Practical application of electromagnetic induction. Electromagnetic induction

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INTRODUCTION

It is no coincidence that the first and most important step in opening this new side of electromagnetic interactions was made the founder of ideas about the electromagnetic field - one of the greatest scientists in the world - Michael Faraday (1791-1867). Faraday was absolutely sure of the unity of electrical and magnetic phenomena. Shortly after Oersted's discovery, he wrote in his diary (1821): "Turn magnetism into electricity." Since then, Faraday, without ceasing, thought about this problem. They say that he constantly carried a magnet in his vest pocket, which was supposed to remind him of the task at hand. Ten years later, in 1831, as a result of hard work and faith in success, the problem was solved. He made a discovery that underlies the construction of all the generators of the world's power plants, which convert mechanical energy into electric current energy. Other sources: galvanic cells, thermo- and photocells provide a negligible share of the generated energy.

Electric current, Faraday reasoned, is capable of magnetizing iron objects. To do this, just put an iron bar inside the coil. Could the magnet, in turn, cause the appearance of an electric current or change its magnitude? For a long time nothing could be found.

HISTORY OF THE DISCOVERY OF THE PHENOMENON OF ELECTROMAGNETIC INDUCTION

Sayings of Signors Nobili and Antinori from the magazine "Antologia"

« Mr Faraday recently discovered new class electrodynamic phenomena. He submitted a memoir about this to the Royal Society of London, but this memoir has not yet been published. We know about himonly a note communicated by Mr. Aclerk of the Academy of Sciences in ParisDecember 26, 1831, on the basis of a letter he received from Mr. Faraday himself.

This message prompted Chevalier Antinori and myself to immediately repeat the basic experiment and study it from various points of view. We flatter ourselves with the hope that the results we have arrived at are of some significance, and therefore we hasten to publish them without having anypreviousmaterials, except for the note that served as the starting point in our research.»

"Mr. Faraday's memoir," as the note says, "is divided into four parts.

In the first, entitled "The Excitation of Galvanic Electricity," we find the following main fact: A galvanic current passing through a metal wire produces another current in the approaching wire; the second current is opposite in direction to the first and lasts only one instant. If the excitatory current is removed, a current arises in the wire under its influence, opposite to that which arose in it in the first case, i.e. in the same direction as the exciting current.

The second part of the memoir tells about the electric currents caused by the magnet. By approaching the coil magnets, Mr. Faraday produced electric currents; when the coils were removed, currents of the opposite direction arose. These currents have a strong effect on the galvanometer, passing, albeit weakly, through brine and other solutions. From this it follows that this scientist, using a magnet, excited the electric currents discovered by Mr. Ampère.

The third part of the memoir refers to the basic electrical state, which Mr. Faraday calls the electromonic state.

The fourth part speaks of an experiment as curious as it is unusual, belonging to Mr. Arago; as is known, this experiment consists in the fact that the magnetic needle rotates under the influence of a rotating metal disk. He found that when a metal disk rotates under the influence of a magnet, electric currents can appear in an amount sufficient to make a new electrical machine out of the disk.

MODERN THEORY OF ELECTROMAGNETIC INDUCTION

Electric currents create a magnetic field around them. Could a magnetic field cause the appearance electric field? Faraday experimentally found that when the magnetic flux penetrating a closed circuit changes, an electric current arises in it. This phenomenon has been called electromagnetic induction. The current that occurs during the phenomenon of electromagnetic induction is called inductive. Strictly speaking, when the circuit moves in a magnetic field, not a certain current is generated, but a certain EMF. A more detailed study of electromagnetic induction showed that the induction EMF that occurs in any closed circuit is equal to the rate of change of the magnetic flux through the surface bounded by this circuit, taken with the opposite sign.

The electromotive force in the circuit is the result of the action of external forces, i.e. forces of non-electric origin. When a conductor moves in a magnetic field, the role of external forces is played by the Lorentz force, under the action of which the charges are separated, as a result of which a potential difference appears at the ends of the conductor. EMF of induction in a conductor characterizes the work of moving a unit positive charge along the conductor.

The phenomenon of electromagnetic induction underlies the operation of electric generators. If the wire frame is uniformly rotated in a uniform magnetic field, then an induced current arises, periodically changing its direction. Even a single frame rotating in a uniform magnetic field is a generator alternating current.

