimenter, obsession, and clear philosophical position could not but be rewarded, but it took eleven long years to wait for the result.

Apart from his intuitive conviction in the universal connection of phenomena, nothing actually supported him in his search for “electricity from magnetism.” Moreover, like his teacher Davy, he relied more on his experiences than on mental constructs. Davy taught him:

– A good experiment is more valuable than the profundity of a genius like Newton.

And yet, it was Faraday who was destined for great discoveries. A great realist, he spontaneously broke the empiricist shackles that Davy had once imposed on him, and at those moments a great insight dawned on him - he acquired the ability to make the deepest generalizations.

The first glimmer of luck appeared only on August 29, 1831. On this day, Faraday was testing a simple device in the laboratory: an iron ring with a diameter of about six inches, wrapped in two pieces of insulated wire. When Faraday connected a battery to the terminals of one winding, his assistant, artillery sergeant Andersen, saw the needle of the galvanometer connected to the other winding twitch.

It twitched and calmed down, although the direct current continued to flow through the first winding. Faraday carefully examined all the details of this simple installation - everything was in order.

But the galvanometer needle stubbornly stood at zero. Out of frustration, Faraday decided to turn off the current, and then a miracle happened - while opening the circuit, the galvanometer needle swung again and froze at zero again!

The galvanometer, remaining completely calm during the entire passage of current, begins to oscillate when the circuit itself is closed and when it is opened. It turned out that at the moment when a current is passed into the first wire, and also when this transmission stops, a current is also excited in the second wire, which in the first case has the opposite direction to the first current and the same with it in the second case and lasts only one instant.

It was here that Ampere’s great ideas - the connection between electric current and magnetism - were revealed to Faraday in all their clarity. After all, the first winding into which he supplied current immediately became a magnet. If we consider it like a magnet, then the experiment on August 29 showed that magnetism seems to give birth to electricity. Only two things remained strange in this case: why did the surge of electricity when the electromagnet was turned on quickly fade away? And moreover, why does the splash appear when the magnet is turned off?

The next day, August 30, a new series of experiments. The effect is clearly expressed, but nevertheless completely incomprehensible.

Faraday senses that a discovery is somewhere nearby.

“Now I am again studying electromagnetism and I think that I have hit upon a successful thing, but I cannot yet confirm this. It may very well be that after all my labors I will end up with seaweed instead of fish.”

By the next morning, September 24, Faraday had prepared many different devices, in which the main elements were no longer windings with electric current, but permanent magnets. And the effect also existed! The arrow deviated and immediately rushed to the spot. This slight movement occurred during the most unexpected manipulations with the magnet, sometimes seemingly by accident.

The next experiment is October 1st. Faraday decides to go back to the very beginning - to two windings: one with current, the other connected to the galvanometer. The difference with the first experiment is the absence of a steel ring - core. The splash is almost unnoticeable. The result is trivial. It is clear that a magnet without a core is much weaker than a magnet with a core. Therefore, the effect is less pronounced.

Faraday is disappointed. For two weeks he does not go near the devices, thinking about the reasons for the failure.

“I took a cylindrical magnetic bar (3/4 inch in diameter and 8 1/4 inches long) and inserted one end into a coil of copper wire (220 feet long) connected to a galvanometer. Then I quickly pushed the magnet inside the spiral to its entire length, and the galvanometer needle experienced a push. Then I just as quickly pulled the magnet out of the spiral, and the arrow swung again, but in the opposite direction. These swings of the needle were repeated every time the magnet was pushed or pushed out.”

The secret is in the movement of the magnet! The impulse of electricity is determined not by the position of the magnet, but by the movement!

This means that “an electric wave arises only when a magnet moves, and not due to the properties inherent in it at rest.”

Rice. 2. Faraday's experiment with a coil

This idea is incredibly fruitful. If the movement of a magnet relative to a conductor creates electricity, then apparently the movement of a conductor relative to a magnet should generate electricity! Moreover, this “electric wave” will not disappear as long as the mutual movement of the conductor and magnet continues. This means that it is possible to create an electric current generator that can operate for as long as desired, as long as the mutual movement of the wire and magnet continues!

On October 28, Faraday installed a rotating copper disk between the poles of a horseshoe magnet, from which electrical voltage could be removed using sliding contacts (one on the axis, the other on the periphery of the disk). It was the first electric generator created by human hands. Thus, a new source of electrical energy was found, in addition to the previously known ones (friction and chemical processes), - induction, and a new type of this energy - inductive electricity.

Experiments similar to Faraday's, as already mentioned, were carried out in France and Switzerland. Professor Colladon of the Academy of Geneva was a sophisticated experimenter (he, for example, made precise measurements of the speed of sound in water on Lake Geneva). Perhaps, fearing the shaking of the instruments, he, like Faraday, removed the galvanometer from the rest of the installation if possible. Many argued that Colladon observed the same fleeting movements of the needle as Faraday, but, expecting a more stable, long-lasting effect, did not attach due importance to these “random” bursts...

Indeed, the opinion of most scientists of that time was that the reverse effect of “creating electricity from magnetism” should apparently have the same stationary character as the “direct” effect - “formation of magnetism” due to electric current. The unexpected "fleetingness" of this effect confused many, including Colladon, and these many paid for their prejudice.

Continuing his experiments, Faraday further discovered that simply bringing a wire twisted into a closed curve close to another through which a galvanic current flows is sufficient to excite an inductive current in the neutral wire in the direction opposite to the galvanic current, and that removing the neutral wire again excites an inductive current in it. the current is already in the same direction as the galvanic current flowing along a stationary wire, and that, finally, these inductive currents are excited only during the approach and removal of the wire to the conductor of the galvanic current, and without this movement the currents are not excited, no matter how close the wires are to each other .

Thus, a new phenomenon was discovered, similar to the above-described phenomenon of induction when the galvanic current closes and stops. These discoveries in turn gave rise to new ones. If it is possible to cause an inductive current by short-circuiting and stopping the galvanic current, then wouldn’t the same result be obtained by magnetizing and demagnetizing iron?

The work of Oersted and Ampere had already established the relationship between magnetism and electricity. It was known that iron becomes a magnet when an insulated wire is wound around it and a galvanic current passes through it, and that the magnetic properties of this iron cease as soon as the current stops.

Based on this, Faraday came up with this kind of experiment: two insulated wires were wound around an iron ring; with one wire wrapped around one half of the ring, and the other around the other. Current from a galvanic battery was passed through one wire, and the ends of the other were connected to a galvanometer. And so, when the current closed or stopped and when, consequently, the iron ring was magnetized or demagnetized, the galvanometer needle quickly oscillated and then quickly stopped, that is, the same instantaneous inductive currents were excited in the neutral wire - this time: already under the influence of magnetism.

Rice. 3. Faraday's experiment with an iron ring

Thus, here for the first time magnetism was converted into electricity. Having received these results, Faraday decided to diversify his experiments. Instead of an iron ring, he began to use an iron strip. Instead of exciting magnetism in iron by galvanic current, he magnetized the iron by touching it to a permanent steel magnet. The result was the same: in the wire that wrapped around the iron, a current was always excited at the moment of magnetization and demagnetization of the iron. Then Faraday introduced a steel magnet into the wire spiral - the approach and removal of the latter caused induced currents in the wire. In a word, magnetism, in the sense of exciting induction currents, acted in exactly the same way as galvanic current.

At that time, physicists were intensely interested in one mysterious phenomenon, discovered in 1824 by Arago and which could not be explained, despite the fact that such outstanding scientists of the time as Arago himself, Ampère, Poisson, Babage and Herschel were strenuously looking for this explanation. The point was as follows. A magnetic needle, hanging freely, quickly comes to rest if a circle of non-magnetic metal is placed under it; If the circle is then put into rotation, the magnetic needle begins to move behind it.

In a calm state, it was impossible to discover the slightest attraction or repulsion between the circle and the arrow, while the same circle, in motion, pulled behind it not only a light arrow, but also a heavy magnet. This truly miraculous phenomenon seemed to the scientists of that time a mysterious mystery, something beyond the limits of the natural. Faraday, based on the above data, made the assumption that a circle of non-magnetic metal, under the influence of a magnet, during rotation is run around by inductive currents, which affect the magnetic needle and drag it along the magnet. And indeed, by introducing the edge of a circle between the poles of a large horseshoe magnet and connecting the center and edge of the circle with a galvanometer with a wire, Faraday obtained a constant electric current when the circle rotated.