EXPERIMENTAL STUDY OF THE PHENOMENA OF ELECTROMAGNETIC INDUCTION

Consider the classical experiments of Faraday, with the help of which the phenomenon of electromagnetic induction was discovered:

When a permanent magnet moves, its lines of force cross the turns of the coil, and an induction current arises, so the galvanometer needle deviates. The readings of the device depend on the speed of movement of the magnet and on the number of turns of the coil.

In this experiment, we pass a current through the first coil, which creates magnetic flux and when the second coil moves inside the first, the magnetic lines intersect, so an induction current arises.

When conducting experiment No. 2, it was recorded that at the moment the switch was turned on, the arrow of the device deviated and showed the value of the EMF, then the arrow returned to its original position. When the switch was turned off, the arrow again deviated, but in the other direction and showed the value of the EMF, then returned to its original position. At the moment the switch is turned on, the current increases, but some kind of force arises that prevents the increase in current. This force induces itself, hence the name EMF self-induction. At the time of shutdown, the same thing happens, only the direction of the EMF has changed, so the arrow of the device deviated in the opposite direction.

This experience shows that the EMF of electromagnetic induction occurs when the magnitude and direction of the current change. This proves that the EMF of induction, which creates itself, is the rate of change of current.

Within one month, Faraday experimentally discovered all the essential features of the phenomenon of electromagnetic induction. It only remained to give the law a strict quantitative form and fully reveal the physical nature of the phenomenon. Faraday himself already grasped the common thing that determines the appearance of an induction current in experiments that look different outwardly.

In a closed conducting circuit, a current arises when the number of magnetic induction lines penetrating the surface bounded by this circuit changes. This phenomenon is called electromagnetic induction.

And the faster the number of lines of magnetic induction changes, the greater the resulting current. In this case, the reason for the change in the number of lines of magnetic induction is completely indifferent.

This may be a change in the number of lines of magnetic induction penetrating a fixed conductor due to a change in the current strength in an adjacent coil, and a change in the number of lines due to the movement of the circuit in an inhomogeneous magnetic field, the density of lines of which varies in space.

LENTZ RULE

The inductive current that has arisen in the conductor immediately begins to interact with the current or magnet that generated it. If a magnet (or a coil with current) is brought closer to a closed conductor, then the emerging induction current with its magnetic field necessarily repels the magnet (coil). Work must be done to bring the magnet and coil closer together. When the magnet is removed, attraction occurs. This rule is strictly followed. Imagine if things were different: you pushed the magnet towards the coil, and it would rush into it by itself. This would violate the law of conservation of energy. After all, the mechanical energy of the magnet would increase and at the same time a current would arise, which in itself requires the expenditure of energy, because the current can also do work. The electric current induced in the generator armature, interacting with the magnetic field of the stator, slows down the rotation of the armature. Only therefore, to rotate the armature, it is necessary to do work, the greater, the greater the current strength. Due to this work, an inductive current arises. It is interesting to note that if the magnetic field of our planet were very large and highly inhomogeneous, then fast movements of conducting bodies on its surface and in the atmosphere would be impossible due to the intense interaction of the current induced in the body with this field. The bodies would move as in a dense viscous medium and at the same time would be strongly heated. Neither airplanes nor rockets could fly. A person could not quickly move either his arms or legs, since human body- a good conductor.

If the coil in which the current is induced is stationary relative to the adjacent coil with alternating current, as, for example, in a transformer, then in this case the direction of the induction current is dictated by the law of conservation of energy. This current is always directed in such a way that the magnetic field it creates tends to reduce current variations in the primary.

The repulsion or attraction of a magnet by a coil depends on the direction of the induction current in it. Therefore, the law of conservation of energy allows us to formulate a rule that determines the direction of the induction current. What is the difference between the two experiments: the approach of the magnet to the coil and its removal? In the first case, the magnetic flux (or the number of magnetic induction lines penetrating the turns of the coil) increases (Fig. a), and in the second case it decreases (Fig. b). Moreover, in the first case, the induction line B " magnetic field, created by the induction current that has arisen in the coil, exit from the upper end of the coil, since the coil repels the magnet, and in the second case, on the contrary, they enter this end. These lines of magnetic induction in the figure are shown with a stroke.

Now we have come to the main point: with an increase in the magnetic flux through the turns of the coil, the induction current has such a direction that the magnetic field it creates prevents the growth of the magnetic flux through the turns of the coil. After all, the induction vector of this field is directed against the field induction vector, the change of which generates an electric current. If the magnetic flux through the coil weakens, then the inductive current creates a magnetic field with induction, which increases the magnetic flux through the turns of the coil.

This is the essence general rule determining the direction of the inductive current, which is applicable in all cases. This rule was established by the Russian physicist E.X. Lenz (1804-1865).

According to Lenz's rule, the inductive current that occurs in a closed circuit has such a direction that the magnetic flux created by it through the surface bounded by the circuit tends to prevent the change in the flux that generates this current. Or, the induction current has such a direction that it prevents the cause causing it.

In the case of superconductors, the compensation for changes in the external magnetic flux will be complete. The flux of magnetic induction through a surface bounded by a superconducting circuit does not change at all with time under any conditions.

LAW OF ELECTROMAGNETIC INDUCTION

electromagnetic induction faraday lenz

Faraday's experiments showed that the strength of the induced current I i in a conducting circuit is proportional to the rate of change in the number of magnetic induction lines penetrating the surface bounded by this circuit. More precisely, this statement can be formulated using the concept of magnetic flux.

The magnetic flux is clearly interpreted as the number of lines of magnetic induction penetrating a surface with an area S. Therefore, the rate of change of this number is nothing but the rate of change of the magnetic flux. If in a short time t magnetic flux changes to D F, then the rate of change of the magnetic flux is equal to.

Therefore, a statement that follows directly from experience can be formulated as follows:

the strength of the induction current is proportional to the rate of change of the magnetic flux through the surface bounded by the contour:

Recall that an electric current arises in the circuit when external forces act on free charges. The work of these forces when moving a single positive charge along a closed circuit is called the electromotive force. Consequently, when the magnetic flux changes through the surface bounded by the contour, external forces appear in it, the action of which is characterized by an EMF, called the EMF of induction. Let's denote it with the letter E i .

The law of electromagnetic induction is formulated specifically for EMF, and not for current strength. With this formulation, the law expresses the essence of the phenomenon, which does not depend on the properties of the conductors in which the induction current occurs.

According to the law of electromagnetic induction (EMR), the EMF of induction in a closed loop is equal in absolute value to the rate of change of the magnetic flux through the surface bounded by the loop:

How to take into account the direction of the induction current (or the sign of the induction EMF) in the law of electromagnetic induction in accordance with the Lenz rule?

The figure shows a closed loop. We will consider positive the direction of bypassing the contour counterclockwise. The normal to the contour forms a right screw with the bypass direction. The sign of the EMF, i.e., specific work, depends on the direction of external forces with respect to the direction of bypassing the circuit.

If these directions coincide, then E i > 0 and, accordingly, I i > 0. Otherwise, the EMF and current strength are negative.

Let the magnetic induction of the external magnetic field be directed along the normal to the contour and increase with time. Then F> 0 and > 0. According to Lenz's rule, the induction current creates a magnetic flux F" < 0. Линии индукции B"The magnetic field of the induction current is shown in the figure with a dash. Therefore, the induction current I i is directed clockwise (against the positive bypass direction) and the induction emf is negative. Therefore, in the law of electromagnetic induction, there must be a minus sign:

In the International System of Units, the law of electromagnetic induction is used to establish the unit of magnetic flux. This unit is called the weber (Wb).

Since the EMF of induction E i is expressed in volts, and time is in seconds, then from the Weber EMP law can be determined as follows:

the magnetic flux through the surface bounded by a closed loop is 1 Wb, if, with a uniform decrease in this flux to zero in 1 s, an induction emf equal to 1 V appears in the circuit: 1 Wb \u003d 1 V 1 s.

PRACTICAL APPLICATION OF THE PHENOMENA OF ELECTROMAGNETIC INDUCTION

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, and so on. Mutually generating each other, these fields form a single variable electromagnetic field - an electromagnetic wave. Having arisen in the place where there is a wire with current, the electromagnetic field propagates in space at the speed of light -300,000 km/s.