Following this, Faraday focused on another phenomenon that was then arousing general curiosity. As you know, if you sprinkle iron filings on a magnet, they group along certain lines called magnetic curves. Faraday, drawing attention to this phenomenon, gave the basis in 1831 to magnetic curves the name “lines of magnetic force,” which then came into general use. The study of these “lines” led Faraday to a new discovery; it turned out that in order to excite induced currents, the source’s approach and distance from the magnetic pole are not necessary. To excite currents, it is enough to cross the lines of magnetic force in a known manner.

Rice. 4. “Magnetic Force Lines”

Faraday's further work in the mentioned direction acquired, from a contemporary point of view, the character of something absolutely miraculous. At the beginning of 1832, he demonstrated a device in which inductive currents were excited without the help of a magnet or galvanic current. The device consisted of an iron strip placed in a wire coil. This device, under ordinary conditions, did not give the slightest sign of the appearance of currents in it; but as soon as it was given a direction corresponding to the direction of the magnetic needle, a current was excited in the wire.

Then Faraday gave the position of the magnetic needle to one coil and then introduced an iron strip into it: the current was again excited. The reason that caused the current in these cases was earthly magnetism, which caused inductive currents like an ordinary magnet or galvanic current. To more clearly show and prove this, Faraday undertook another experiment, which fully confirmed his considerations.

He reasoned that if a circle of non-magnetic metal, such as copper, rotating in a position in which it intersects the lines of magnetic force of an adjacent magnet produces an inductive current, then the same circle, rotating in the absence of a magnet, but in a position in which the circle will cross the lines of earthly magnetism, must also give an inductive current. And indeed, a copper circle rotated in a horizontal plane produced an inductive current that produced a noticeable deflection of the galvanometer needle. Faraday ended his series of studies in the field of electrical induction with the discovery, made in 1835, of the “inductive influence of current on itself.”

He found out that when a galvanic current is closed or opened, instantaneous inductive currents are excited in the wire itself, which serves as a conductor for this current.

Russian physicist Emil Khristoforovich Lenz (1804-1861) gave a rule for determining the direction of induction current. “Induction current is always directed in such a way that the magnetic field it creates complicates or inhibits the movement causing induction,” notes A.A. Korobko-Stefanov in his article on electromagnetic induction. - For example, when a coil approaches a magnet, the resulting induced current has such a direction that the magnetic field it creates will be opposite to the magnetic field of the magnet. As a result, repulsive forces arise between the coil and the magnet. Lenz's rule follows from the law of conservation and transformation of energy. If induced currents accelerated the motion that caused them, then work would be created out of nothing. The coil itself, after a slight push, would rush towards the magnet, and at the same time the induction current would release heat in it. In reality, the induced current is created due to the work of bringing the magnet and the coil closer together.

Rice. 5. Lenz's rule

Why does induced current occur? A profound explanation of the phenomenon of electromagnetic induction was given by the English physicist James Clerk Maxwell, the creator of a complete mathematical theory of the electromagnetic field. To better understand the essence of the matter, consider a very simple experiment. Let the coil consist of one turn of wire and be penetrated by an alternating magnetic field perpendicular to the plane of the turn. An induced current naturally arises in the coil. Maxwell interpreted this experiment exceptionally boldly and unexpectedly.

When a magnetic field changes in space, according to Maxwell, a process arises for which the presence of a wire coil has no significance. The main thing here is the emergence of closed annular electric field lines, covering a changing magnetic field. Under the influence of the resulting electric field, electrons begin to move, and an electric current arises in the coil. A coil is simply a device that detects an electric field. The essence of the phenomenon of electromagnetic induction is that an alternating magnetic field always generates an electric field with closed lines of force in the surrounding space. Such a field is called a vortex field.”

Research in the field of induction produced by terrestrial magnetism gave Faraday the opportunity to express the idea of ​​​​a telegraph back in 1832, which then formed the basis of this invention. In general, the discovery of electromagnetic induction is not without reason considered one of the most outstanding discoveries of the 19th century - the work of millions of electric motors and electric current generators all over the world is based on this phenomenon...

Practical application of the phenomenon of electromagnetic induction

1. Radio broadcasting

An alternating magnetic field excited by a changing current creates an electric field in the surrounding space, which in turn excites a magnetic field, etc. Mutually generating each other, these fields form a single alternating electromagnetic field - an electromagnetic wave. Having arisen in the place where there is a current-carrying wire, the electromagnetic field propagates through space at the speed of light -300,000 km/s.

Rice. 6. Radio

2. Magnetic therapy

Radio waves, light, X-rays and other electromagnetic radiation occupy different places in the frequency spectrum. They are usually characterized by continuously coupled electric and magnetic fields.

3. Synchrophasotrons

Currently, a magnetic field is understood as a special form of matter consisting of charged particles. In modern physics, beams of charged particles are used to penetrate deep into atoms in order to study them. The force with which a magnetic field acts on a moving charged particle is called the Lorentz force.

4. Flow meters

The method is based on the application of Faraday's law for a conductor in a magnetic field: in a flow of electrically conductive liquid moving in a magnetic field, an EMF is induced, proportional to the flow speed, converted by the electronic part into an electrical analogue/digital signal.

5. DC generator

In generator mode, the machine's armature rotates under the influence of an external torque. Between the stator poles there is a constant magnetic flux that penetrates the armature. The conductors of the armature winding move in a magnetic field and, therefore, an EMF is induced in them, the direction of which can be determined by the “right hand” rule. In this case, a positive potential arises on one brush relative to the second. If you connect a load to the generator terminals, current will flow through it.

6. Transformers

Transformers are widely used in transmitting electrical energy over long distances, distributing it between receivers, as well as in various rectifying, amplifying, signaling and other devices.

Energy conversion in a transformer is carried out by an alternating magnetic field. A transformer is a core made of thin steel plates insulated from one another, on which two and sometimes more windings (coils) of insulated wire are placed. The winding to which the source of alternating current electrical energy is connected is called the primary winding, the remaining windings are called secondary.

If the secondary winding of a transformer has three times more turns wound than the primary winding, then the magnetic field created in the core by the primary winding, crossing the turns of the secondary winding, will create three times the voltage in it.

By using a transformer with a reverse turns ratio, you can just as easily obtain a reduced voltage.

List of used literature

1. [Electronic resource]. Electromagnetic induction.

< https://ru.wikipedia.org/>

2. [Electronic resource]. Faraday. Discovery of electromagnetic induction.

< http://www.e-reading.club/chapter.php/26178/78/Karcev_-_Maksvell.html >

3. [Electronic resource]. Discovery of electromagnetic induction.

4. [Electronic resource]. Practical application of the phenomenon of electromagnetic induction.

Khudoley Andrey, Khnykov Igor

Practical application of the phenomenon of electromagnetic induction.

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Electromagnetic induction in modern technology Performed by students of class 11 "A" MOUSOSH No. 2 of the city of Suvorov Khnykov Igor, Khudoley Andrey

The phenomenon of electromagnetic induction was discovered on August 29, 1831 by Michael Faraday. The phenomenon of electromagnetic induction consists in the occurrence of an electric current in a conducting circuit, which is either at rest in a time-varying magnetic field or moves in a constant magnetic field in such a way that the number of magnetic induction lines penetrating the circuit changes.

The EMF of electromagnetic induction in a closed loop is numerically equal and opposite in sign to the rate of change of the magnetic flux through the surface bounded by this loop. The direction of the induced current (as well as the magnitude of the EMF) is considered positive if it coincides with the selected direction of bypassing the circuit.

Faraday's experiment: a permanent magnet is inserted into or removed from a coil connected to a galvanometer. When a magnet moves, an electric current arises in the circuit. Within one month, Faraday experimentally discovered all the essential features of the phenomenon of electromagnetic induction. Nowadays, anyone can conduct Faraday's experiments.

The main sources of the electromagnetic field The main sources of the electromagnetic field can be identified: Power lines. Electrical wiring (inside buildings and structures). Household electrical appliances. Personal computers. TV and radio broadcasting stations. Satellite and cellular communications (devices, repeaters). Electric transport. Radar installations.