Magnetotherapy

In the frequency spectrum different places occupied by radio waves, light, x-rays other electromagnetic radiation. They are usually characterized by continuously interconnected electric and magnetic fields.

Synchrophasotrons

At present, 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 - meters

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

DC generator

In the generator mode, the armature of the machine rotates under the influence of an external moment. Between the poles of the stator there is a constant magnetic flux penetrating the armature. The armature winding conductors 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 a load is connected to the generator terminals, then current will flow in it.

The EMR phenomenon is widely used in transformers. Let's consider this device in more detail.

TRANSFORMERS

Transformer (from lat. transformo - transform) - static electromagnetic device having two or more inductively coupled windings and intended to be converted by electromagnetic induction from one or more alternating current systems into one or more other alternating current systems.

The inventor of the transformer is the Russian scientist P.N. Yablochkov (1847 - 1894). In 1876, Yablochkov used an induction coil with two windings as a transformer to power the electric candles he invented. The Yablochkov transformer had an open core. Closed-core transformers, similar to those used today, appeared much later, in 1884. With the invention of the transformer, a technical interest arose in alternating current, which had not been applied until that time.

Transformers are widely used in transmission electrical energy over long distances, its distribution between receivers, as well as in various rectifying, amplifying, signaling and other devices.

The transformation of energy in the transformer is carried out by an alternating magnetic field. The transformer is a core 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 AC electrical energy is connected is called the primary winding, the remaining windings are called secondary.

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

Using a transformer with a reverse turns ratio, you can just as easily and simply get a reduced voltage.

Atideal transformer equation

An ideal transformer is a transformer that has no energy losses for heating the windings and winding leakage fluxes. In an ideal transformer, all lines of force pass through all turns of both windings, and since the changing magnetic field generates the same EMF in each turn, the total EMF induced in the winding is proportional to the total number of its turns. Such a transformer transforms all incoming energy from the primary circuit into a magnetic field and then into the energy of the secondary circuit. In this case, the incoming energy is equal to the converted energy:

Where P1 is the instantaneous value of the power supplied to the transformer from the primary circuit,

P2 is the instantaneous value of the power converted by the transformer entering the secondary circuit.

Combining this equation with the ratio of voltages at the ends of the windings, we get the equation for an ideal transformer:

Thus, we obtain that with an increase in the voltage at the ends of the secondary winding U2, the current of the secondary circuit I2 decreases.

To convert the resistance of one circuit to the resistance of another, you need to multiply the value by the square of the ratio. For example, the resistance Z2 is connected to the ends of the secondary winding, its reduced value to the primary circuit will be

This rule is also valid for the secondary circuit:

Designation on the diagrams

In the diagrams, the transformer is indicated as follows:

The central thick line corresponds to the core, 1 is the primary winding (usually on the left), 2.3 is the secondary windings. The number of semicircles in some rough approximation symbolizes the number of turns of the winding (more turns - more semicircles, but without strict proportionality).

TRANSFORMER APPLICATIONS

Transformers are widely used in industry and everyday life for various purposes:

1. For the transmission and distribution of electrical energy.

Typically, at power plants, alternating current generators generate electrical energy at a voltage of 6-24 kV, and it is profitable to transmit electricity over long distances at much higher voltages (110, 220, 330, 400, 500, and 750 kV). Therefore, at each power plant, transformers are installed that increase the voltage.

Distribution of electrical energy between industrial enterprises, settlements, in cities and rural areas, as well as inside industrial enterprises produced by overhead and cable lines, at a voltage of 220, 110, 35, 20, 10 and 6 kV. Therefore, transformers must be installed in all distribution nodes that reduce the voltage to 220, 380 and 660 V

2. To provide the desired circuit for switching on valves in converter devices and to match the voltage at the output and input of the converter. Transformers used for these purposes are called transformers.

3. For various technological purposes: welding ( welding transformers), power supply of electrothermal installations (electric furnace transformers), etc.

4. For powering various circuits of radio equipment, electronic equipment, communication and automation devices, household appliances, for separating electrical circuits of various elements of these devices, for voltage matching, etc.

5. To include electrical measuring instruments and some devices (relays, etc.) in high voltage electrical circuits or in circuits through which large currents pass, in order to expand the measurement limits and ensure electrical safety. Transformers used for these purposes are called measuring.