Power lines Wires of a working power line create an electromagnetic field of industrial frequency (50 Hz) in the adjacent space (at distances of the order of tens of meters from the wire). Moreover, the field strength near the line can vary within wide limits, depending on its electrical load. In fact, the boundaries of the sanitary protection zone are established along the boundary line of maximum electric field strength, which is 1 kV/m, farthest from the wires.

Electrical wiring Electrical wiring includes: power supply cables for building life support systems, current distribution wires, as well as branch boards, power boxes and transformers. Electrical wiring is the main source of industrial frequency electromagnetic fields in residential premises. In this case, the level of electric field strength emitted by the source is often relatively low (does not exceed 500 V/m).

Household electrical appliances Sources of electromagnetic fields are all household appliances that operate using electric current. In this case, the radiation level varies within wide limits depending on the model, device design and specific operating mode. Also, the level of radiation strongly depends on the power consumption of the device - the higher the power, the higher the level of the electromagnetic field during operation of the device. The electric field strength near electrical household appliances does not exceed tens of V/m.

Personal computers The main source of adverse effects on the health of a computer user is the visual display device (VDI) of the monitor. In addition to the monitor and system unit, a personal computer may also include a large number of other devices (such as printers, scanners, surge protectors, etc.). All these devices operate using electric current, which means they are sources of an electromagnetic field.

The electromagnetic field of personal computers has a very complex wave and spectral composition and is difficult to measure and quantify. It has magnetic, electrostatic and radiation components (in particular, the electrostatic potential of a person sitting in front of a monitor can range from –3 to +5 V). Considering the fact that personal computers are now actively used in all sectors of human activity, their impact on human health is subject to careful study and control

Television and radio broadcasting stations A significant number of radio broadcasting stations and centers of various affiliations are currently located on the territory of Russia. Transmitting stations and centers are located in specially designated areas and can occupy fairly large areas (up to 1000 hectares). In their structure, they include one or more technical buildings where radio transmitters are located, and antenna fields on which up to several dozen antenna-feeder systems (AFS) are located. Each system includes a transmitting antenna and a feed line supplying the broadcast signal.

Satellite communications Satellite communications systems consist of a transmitting station on Earth and relay satellites in orbit. Satellite communication transmitting stations emit a narrowly directed wave beam, the energy flux density of which reaches hundreds of W/m. Satellite communication systems create high electromagnetic field strengths at significant distances from the antennas. For example, a 225 kW station operating at a frequency of 2.38 GHz creates an energy flux density of 2.8 W/m2 at a distance of 100 km. Energy dissipation relative to the main beam is very small and occurs most of all in the area where the antenna is directly located.

Cellular communications Cellular radiotelephony is one of the most rapidly developing telecommunication systems today. The main elements of a cellular communication system are base stations and mobile radiotelephones. Base stations maintain radio communication with mobile devices, as a result of which they are sources of electromagnetic fields. The system uses the principle of dividing the coverage area into zones, or so-called “cells,” with a radius of km.

The radiation intensity of a base station is determined by the load, that is, the presence of cell phone owners in the service area of ​​a particular base station and their desire to use the phone for a conversation, which, in turn, fundamentally depends on the time of day, location of the station, day of the week and other factors. At night, the station load is almost zero. The intensity of radiation from mobile devices depends to a large extent on the state of the communication channel “mobile radiotelephone - base station” (the greater the distance from the base station, the higher the radiation intensity of the device).

Electric transport Electric transport (trolleybuses, trams, subway trains, etc.) is a powerful source of electromagnetic field in the Hz frequency range. In this case, in the vast majority of cases, the role of the main emitter is played by the traction electric motor (for trolleybuses and trams, aerial pantographs compete with the electric motor in terms of the intensity of the emitted electric field).

Radar installations Radar and radar installations usually have reflector-type antennas (“dishes”) and emit a narrowly directed radio beam. Periodic movement of the antenna in space leads to spatial intermittency of the radiation. Temporary intermittency of radiation is also observed, due to the cyclic operation of the radar on radiation. They operate at frequencies from 500 MHz to 15 GHz, but some special installations can operate at frequencies up to 100 GHz or more. Due to the special nature of the radiation, they can create areas with a high energy flux density (100 W/m2 or more).

Metal Detectors Technologically, the operating principle of a metal detector is based on the phenomenon of recording an electromagnetic field that is created around any metal object when placed in an electromagnetic field. This secondary electromagnetic field varies both in intensity (field strength) and in other parameters. These parameters depend on the size of the object and its conductivity (gold and silver have much better conductivity than, for example, lead) and, naturally, on the distance between the metal detector antenna and the object itself (depth).

The above technology determined the composition of the metal detector: it consists of four main blocks: an antenna (sometimes the emitting and receiving antennas are different, and sometimes it is the same antenna), an electronic processing unit, an information output unit (visual - LCD display or dial indicator and audio - speakers or headphone jacks) and power supply.

Metal detectors are: Search Inspection For construction purposes

Search This metal detector is designed to search for all kinds of metal objects. As a rule, these are the largest models in size, cost and, naturally, in terms of functions performed. This is due to the fact that sometimes it is necessary to find objects at a depth of up to several meters in the thickness of the earth. A powerful antenna is capable of creating a high level of electromagnetic field and detecting even the slightest currents at great depths with high sensitivity. For example, a search metal detector detects a metal coin at a depth of 2-3 meters in the thickness of the earth, which may even contain ferruginous geological compounds.

Searchers Used by intelligence services, customs officers and security officers of various organizations to search for metal objects (weapons, precious metals, explosive wires, etc.) hidden on a person’s body and clothing. These metal detectors are distinguished by their compactness, ease of use, and the presence of such modes as silent vibration of the handle (so that the person being searched does not know that the employee conducting the search has found something). The detection range (depth) of ruble coins in such metal detectors reaches 10-15 cm.

Also widely used are arched metal detectors, which resemble an arch in appearance and require a person to pass through it. Ultra-sensitive antennas are laid along their vertical walls, which detect metal objects at all levels of human growth. They are usually installed in front of places of cultural entertainment, in banks, institutions, etc. The main feature of arched metal detectors is their high sensitivity (adjustable) and high speed of processing the flow of people.

For construction purposes This class of metal detectors, using sound and light alarms, helps builders find metal pipes, structural elements or drives located both in the thickness of walls and behind partitions and false panels. Some metal detectors for construction purposes are often combined in one device with wooden structure detectors, voltage detectors on live wires, leakage detectors, etc.

After the discoveries of Oersted and Ampere, it became clear that electricity has magnetic force. Now it was necessary to confirm the influence of magnetic phenomena on electrical ones. Faraday brilliantly solved this problem.

In 1821, M. Faraday wrote in his diary: “Convert magnetism into electricity.” After 10 years, he solved this problem.

So, Michael Faraday (1791-1867) - English physicist and chemist.

One of the founders of quantitative electrochemistry. For the first time (1823) he obtained chlorine in a liquid state, then hydrogen sulfide, carbon dioxide, ammonia and nitrogen dioxide. He discovered benzene (1825) and studied its physical and some chemical properties. Introduced the concept of dielectric constant. Faraday's name entered the system of electrical units as a unit of electrical capacity.

Many of these works could themselves immortalize the name of their author. But the most important of Faraday's scientific works are his studies in the field of electromagnetism and electrical induction. Strictly speaking, an important branch of physics that treats the phenomena of electromagnetism and inductive electricity, and which is currently of such enormous importance for technology, was created by Faraday out of nothing.

When Faraday finally devoted himself to research in the field of electricity, it was found that under ordinary conditions the presence of an electrified body is sufficient for its influence to excite electricity in any other body.

At the same time, it was known that a wire through which current passes and which also represents an electrified body does not have any effect on other wires placed nearby. What caused this exception? This is the question that interested Faraday and the solution of which led him to the most important discoveries in the field of induction electricity.