CONCLUSION

The phenomenon of electromagnetic induction and its special cases are widely used in electrical engineering. Used to convert mechanical energy into electrical energy synchronous generators. Transformers are used to step up or step down AC voltage. The use of transformers makes it possible to economically transfer electricity from power plants to consumption nodes.

BIBLIOGRAPHY:

1. Physics course, textbook for universities. T.I. Trofimova, 2007.

2. Fundamentals of the theory of circuits, G.I. Atabekov, Lan, St. Petersburg, - M., - Krasnodar, 2006.

3. Electrical machines, L.M. Piotrovsky, L., Energy, 1972.

4. Power transformers. Reference book / Ed. S.D. Lizunova, A.K. Lokhanin. M.: Energoizdat 2004.

5. Design of transformers. A.V. Sapozhnikov. M.: Gosenergoizdat. 1959.

6. Calculation of transformers. Textbook for universities. P.M. Tikhomirov. Moscow: Energy, 1976.

7. Physics -tutorial for technical schools, author V.F. Dmitriev, edition Moscow "Higher School" 2004.

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in the discipline "Physics"

Topic: "Discovery of the phenomenon of electromagnetic induction"

Completed:

Student group 13103/1

St. Petersburg

2. Experiments of Faraday. 3

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

4. List of used literature .. 12

Electromagnetic induction - the phenomenon of the occurrence of an 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 found that the electromotive force that occurs 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 causes the change in flux - a change in the magnetic field itself or the movement of a circuit (or part of it) in a magnetic field. The electric current caused by this EMF is called the induction current.

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

Michael Faraday

Michael Faraday (1791-1867) was born in London, one of the poorest parts of it. His father was a blacksmith, and his mother was the daughter of a tenant farmer. When Faraday reached school age, he was sent to elementary school. The course taken by Faraday here was very narrow and limited only to teaching reading, writing, and the beginning of counting.

A few steps from the house where the Faraday family lived, there was a bookstore, which was also a bookbinding establishment. This is where Faraday got to, having completed the course elementary school when the question arose about choosing a profession for him. Michael at that time was only 13 years old. Already in his youth, when Faraday had just begun his self-education, he strove to rely solely on facts and verify the reports of others with his own experiences.

These aspirations dominated him all his life as the main features of his scientific activity Faraday began to make physical and chemical experiments as a boy at the first acquaintance with physics and chemistry. Once 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 offered Faraday to work with him as a secretary. Soon Davy went on a trip to Europe and took Faraday with him. For 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 small memoirs on chemistry. Faraday's first work on physics dates back to 1818.

Drawing on the experiences of his predecessors and combining several of his own experiences, by September 1821, Michael had printed "The History of the Successes of Electromagnetism". Already at that time, he made up a completely correct concept of the essence of the phenomenon of deflection of a magnetic needle under the action of a 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 first achieved the liquefaction of a gas, and at the same time established a simple but valid method for converting gases into a 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 turns from physics to chemistry, and the result of his work in this area is the discovery of gasoline and sulfuric naphthalene acid.

In 1831, Faraday published a treatise On a Special Kind of Optical Illusion, which served as the basis for a beautiful 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 by themselves immortalize the name of their author. But the most important of scientific works Faraday are his research in the field of electromagnetism and electrical induction.

Faraday's experiments

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

Its logic was simple: mechanical work easily turns into heat; Conversely, heat can be converted into mechanical work(let's say in 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 by means of electricity Ampère obtained magnets, then, apparently, it is possible to "obtain electricity from ordinary magnetism." Arago and Ampère set themselves the same task in Paris, Colladon in Geneva.

Strictly speaking, an important branch of physics, which 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 with ordinary conditions the presence of an electrified body is sufficient for its influence to excite electricity in every other body. At the same time, it was known that the wire through which the current passes and which is also 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 major discoveries in the field of induction electricity. Faraday puts on a lot of experiments, keeps 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"). At least the fact that the last paragraph of the Diary is marked with the number 16041 speaks of Faraday's efficiency.