Faraday wound two insulated wires parallel to each other on the same wooden rolling pin. He connected the ends of one wire to a battery of ten cells, and the ends of the other to a sensitive galvanometer. When a current was passed through the first wire, Faraday turned all his attention to the galvanometer, expecting to notice by its vibrations the appearance of a current in the second wire. However, nothing of the kind happened: the galvanometer remained calm. Faraday decided to increase the current strength and introduced 120 galvanic elements into the circuit. The result was the same. Faraday repeated this experiment dozens of times and still with the same success. Anyone else in his place would have left the experiments convinced that the current passing through a wire has no effect on the neighboring wire. But Faraday always tried to extract from his experiments and observations everything that they could give, and therefore, not receiving a direct effect on the wire connected to the galvanometer, he began to look for side effects.

electromagnetic induction electric current field

He immediately noticed that the galvanometer, remaining completely calm during the entire passage of current, began to oscillate when the circuit itself was closed, and when it was opened, it turned out that at the moment when current was passed into the first wire, and also when this transmission stopped, the second wire is also excited by a current, which in the first case has the opposite direction to the first current and the same with it in the second case and lasts only one instant. These secondary instantaneous currents, caused by the influence of the primary ones, were called inductive by Faraday, and this name has remained with them to this day.

Being instantaneous, instantly disappearing after their appearance, inductive currents would have no practical significance if Faraday had not found a way, with the help of an ingenious device (a commutator), to constantly interrupt and again conduct the primary current coming from the battery along the first wire, thanks to which the second wire is continuously excited by more and more inductive currents, thus becoming constant. Thus, a new source of electrical energy was found, in addition to the previously known ones (friction and chemical processes), - induction, and a new type of this energy - inductive electricity.

ELECTROMAGNETIC INDUCTION(Latin inductio - guidance) - the phenomenon of generating a vortex electric field by an alternating magnetic field. If you introduce a closed conductor into an alternating magnetic field, an electric current will appear in it. The appearance of this current is called current induction, and the current itself is called induction.

We already know that an electric current moving through a conductor creates a magnetic field around it. Based on this phenomenon, man invented and widely uses a wide variety of electromagnets. But the question arises: if electric charges, when moving, cause the appearance of a magnetic field, doesn’t this also work vice versa?

That is, can a magnetic field cause the occurrence of an electric current in a conductor? In 1831, Michael Faraday established that an electric current arises in a closed conducting electrical circuit when a magnetic field changes. Such a current is called an induction current, and the phenomenon of the occurrence of a current in a closed conducting circuit when the magnetic field penetrating this circuit changes is called electromagnetic induction.

The phenomenon of electromagnetic induction

The name “electromagnetic” itself consists of two parts: “electro” and “magnetic”. Electrical and magnetic phenomena are inextricably linked with each other. And if electric charges, moving, change the magnetic field around them, then the magnetic field, changing, will inevitably force the electric charges to move, forming an electric current.

In this case, it is the changing magnetic field that causes the generation of electric current. A constant magnetic field will not cause the movement of electric charges, and accordingly, no induced current will be generated. A more detailed examination of the phenomenon of electromagnetic induction, the derivation of formulas and the law of electromagnetic induction refers to the ninth grade course.

Application of electromagnetic induction

In this article we will talk about the use of electromagnetic induction. The operation of many motors and current generators is based on the use of the laws of electromagnetic induction. The principle of their operation is quite simple to understand.

A change in the magnetic field can be caused, for example, by moving a magnet. Therefore, if you move a magnet inside a closed circuit by any external influence, then a current will arise in this circuit. This way you can create a current generator.

If, on the contrary, you pass current from a third-party source through the circuit, then the magnet located inside the circuit will begin to move under the influence of the magnetic field formed by the electric current. This way you can assemble an electric motor.

The current generators described above convert mechanical energy into electrical energy in power plants. Mechanical energy is the energy of coal, diesel fuel, wind, water and so on. Electricity travels through wires to consumers and is converted back into mechanical energy in electric motors.

Electric motors of vacuum cleaners, hair dryers, mixers, coolers, electric meat grinders and other numerous devices that we use every day are based on the use of electromagnetic induction and magnetic forces. There is no need to talk about the use of these same phenomena in industry; it is clear that it is everywhere.

Broadcasting. An alternating magnetic field excited by a changing current creates an electric field in the surrounding space, which in turn excites a magnetic field, etc. Mutually generating each other, these fields form a single alternating electromagnetic field - an electromagnetic wave. Having arisen in the place where there is a current-carrying wire, the electromagnetic field propagates through space at the speed of light -300,000 km/s.

Magnetotherapy.Radio waves, light, X-rays and other electromagnetic radiation occupy different places in the frequency spectrum. They are usually characterized by continuously coupled electric and magnetic fields.

Synchrophasotrons Currently, a magnetic field is understood as a special form of matter consisting of charged particles. In modern physics, beams of charged particles are used to penetrate deep into atoms in order to study them. The force with which a magnetic field acts on a moving charged particle is called the Lorentz force.

Flow meters - counters. The method is based on the application of Faraday's law for a conductor in a magnetic field: in a flow of electrically conductive liquid moving in a magnetic field, an EMF is induced, proportional to the flow speed, converted by the electronic part into an electrical analogue/digital signal.

DC generator.In generator mode, the machine's armature rotates under the influence of an external torque. Between the stator poles there is a constant magnetic flux that penetrates the armature. The conductors of the armature winding move in a magnetic field and, therefore, an EMF is induced in them, the direction of which can be determined by the “right hand” rule. In this case, a positive potential arises on one brush relative to the second. If you connect a load to the generator terminals, current will flow through it.

The EMR phenomenon is widely used in transformers. Let's take a closer look at this device.

TRANSFORMERS.) - a static electromagnetic device having two or more inductively coupled windings and designed to convert, by electromagnetic induction, one or more alternating current systems into one or more other alternating current systems.

The occurrence of induction current in a rotating circuit and its application.

The phenomenon of electromagnetic induction is used to convert mechanical energy into electrical energy. For this purpose they are used generators, operating principle

which can be considered using the example of a flat frame rotating in a uniform magnetic field

Let the frame rotate in a uniform magnetic field (B = const) uniformly with angular velocity u = const.

Magnetic flux coupled to a frame with an area S, at any time t equals

where a - ut- angle of rotation of the frame at the moment of time t(the origin is chosen so that at /. = 0 there is a = 0).

When the frame rotates, a variable induced emf will appear in it

changing over time according to a harmonic law. EMF %" maximum at sin Wt= 1, i.e.

Thus, if in a homogeneous

When the frame rotates uniformly in a magnetic field, an alternating emf appears in it, changing according to a harmonic law.

The process of converting mechanical energy into electrical energy is reversible. If a current is passed through a frame placed in a magnetic field, a torque will act on it and the frame will begin to rotate. This principle is the basis for the operation of electric motors designed to convert electrical energy into mechanical energy.

Ticket 5.

Magnetic field in matter.

Experimental studies have shown that all substances have magnetic properties to a greater or lesser extent. If two turns with currents are placed in any medium, then the strength of the magnetic interaction between the currents changes. This experiment shows that the induction of a magnetic field created by electric currents in a substance differs from the induction of a magnetic field created by the same currents in a vacuum.

A physical quantity showing how many times the magnetic field induction in a homogeneous medium differs in magnitude from the magnetic field induction in a vacuum is called magnetic permeability:

The magnetic properties of substances are determined by the magnetic properties of atoms or elementary particles (electrons, protons and neutrons) that make up the atoms. It has now been established that the magnetic properties of protons and neutrons are almost 1000 times weaker than the magnetic properties of electrons. Therefore, the magnetic properties of substances are mainly determined by the electrons that make up the atoms.

Substances are extremely diverse in their magnetic properties. For most substances, these properties are weakly expressed. Weakly magnetic substances are divided into two large groups - paramagnetic and diamagnetic. They differ in that when introduced into an external magnetic field, paramagnetic samples are magnetized so that their own magnetic field is directed along the external field, and diamagnetic samples are magnetized against the external field. Therefore, for paramagnetic materials μ > 1, and for diamagnetic materials μ< 1. Отличие μ от единицы у пара- и диамагнетиков чрезвычайно мало. Например, у алюминия, который относится к парамагнетикам, μ – 1 ≈ 2,1·10–5, у хлористого железа (FeCl3) μ – 1 ≈ 2,5·10–3. К парамагнетикам относятся также платина, воздух и многие другие вещества. К диамагнетикам относятся медь (μ – 1 ≈ –3·10–6), вода (μ – 1 ≈ –9·10–6), висмут (μ – 1 ≈ –1,7·10–3) и другие вещества. Образцы из пара- и диамагнетика, помещенные в неоднородное магнитное поле между полюсами электромагнита, ведут себя по-разному – парамагнетики втягиваются в область сильного поля, диамагнетики – выталкиваются (рис. 1.19.1).