In addition to an intuitive conviction in the universal connection of phenomena, nothing, in fact, supported him in his search for "electricity from magnetism". In addition, he, like his teacher Devi, relied more on his own experiments than on mental constructions. Davy taught him:

“A good experiment has more value than the thoughtfulness of a genius like Newton.

Nevertheless, it was Faraday who was destined for great discoveries. A great realist, he spontaneously tore the fetters of empiricism, once imposed on him by Devi, and in those moments a great insight dawned on him - he acquired the ability for 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 about six inches in diameter, wrapped around 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 a galvanometer connected to the other winding twitch.

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

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

The galvanometer, remaining perfectly still during the entire passage of the current, begins to oscillate when the circuit 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 with the first current and is 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 in all clarity to Faraday. After all, the first winding into which he applied current immediately became a magnet. If we consider it as a magnet, then the experiment on August 29 showed that magnetism seemed to give rise 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 surge appear when the magnet is turned off?

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

Faraday feels that the opening is somewhere nearby.

“I am now again engaged in electromagnetism and I think that I have attacked a successful thing, but I cannot yet confirm this. It may very well be that after all my labors, I will eventually pull out seaweed instead of fish.

By the next morning, September 24, Faraday had prepared a lot various devices, in which the main elements were no longer windings with electric current, but permanent magnets. And there was an effect too! The arrow deviated and immediately rushed into place. This slight movement occurred during the most unexpected manipulations with the magnet, sometimes, it seemed, by accident.

The next experiment is October 1st. Faraday decides to return to the very beginning - to two windings: one with a current, the other connected to a galvanometer. The difference with the first experiment is the absence of a steel ring - the core. The splash is almost imperceptible. 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 approach the instruments, thinking about the reasons for the failure.

"I took a cylindrical magnetic bar (3/4" in diameter and 8 1/4" long) and inserted one end of it into a spiral of copper wire(220 feet long) connected to a galvanometer. Then, with a quick movement, I pushed the magnet into the entire length of the spiral, and the needle of the galvanometer experienced a shock. Then I just as quickly pulled the magnet out of the spiral, and the needle swung again, but in the opposite direction. These swings of the needle were repeated each time the magnet was pushed in or 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 the magnet moves, and not due to the properties inherent in it at rest."

Rice. 2. Faraday's experiment with a coil

This idea is remarkably fruitful. If the movement of a magnet relative to a conductor creates electricity, then, apparently, the movement of a conductor relative to a magnet must also generate electricity! Moreover, this "electric wave" will not disappear as long as the mutual movement of the conductor and the magnet continues. This means that it is possible to create an electric current generator that operates for an arbitrarily long time, as long as the mutual movement of the wire and the magnet continues!

On October 28, Faraday installed a rotating copper disk between the poles of a horseshoe magnet, from which, with the help of sliding contacts (one on the axis, the other on the periphery of the disk), it was possible to remove electrical voltage. It was the first electrical generator created by human hands. So a new source of electrical energy was found, in addition to the previously known (friction and chemical processes), - induction, and the new kind of this energy is induction electricity.

Experiments similar to Faraday's, as already mentioned, were carried out in France and Switzerland. Colladon, a professor at the Geneva Academy, was a sophisticated experimenter (he, for example, produced on Lake Geneva accurate measurements speed of sound in water). Perhaps, fearing the shaking of the instruments, he, like Faraday, removed the galvanometer as far as possible from the rest of the installation. Many claimed that Colladon observed the same fleeting movements of the arrow as Faraday, but, expecting a more stable, 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 - "forming magnetism" due to electric current. The unexpected "transience" of this effect baffled many, including Colladon, and these many paid for their prejudice.

Continuing his experiments, Faraday further discovered that a simple approximation of a wire twisted into a closed curve to another, along which a galvanic current flows, is sufficient to excite an inductive current in the neutral wire in the direction opposite to the galvanic current, that the removal of 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 fixed 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 during the closing and termination of the galvanic current. These discoveries in turn gave rise to new ones. If it is possible to produce an inductive current by closing and stopping the galvanic current, would not the same result be obtained from the magnetization and demagnetization of iron?

The work of Oersted and Ampère 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 the latter, 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; moreover, one wire was wound around one half of the ring, and the other around the other. A 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 oscillated rapidly and then quickly stopped, that is, all 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 band. Instead of exciting magnetism in iron with a galvanic current, he magnetized the iron by touching it to a permanent steel magnet. The result was the same: in the wire 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 induction currents in the wire. In a word, magnetism, in the sense of excitation of inductive currents, acted in exactly the same way as the galvanic current.