Problems of magnetostatics in matter.

Magnetic characteristics of matter – magnetization vector, magnetic

susceptibility and magnetic permeability of a substance.

Magnetization vector - magnetic moment of an elementary volume, used to describe the magnetic state of a substance. In relation to the direction of the magnetic field vector, longitudinal magnetization and transverse magnetization are distinguished. Transverse magnetization reaches significant values ​​in anisotropic magnets, and is close to zero in isotropic magnets. Therefore, in the latter it is possible to express the magnetization vector through the magnetic field strength and the coefficient x called magnetic susceptibility:

Magnetic susceptibility- a physical quantity characterizing the relationship between the magnetic moment (magnetization) of a substance and the magnetic field in this substance.

Magnetic permeability - a physical quantity characterizing the relationship between magnetic induction and magnetic field strength in a substance.

Usually denoted by a Greek letter. It can be either a scalar (for isotropic substances) or a tensor (for anisotropic substances).

In general, it is introduced as a tensor as follows:

Ticket 6.

Classification of magnetic materials

Magnets are substances that are capable of acquiring their own magnetic field in an external magnetic field, i.e., being magnetized. The magnetic properties of a substance are determined by the magnetic properties of electrons and atoms (molecules) of the substance. Based on their magnetic properties, magnets are divided into three main groups: diamagnetic, paramagnetic and ferromagnetic.

1. Magnets with linear dependence:

1) Paramagnetic materials are substances that are weakly magnetized in a magnetic field, and the resulting field in paramagnetic materials is stronger than in a vacuum, the magnetic permeability of paramagnetic materials is m > 1; Aluminum, platinum, oxygen, etc. have such properties;

paramagnets ,

2) Diamagnets - substances that are weakly magnetized against the field, that is, the field in diamagnets is weaker than in a vacuum, magnetic permeability m< 1. К диамагнетикам относятся медь, серебро, висмут и др.;

diamagnetic materials ;

With nonlinear dependence:

3) ferromagnets - substances that can be strongly magnetized in a magnetic field. These are iron, cobalt, nickel and some alloys. 2.

Ferromagnets.

Depends on background and is a function of tension; exists hysteresis.

And it can reach high values ​​compared to para- and diamagnetic materials.

The law of total current for the magnetic field in matter (the theorem on the circulation of vector B)

Where I and I" are respectively the algebraic sums of macrocurrents (conduction currents) and microcurrents (molecular currents) covered by an arbitrary closed loop L. Thus, the circulation of the magnetic induction vector B along an arbitrary closed loop is equal to the algebraic sum of conduction currents and molecular currents covered by this contour multiplied by the magnetic constant. Vector B thus characterizes the resulting field created by both macroscopic currents in conductors (conduction currents) and microscopic currents in magnets, therefore the lines of the magnetic induction vector B have no sources and are closed.

Magnetic field strength vector and its circulation.

Magnetic field strength - (standard designation H) is a vector physical quantity equal to the difference between the magnetic induction vector B and the magnetization vector M.

In SI: where is the magnetic constant

Conditions at the interface between two media

Let's explore the connection between vectors E And D at the interface between two homogeneous isotropic dielectrics (whose dielectric constants are ε 1 and ε 2) in the absence of free charges at the boundary.

Replacing the vector projections E vector projections D, divided by ε 0 ε, we get

Let's build a straight cylinder of negligibly small height at the interface between two dielectrics (Fig. 2); one base of the cylinder is in the first dielectric, the other in the second. The bases ΔS are so small that within each of them the vector D is the same. According to Gauss's theorem for the electrostatic field in a dielectric

(normals n And n" oppositely directed towards the bases of the cylinder). That's why

Replacing the vector projections D vector projections E, multiplied by ε 0 ε, we get

This means that when crossing the interface between two dielectric media, the tangential component of the vector E(E τ) and the normal component of the vector D(D n) change continuously (do not experience a jump), and the normal component of the vector E(E n) and tangential component of the vector D(D τ) experience a jump.

From conditions (1) - (4) for the component vectors E And D we see that the lines of these vectors experience a break (are refracted). Let's find how the angles α 1 and α 2 are related (in Fig. 3 α 1 >α 2). Using (1) and (4), E τ2 = E τ1 and ε 2 E n2 = ε 1 E n1 . Let's expand the vectors E 1 And E 2 into tangential and normal components at the interface. From Fig. 3 we see that

Taking into account the conditions written above, we find the law of refraction of lines of tension E(and therefore displacement lines D)

From this formula we can conclude that, entering a dielectric with a higher dielectric constant, lines E And D move away from the normal.

Ticket 7.

Magnetic moments of atoms and molecules.

Elementary particles, atomic nuclei, and electronic shells of atoms and molecules have a magnetic moment. The magnetic moment of elementary particles (electrons, protons, neutrons and others), as shown by quantum mechanics, is due to the existence of their own mechanical moment - spin. The magnetic moment of nuclei consists of the own (spin) magnetic moment of the protons and neutrons forming these nuclei, as well as the magnetic moment associated with their orbital motion inside the nucleus. The magnetic moment of the electron shells of atoms and molecules consists of the spin and orbital magnetic moments of electrons. The electron spin magnetic moment msp can have two equal and oppositely directed projections to the direction of the external magnetic field H. The absolute value of the projection

where mв= (9.274096 ±0.000065)·10-21erg/gs - Bohr magneton where h is Planck's constant, e and me are the charge and mass of the electron, c is the speed of light; SH is the projection of the spin mechanical moment onto the field direction H. The absolute value of the spin magnetic moment

Types of magnets.

MAGNETIC, a substance with magnetic properties, which are determined by the presence of its own or induced by an external magnetic field magnetic moments, as well as the nature of the interaction between them. A distinction is made between diamagnetic materials, in which an external magnetic field creates a resulting magnetic moment directed opposite to the external field, and paramagnetic materials, in which these directions coincide.

Diamagnets- substances that are magnetized against the direction of the external magnetic field. In the absence of an external magnetic field, diamagnetic materials are nonmagnetic. Under the influence of an external magnetic field, each atom of a diamagnetic material acquires a magnetic moment I (and each mole of the substance acquires a total magnetic moment), proportional to the magnetic induction H and directed towards the field.

Paramagnets- substances that are magnetized in an external magnetic field in the direction of the external magnetic field. Paramagnetic substances are weakly magnetic substances; their magnetic permeability differs slightly from unity.

Atoms (molecules or ions) of a paramagnetic material have their own magnetic moments, which, under the influence of external fields, are oriented along the field and thereby create a resulting field that exceeds the external one. Paramagnetic substances are drawn into a magnetic field. In the absence of an external magnetic field, a paramagnetic material is not magnetized, since due to thermal motion the intrinsic magnetic moments of the atoms are oriented completely randomly.

Orbital magnetic and mechanical moments.

An electron in an atom moves around the nucleus. In classical physics, the movement of a point along a circle corresponds to the angular momentum L=mvr, where m is the mass of the particle, v is its speed, r is the radius of the trajectory. In quantum mechanics, this formula is not applicable, since the radius and speed are both uncertain (see “Uncertainty relation”). But the magnitude of angular momentum itself exists. How to define it? From the quantum mechanical theory of the hydrogen atom it follows that the modulus of the angular momentum of the electron can take on the following discrete values:

where l is the so-called orbital quantum number, l = 0, 1, 2, ... n-1. Thus, the angular momentum of the electron, like the energy, is quantized, i.e. takes discrete values. Note that for large values ​​of the quantum number l (l >>1), equation (40) takes the form . This is nothing more than one of N. Bohr's postulates.

Another important conclusion follows from the quantum mechanical theory of the hydrogen atom: the projection of the angular momentum of the electron onto any given direction in space z (for example, on the direction of the magnetic or electric field lines) is also quantized according to the rule:

where m = 0, ± 1, ± 2, …± l is the so-called magnetic quantum number.

An electron moving around a nucleus represents an elementary circular electric current. This current corresponds to a magnetic moment pm. Obviously, it is proportional to the mechanical angular momentum L. The ratio of the magnetic moment pm of the electron to the mechanical angular momentum L is called the gyromagnetic ratio. For an electron in a hydrogen atom

the minus sign shows that the vectors of magnetic and mechanical moments are directed in opposite directions). From here you can find the so-called orbital magnetic moment of the electron:

Hydromagnetic relation.