At that time, physicists were intensely occupied with one mysterious phenomenon discovered in 1824 by Arago and could not find an explanation, despite the fact that such outstanding scientists of that time as Arago himself, Ampère, Poisson, Babaj and Herschel were intensively looking for this explanation. The matter was as follows. A magnetic needle, freely hanging, quickly comes to rest if a circle of non-magnetic metal is brought under it; if the circle is then put into rotational motion, the magnetic needle begins to follow 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, which was 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 riddle, something beyond the natural. Faraday, based on his above data, made the assumption that a circle of non-magnetic metal, under the influence of a magnet, is circulated during rotation by inductive currents that affect the magnetic needle and draw it behind the magnet. Indeed, by introducing the edge of the circle between the poles of a large horseshoe-shaped magnet and connecting the center and edge of the circle with a galvanometer with a wire, Faraday received a constant electric current during the rotation of the circle.

Following this, Faraday settled on another phenomenon that aroused general curiosity at that time. As you know, if iron filings are sprinkled on a magnet, they are grouped along certain lines, called magnetic curves. Faraday, drawing attention to this phenomenon, gave the foundations 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 for the excitation of inductive currents, the approach and removal of the source from the magnetic pole is not necessary. To excite currents, it is enough to cross the lines of magnetic force in a known way.

Rice. 4. "Lines of magnetic force"

Further work Faraday in the aforementioned direction acquired, from the contemporary point of view, the character of something completely miraculous. At the beginning of 1832, he demonstrated an apparatus 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 he 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 terrestrial magnetism, which caused inductive currents like an ordinary magnet or galvanic current. In order to show and prove this more clearly, Faraday undertook another experiment that fully confirmed his ideas.

He reasoned that if a circle of non-magnetic metal, for example, copper, rotating in a position in which it intersects the lines of magnetic force of a neighboring magnet, gives 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 terrestrial magnetism, must also give an inductive current. And indeed, a copper circle, rotated in a horizontal plane, gave an inductive current, which produced a noticeable deviation of the galvanometer needle. Faraday ended a series of studies in the field of electrical induction with the discovery, made in 1835, of "the inductive effect 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.

The Russian physicist Emil Khristoforovich Lenz (1804-1861) gave a rule for determining the direction of the induced current. “The induction current is always directed in such a way that the magnetic field it creates impedes or slows down the movement that causes induction,” notes A.A. Korobko-Stefanov in his article on electromagnetic induction. - For example, when the coil approaches the magnet, the resulting inductive current has such a direction that the magnetic field created by it 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 induction currents accelerated the movement that caused them, then work would be created from nothing. The coil itself, after a small push, would rush towards the magnet, and at the same time the induction current would release heat in it. In reality, the induction current is created due to the work of bringing the magnet and coil closer together.

Rice. 5. Lenz's rule

Why is there an induced current? A deep explanation of the phenomenon of electromagnetic induction was given by the English physicist James Clerk Maxwell, the creator of the completed mathematical theory 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 pierced by an alternating magnetic field perpendicular to the plane of the turn. In the coil, of course, there is an induction current. Maxwell interpreted this experiment with exceptional courage and unexpectedness.

When the magnetic field changes in space, according to Maxwell, a process arises for which the presence of a wire coil is of no importance. The main thing here is the appearance of closed ring lines of the electric field, covering the changing magnetic field. Under the action of the emerging electric field, electrons begin to move, and an electric current arises in the coil. A coil is just a device that allows you to detect 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 as early as 1832, which then formed the basis of this invention. In general, the discovery of electromagnetic induction is not without reason attributed to the most outstanding discoveries XIX century - the work of millions of electric motors and electric current generators around the world is based on this phenomenon ...

Practical application of the phenomenon of electromagnetic induction

1. Broadcasting

Rice. 6. Radio

2. Magnetotherapy

In the frequency spectrum different places are occupied by radio waves, light, x-rays and other electromagnetic radiation. They are usually characterized by continuously interconnected electric and magnetic fields.