Ticket 8.

An atom in an external magnetic field. Precession of the orbital plane of an electron in an atom.

When an atom is introduced into a magnetic field with induction, a moment of force acts on an electron moving in an orbit equivalent to a closed circuit with current:

The vector of the orbital magnetic moment of the electron changes similarly:

It follows from this that the vectors and , and the orbit itself precesses around the direction of the vector. Figure 6.2 shows the precessional motion of the electron and its orbital magnetic moment, as well as the additional (precessional) motion of the electron.

This precession is called Larmor precession . The angular velocity of this precession depends only on the magnetic field induction and coincides with it in direction.

Induced orbital magnetic moment.

Larmore's theorem:the only result of the influence of a magnetic field on the orbit of an electron in an atom is the precession of the orbit and vector - the orbital magnetic moment of the electron with an angular velocity around an axis passing through the atomic nucleus parallel to the magnetic field induction vector.

Precession of the electron orbit in an atom leads to the appearance of an additional orbital current directed opposite to the current I:

where is the area of ​​the projection of the electron orbit onto a plane perpendicular to the vector. The minus sign says it is the opposite of the vector. Then the total orbital momentum of the atom is:

Diamagnetic effect.

The diamagnetic effect is an effect in which the components of the magnetic fields of atoms add up and form the substance’s own magnetic field, which weakens the external magnetic field.

Since the diamagnetic effect is caused by the action of an external magnetic field on the electrons of the atoms of a substance, diamagnetism is characteristic of all substances.

The diamagnetic effect occurs in all substances, but if the molecules of a substance have their own magnetic moments, which are oriented in the direction of the external magnetic field and enhance it, then the diamagnetic effect is overlapped by a stronger paramagnetic effect and the substance turns out to be paramagnetic.

The diamagnetic effect occurs in all substances, but if the molecules of a substance have their own magnetic moments, which are oriented in the direction of the external magnetic field and enhance erOj, then the diamagnetic effect is overlapped by a stronger paramagnetic effect and the substance turns out to be paramagnetic.

Larmore's theorem.

If an atom is placed in an external magnetic field with induction (Fig. 12.1), then the electron moving in orbit will be affected by a rotational moment of forces, tending to establish the magnetic moment of the electron in the direction of the magnetic field lines (mechanical moment - against the field).

Ticket 9

9.Strongly magnetic substances - ferromagnets- substances that have spontaneous magnetization, i.e. they are magnetized even in the absence of an external magnetic field. In addition to their main representative - iron - ferromagnets include, for example, cobalt, nickel, gadolinium, their alloys and compounds.

For ferromagnets the dependence J from N quite complicated. As you increase N magnetization J first it grows quickly, then more slowly, and finally the so-called magnetic saturationJ us, no longer depending on the field strength.

Magnetic induction IN=m 0 ( H+J) in weak fields increases rapidly with increasing N due to increase J, and in strong fields, since the second term is constant ( J=J us), IN grows with increasing N according to a linear law.

An essential feature of ferromagnets is not only large values ​​of m (for example, for iron - 5000), but also the dependence of m on N. Initially, m increases with increasing N, then, reaching a maximum, it begins to decrease, tending to 1 in the case of strong fields (m= V/(m 0 N)= 1+J/N, therefore when J=J us =const with growth N attitude J/H->0, and m.->1).

A characteristic feature of ferromagnets is also that for them the dependence J from H(and consequently, and B from N) determined by the history of the magnetization of the ferromagnet. This phenomenon is called magnetic hysteresis. If you magnetize a ferromagnet to saturation (point 1 , rice. 195), and then begin to reduce tension N magnetizing field, then, as experience shows, a decrease J described by a curve 1 -2, above the curve 1 -0. At H=0 J different from zero, i.e. observed in a ferromagnet residual magnetizationJ oc . The presence of residual magnetization is associated with the existence permanent magnets. Magnetization becomes zero under the influence of the field N C, having a direction opposite to the field that caused the magnetization.

Tension H C called coercive force.

With a further increase in the opposite field, the ferromagnet is remagnetized (curve 3-4), and at H=-H we reach saturation (point 4). Then the ferromagnet can be demagnetized again (curve 4-5 -6) and re-magnetize again until saturation (curve 6- 1 ).

Thus, when a ferromagnet is exposed to an alternating magnetic field, the magnetization J changes in accordance with the curve 1 -2-3-4-5-6-1, which is called hysteresis loop. Hysteresis leads to the fact that the magnetization of a ferromagnet is not an unambiguous function of H, i.e., to the same value H matches multiple values J.

Different ferromagnets give different hysteresis loops. Ferromagnets with low (ranging from several thousandths to 1-2 A/cm) coercive force H C(with a narrow hysteresis loop) are called soft, with a large (from several tens to several thousand amperes per centimeter) coercive force (with a wide hysteresis loop) - tough. Quantities H C, J oc and m max determine the applicability of ferromagnets for certain practical purposes. Thus, hard ferromagnets (for example, carbon and tungsten steels) are used to make permanent magnets, and soft ferromagnets (for example, soft iron, an alloy of iron and nickel) are used to make transformer cores.

Ferromagnets have another significant feature: for each ferromagnet there is a certain temperature, called Curie point, at which it loses its magnetic properties. When a sample is heated above the Curie point, the ferromagnet turns into an ordinary paramagnet.

The process of magnetization of ferromagnets is accompanied by a change in its linear dimensions and volume. This phenomenon is called magnetostriction.

The nature of ferromagnetism. According to Weiss's ideas, ferromagnets at temperatures below the Curie point have spontaneous magnetization, regardless of the presence of an external magnetizing field. Spontaneous magnetization, however, is in apparent contradiction with the fact that many ferromagnetic materials, even at temperatures below the Curie point, are not magnetized. To eliminate this contradiction, Weiss introduced a hypothesis according to which a ferromagnet below the Curie point is divided into a large number of small macroscopic regions - domains, spontaneously magnetized to saturation.

In the absence of an external magnetic field, the magnetic moments of individual domains are oriented randomly and compensate each other, therefore the resulting magnetic moment of the ferromagnet is zero and the ferromagnet is not magnetized. An external magnetic field orients along the field the magnetic moments of not individual atoms, as is the case with paramagnets, but entire regions of spontaneous magnetization. Therefore, with growth N magnetization J and magnetic induction IN already in fairly weak fields they grow very quickly. This also explains the increase in m ferromagnets to the maximum value in weak fields. Experiments have shown that the dependence of B on R is not as smooth as shown in Fig. 193, but has a stepped appearance. This indicates that inside the ferromagnet the domains rotate abruptly along the field.

When the external magnetic field is weakened to zero, ferromagnets retain residual magnetization, since thermal motion is not able to quickly disorient the magnetic moments of such large formations as domains. Therefore, the phenomenon of magnetic hysteresis is observed (Fig. 195). In order to demagnetize a ferromagnet, a coercive force must be applied; Shaking and heating the ferromagnet also contribute to demagnetization. The Curie point turns out to be the temperature above which destruction of the domain structure occurs.

The existence of domains in ferromagnets has been proven experimentally. The direct experimental method for observing them is powder figure method. An aqueous suspension of fine ferromagnetic powder (for example, magnetite) is applied to the carefully polished surface of the ferromagnetic material. Particles settle predominantly in places of maximum inhomogeneity of the magnetic field, i.e., at the boundaries between domains. Therefore, the settled powder outlines the boundaries of the domains and a similar picture can be photographed under a microscope. The linear dimensions of the domains turned out to be 10 -4 -10 -2 cm.

Operating principle of transformers, used to increase or decrease alternating current voltage, is based on the phenomenon of mutual induction.

Primary and secondary coils (windings), having respectively n 1 And N 2 turns, mounted on a closed iron core. Since the ends of the primary winding are connected to an alternating voltage source with emf. ξ 1 , then an alternating current appears in it I 1 , creating an alternating magnetic flux F in the transformer core, which is almost completely localized in the iron core and, therefore, almost completely penetrates the turns of the secondary winding. A change in this flux causes the appearance of an emf in the secondary winding. mutual induction, and in the primary - emf. self-induction.

Current I 1 of the primary winding is determined according to Ohm’s law: where R 1 - resistance of the primary winding. Voltage drop I 1 R 1 on resistance R 1 for rapidly varying fields is small compared to each of the two emfs, therefore . E.m.f. mutual induction arising in the secondary winding,

We get that e.m.f., arising in the secondary winding, where the minus sign indicates that the emf. in the primary and secondary windings are opposite in phase.

Turns ratio N 2 /N 1 , showing how many times the e.m.f. in the secondary winding of a transformer there is more (or less) than in the primary winding, called transformation ratio.

Neglecting energy losses, which in modern transformers do not exceed 2% and are associated mainly with the release of Joule heat in the windings and the appearance of eddy currents, and applying the law of conservation of energy, we can write that the current powers in both windings of the transformer are almost the same: ξ 2 I 2 »ξ 1 I 1 , let's find ξ 2 /ξ 1 = I 1 /I 2 = N 2 /N 1, i.e. the currents in the windings are inversely proportional to the number of turns in these windings.

If N 2 /N 1 >1, then we are dealing with step-up transformer, increasing the variable e.m.f. and reducing current (used, for example, to transmit electricity over long distances, since in this case the losses due to Joule heat, proportional to the square of the current strength, are reduced); If N2/N 1 <1, then we are dealing with step-down transformer, reducing e.m.f. and increasing current (used, for example, in electric welding, since it requires high current at low voltage).

A transformer consisting of one winding is called autotransformer. In the case of a step-up autotransformer, the emf. is supplied to part of the winding, and the secondary emf. is removed from the entire winding. In a step-down autotransformer, the mains voltage is supplied to the entire winding, and the secondary emf. is removed from part of the winding.

11.Harmonic oscillation is a phenomenon of periodic change of any quantity, in which the dependence on the argument has the character of a sine or cosine function. For example, a quantity oscillates harmoniously and changes over time as follows:

Or, where x is the value of the changing quantity, t is time, the remaining parameters are constant: A is the amplitude of oscillations, ω is the cyclic frequency of oscillations, is the full phase of oscillations, is the initial phase of oscillations. Generalized harmonic oscillation in differential form

Types of vibrations:

Free vibrations occur under the influence of the internal forces of the system after the system has been removed from its equilibrium position. For free oscillations to be harmonic, it is necessary that the oscillatory system be linear (described by linear equations of motion), and there is no energy dissipation in it (the latter would cause attenuation).

Forced vibrations occur under the influence of an external periodic force. For them to be harmonic, it is enough that the oscillatory system is linear (described by linear equations of motion), and the external force itself changes over time as a harmonic oscillation (that is, that the time dependence of this force is sinusoidal).

Mechanical harmonic oscillation is a rectilinear uneven movement in which the coordinates of an oscillating body (material point) change according to the cosine or sine law depending on time.

According to this definition, the law of change of coordinates depending on time has the form:

where wt is the value under the cosine or sine sign; w is the coefficient, the physical meaning of which will be revealed below; A is the amplitude of mechanical harmonic vibrations. Equations (4.1) are the basic kinematic equations of mechanical harmonic vibrations.

Electromagnetic oscillations are called periodic changes in intensity E and induction B. Electromagnetic oscillations are radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x-rays, gamma rays.

Derivation of the formula

Electromagnetic waves as a universal phenomenon were predicted by the classical laws of electricity and magnetism known as Maxwell's equations. If you look closely at Maxwell's equation in the absence of sources (charges or currents), you will find that, along with the possibility that nothing will happen, the theory also allows for non-trivial solutions to changes in the electric and magnetic fields. Let's start with Maxwell's equations for vacuum:

where is the vector differential operator (nabla)

One of the solutions is the simplest.

To find another, more interesting solution, we will use the vector identity, which is valid for any vector, in the form:

To see how we can use it, let's take the vortex operation from expression (2):

The left side is equivalent to:

where we simplify using the above equation (1).

The right side is equivalent to:

Equations (6) and (7) are equal, so these results in a vector-valued differential equation for the electric field, namely

Applying similar initial results to a similar differential equation for the magnetic field:

These differential equations are equivalent to the wave equation:

where c0 is the wave speed in vacuum; f describes the displacement.

Or even simpler: where is the D’Alembert operator:

Note that in the case of electric and magnetic fields, the speed is:

Differential equation of harmonic oscillations of a material point, or, where m is the mass of the point; k is the coefficient of quasi-elastic force (k=tω2).

A harmonic oscillator in quantum mechanics is a quantum analogue of a simple harmonic oscillator; in this case, it is not the forces acting on the particle that are considered, but the Hamiltonian, that is, the total energy of the harmonic oscillator, and the potential energy is assumed to depend quadratically on the coordinates. Taking into account the following terms in the expansion of potential energy along a coordinate leads to the concept of an anharmonic oscillator

A harmonic oscillator (in classical mechanics) is a system that, when displaced from an equilibrium position, experiences a restoring force F proportional to the displacement x (according to Hooke’s law):

where k is a positive constant describing the rigidity of the system.

The Hamiltonian of a quantum oscillator of mass m, whose natural frequency is ω, looks like this:

In coordinate representation, . The problem of finding the energy levels of a harmonic oscillator is reduced to finding such numbers E for which the following partial differential equation has a solution in the class of quadratically integrable functions.

An anharmonic oscillator is understood as an oscillator with a non-quadratic dependence of the potential energy on the coordinate. The simplest approximation of an anharmonic oscillator is to approximate the potential energy to the third term in the Taylor series:

12. Spring pendulum is a mechanical system consisting of a spring with elasticity coefficient (stiffness) k (Hooke’s law), one end of which is rigidly fixed, and on the other there is a load of mass m.

When an elastic force acts on a massive body, returning it to an equilibrium position, it oscillates around this position. Such a body is called a spring pendulum. Oscillations occur under the influence of an external force. Oscillations that continue after the external force has ceased to act are called free. Oscillations caused by the action of an external force are called forced. In this case, the force itself is called forcing.

In the simplest case, a spring pendulum is a rigid body moving along a horizontal plane, attached by a spring to a wall.

Newton's second law for such a system, provided there are no external forces and friction forces, has the form:

If the system is influenced by external forces, then the vibration equation will be rewritten as follows:

Where f(x) is the resultant of external forces related to a unit mass of the load.

In the case of attenuation proportional to the oscillation speed with coefficient c:

Period of a spring pendulum:

A mathematical pendulum is an oscillator, which is a mechanical system consisting of a material point located on a weightless inextensible thread or on a weightless rod in a uniform field of gravitational forces. The period of small natural oscillations of a mathematical pendulum of length l, motionlessly suspended in a uniform gravitational field with free fall acceleration g, is equal to and does not depend on the amplitude and mass of the pendulum.

Differential equation of a spring pendulum x=Асos (wot+jo).

Equation of pendulum oscillations

The oscillations of a mathematical pendulum are described by an ordinary differential equation of the form

where w is a positive constant determined solely from the parameters of the pendulum. Unknown function; x(t) is the angle of deflection of the pendulum at the moment from the lower equilibrium position, expressed in radians; , where L is the length of the suspension, g is the acceleration of free fall. The equation for small oscillations of a pendulum near the lower equilibrium position (the so-called harmonic equation) has the form:

A pendulum performing small oscillations moves in a sinusoid. Since the equation of motion is an ordinary second-order differential equation, to determine the law of motion of a pendulum, it is necessary to set two initial conditions - coordinate and speed, from which two independent constants are determined:

where A is the amplitude of the pendulum's oscillations, is the initial phase of the oscillations, w is the cyclic frequency, which is determined from the equation of motion. The movement made by a pendulum is called harmonic oscillations

A physical pendulum is an oscillator, which is a solid body that oscillates in a field of any forces relative to a point that is not the center of mass of this body, or a fixed axis perpendicular to the direction of action of the forces and not passing through the center of mass of this body.

Moment of inertia about an axis passing through the suspension point:

Neglecting the resistance of the medium, the differential equation of oscillations of a physical pendulum in a gravity field is written as follows:

The reduced length is a conditional characteristic of a physical pendulum. It is numerically equal to the length of a mathematical pendulum, the period of which is equal to the period of a given physical pendulum. The given length is calculated as follows:

where I is the moment of inertia relative to the suspension point, m is the mass, a is the distance from the suspension point to the center of mass.

An oscillating circuit is an oscillator, which is an electrical circuit containing a connected inductor and capacitor. In such a circuit, current (and voltage) oscillations can be excited. An oscillatory circuit is the simplest system in which free electromagnetic oscillations can occur

The resonant frequency of the circuit is determined by the so-called Thomson formula:

Parallel oscillatory circuit

Let a capacitor of capacitance C be charged to voltage. The energy stored in the capacitor is

The magnetic energy concentrated in the coil is maximum and equal to

Where L is the inductance of the coil, is the maximum current value.

Energy of harmonic vibrations

During mechanical vibrations, the oscillating body (or material point) has kinetic and potential energy. Kinetic energy of body W:

Total energy in the circuit:

Electromagnetic waves carry energy. When waves propagate, a flow of electromagnetic energy arises. If we select an area S oriented perpendicular to the direction of wave propagation, then in a short time Δt the energy ΔWem will flow through the area, equal to ΔWeem = (we + wm)υSΔt

13. Addition of harmonic vibrations of the same direction and the same frequency

An oscillating body can take part in several oscillatory processes, then the resulting oscillation must be found, in other words, the oscillations must be added. In this section we will add harmonic vibrations of the same direction and the same frequency

Using the rotating amplitude vector method, we will graphically construct vector diagrams of these oscillations (Fig. 1). Tax as vectors A1 and A2 rotate with the same angular velocity ω0, then the phase difference (φ2 - φ1) between them will remain constant. This means that the equation of the resulting oscillation will be (1)

In formula (1), the amplitude A and the initial phase φ are respectively determined by the expressions

This means that a body, participating in two harmonic oscillations of the same direction and the same frequency, also performs a harmonic oscillation in the same direction and with the same frequency as the added oscillations. The amplitude of the resulting oscillation depends on the phase difference (φ2 - φ1) of the added oscillations.

Addition of harmonic vibrations of the same direction with similar frequencies

Let the amplitudes of the added oscillations be equal to A, and the frequencies equal to ω and ω+Δω, and Δω<<ω. Выберем начало отсчета так, чтобы начальные фазы обоих колебаний были равны нулю:

Adding these expressions and taking into account that in the second factor Δω/2<<ω, получим

Periodic changes in the amplitude of vibrations that occur when two harmonic vibrations of the same direction with similar frequencies are added are called beats.

Beats arise from the fact that one of the two signals is constantly behind the other in phase and at those moments when the oscillations occur in phase, the total signal is amplified, and at those moments when the two signals are in antiphase, they cancel each other out. These moments periodically replace each other as the lag increases.

Vibration graph during beating

Let us find the result of adding two harmonic oscillations of the same frequency ω, which occur in mutually perpendicular directions along the x and y axes. For simplicity, we choose the starting point so that the initial phase of the first oscillation is equal to zero, and we write it in the form (1)

where α is the phase difference between both oscillations, A and B are equal to the amplitudes of the added oscillations. The equation for the trajectory of the resulting oscillation will be determined by excluding time t from formulas (1). Writing the folded oscillations as

and replacing in the second equation by and by , we find after simple transformations the equation of an ellipse whose axes are oriented arbitrarily relative to the coordinate axes: (2)

Since the trajectory of the resulting oscillation has the shape of an ellipse, such oscillations are called elliptically polarized.

The dimensions of the ellipse axes and its orientation depend on the amplitudes of the added oscillations and the phase difference α. Let us consider some special cases that are of physical interest to us:

1) α = mπ (m=0, ±1, ±2, ...). In this case, the ellipse becomes a straight line segment (3)

where the plus sign corresponds to zero and even values ​​of m (Fig. 1a), and the minus sign to odd values ​​of m (Fig. 2b). The resulting oscillation is a harmonic oscillation with frequency ω and amplitude, which occurs along a straight line (3), making an angle with the x-axis. In this case we are dealing with linearly polarized oscillations;

2) α = (2m+1)(π/2) (m=0, ± 1, ±2,...). In this case, the equation will take the form

Lissajous figures are closed trajectories drawn by a point that simultaneously performs two harmonic oscillations in two mutually perpendicular directions. First studied by the French scientist Jules Antoine Lissajous. The appearance of the figures depends on the relationship between the periods (frequencies), phases and amplitudes of both oscillations. In the simplest case of equality of both periods, the figures are ellipses, which, with a phase difference of 0, either degenerate into straight segments, and with a phase difference of P/2 and equal amplitudes, they turn into a circle. If the periods of both oscillations do not coincide exactly, then the phase difference changes all the time, as a result of which the ellipse is deformed all the time. At significantly different periods, Lissajous figures are not observed. However, if the periods are related as integers, then after a period of time equal to the smallest multiple of both periods, the moving point returns to the same position again - Lissajous figures of a more complex shape are obtained. Lissajous figures fit into a rectangle, the center of which coincides with the origin, and the sides are parallel to the coordinate axes and located on both sides of them at distances equal to the vibration amplitudes.

where A, B - oscillation amplitudes, a, b - frequencies, δ - phase shift

14. Damped oscillations occur in a closed mechanical system

In which there is a loss of energy to overcome forces

resistance (β ≠ 0) or in a closed oscillatory circuit, in

in which the presence of resistance R leads to losses of oscillation energy on

heating of conductors (β ≠ 0).

In this case, the general differential equation of oscillations (5.1)

will take the form: x′′ + 2βx′ + ω0 x = 0 .

The logarithmic damping decrement χ is a physical quantity inverse to the number of oscillations, after which the amplitude A decreases by e times.

APERIODIC PROCESS - transient process in dynamic. system, in which the output value, characterizing the transition of the system from one state to another, either monotonically tends to a steady value, or has one extremum (see figure). Theoretically, it can last indefinitely. A.p. take place, for example, in automatic systems. management.

Graphs of aperiodic processes of changing the parameter x(t) of the system over time: hust - steady-state (limit) value of the parameter

The smallest active resistance of the circuit at which the process is aperiodic is called critical resistance

It is also the kind of resistance at which a mode of free undamped oscillations is realized in the circuit.

15. Oscillations that arise under the influence of an external periodically varying force or an external periodically varying emf are called forced mechanical and forced electromagnetic oscillations, respectively.

The differential equation will take the following form:

q′′ + 2βq′ + ω0 q = cos(ωt) .

Resonance (French resonance, from Latin resono - I respond) is the phenomenon of a sharp increase in the amplitude of forced oscillations, which occurs when the frequency of external influence approaches certain values ​​(resonant frequencies) determined by the properties of the system. An increase in amplitude is only a consequence of resonance, and the reason is the coincidence of the external (exciting) frequency with the internal (natural) frequency of the oscillatory system. Using the phenomenon of resonance, even very weak periodic oscillations can be isolated and/or amplified. Resonance is the phenomenon that at a certain frequency of the driving force the oscillatory system is especially responsive to the action of this force. The degree of responsiveness in the theory of oscillations is described by a quantity called quality factor. The phenomenon of resonance was first described by Galileo Galilei in 1602 in works devoted to the study of pendulums and musical strings.

The most familiar mechanical resonance system to most people is a regular swing. If you push the swing according to its resonant frequency, the range of movement will increase, otherwise the movement will fade. The resonant frequency of such a pendulum can be found with sufficient accuracy in the range of small displacements from the equilibrium state using the formula:

where g is the acceleration of gravity (9.8 m/s² for the Earth's surface), and L is the length from the point of suspension of the pendulum to its center of mass. (The more precise formula is quite complex, and involves an elliptic integral.) It is important that the resonant frequency does not depend on the mass of the pendulum. It is also important that the pendulum cannot be swung at multiple frequencies (higher harmonics), but it can be done at frequencies equal to fractions of the fundamental (lower harmonics).

Amplitude and phase of forced oscillations.

Let us consider the dependence of the amplitude A of forced oscillations on the frequency ω (8.1)

From formula (8.1) it follows that the displacement amplitude A has a maximum. To determine the resonant frequency ωres - the frequency at which the displacement amplitude A reaches its maximum - you need to find the maximum of function (1), or, what is the same, the minimum of the radical expression. Having differentiated the radical expression with respect to ω and equating it to zero, we obtain the condition that determines ωres:

This equality holds for ω=0, ± , for which only a positive value has a physical meaning. Therefore, the resonant frequency (8.2)