3. Synchrophasotrons

4. Flow meters

5. DC generator

6. Transformers

Transformers are widely used in the transmission of electrical energy over long distances, its distribution between receivers, as well as in various rectifying, amplifying, signaling and other devices.

Using a transformer with a reverse ratio of turns, you can just as easily and simply get 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.

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

In 1821, M. Faraday made an entry in his diary: "Turn magnetism into electricity." After 10 years, this problem was solved by him.

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

One of the founders of quantitative electrochemistry. First received (1823) in liquid state chlorine, then hydrogen sulfide, carbon dioxide, ammonia and nitrogen dioxide. Discovered (1825) benzene, studied its physical and some Chemical properties. Introduced the concept of dielectric permittivity. Faraday's name entered the system of electrical units as a unit of electrical capacitance.

Many of these works could, by themselves, immortalize the name of their author. But the most important of Faraday's scientific works are his researches in the field of electromagnetism and electric induction. Strictly speaking, an important branch of physics, which 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 the wire through which the current passes and which is also 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 elements, and the ends of the other to a sensitive galvanometer. When the current was passed through the first wire, Faraday turned all his attention to the galvanometer, expecting to notice from its oscillations the appearance of a current in the second wire. However, there was nothing of the kind: the galvanometer remained calm. Faraday decided to increase the current and introduced 120 galvanic cells into the circuit. The result is the same. Faraday repeated this experiment dozens of times, all with the same success. Anyone else in his place would have left the experiment, convinced that the current passing through the wire has no effect on the adjacent wire. But Faraday always tried to extract from his experiments and observations everything that they could give, and therefore, not having received 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 the current, began to oscillate at the very closing of the circuit, and when it was opened, it turned out that at the moment when the current was passed into the first wire, and also when this transmission ceased, during the second wire is also excited by a current, which in the first case has the opposite direction with the first current and is the same with it in the second case and lasts only one instant.

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 (commutator), to constantly interrupt and again conduct the primary current coming from the battery through the first wire, due to which in 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 (friction and chemical processes), - induction, and a new type of this energy - induction electricity.

ELECTROMAGNETIC INDUCTION(lat. 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, then an electric current will appear in it. The appearance of this current is called current induction, and the current itself is called inductive.

The study of the occurrence of electric current has always worried scientists. After the Danish scientist Oersted found out at the beginning of the 19th century that a magnetic field arises around an electric current, scientists wondered if a magnetic field could generate an electric current and vice versa. The first scientist who succeeded was the scientist Michael Faraday.

Faraday's experiments

After numerous experiments, Faraday was able to achieve some results.

1. The occurrence of electric current

To conduct the experiment, he took a coil with large quantity turns and connected it to a milliammeter (a device that measures current). In the up and down direction, the scientist moved the magnet around the coil.

During the experiment, an electric current actually appeared in the coil due to a change in the magnetic field around it.

According to Faraday's observations, the milliammeter needle deviated and indicated that the movement of the magnet generates an electric current. When the magnet stopped, the arrow showed zero markings, i.e. no current circulates in the circuit.

rice. 1 Change in the current strength in the coil due to the movement of the rejctate

This phenomenon, in which the current occurs under the influence of an alternating magnetic field in the conductor, was called the phenomenon of electromagnetic induction.

2.Changing the direction of the induction current

In his subsequent research, Michael Faraday tried to find out what influences the direction of the resulting inductive electric current. While conducting experiments, he noticed that by changing the number of coils on the coil or the polarity of the magnets, the direction of the electric current that occurs in a closed network changes.

3. The phenomenon of electromagnetic induction

To conduct the experiment, the scientist took two coils, which he placed close to each other. The first coil with a large number of turns of wire, was connected to a current source and a key that opens and closes the circuit. He connected the second same coil to a milliammeter without being connected to a current source.

While conducting an experiment, Faraday noticed that when an electrical circuit is closed, an induced current occurs, which can be seen from the movement of the arrow of a milliammeter. When the circuit was opened, the milliammeter also showed that there was an electric current in the circuit, but the readings were exactly the opposite. When the circuit was closed and the current circulated evenly, there was no current in the electrical circuit according to the data of the milliammeter.

https://youtu.be/iVYEeX5mTJ8

Conclusion from experiments

As a result of Faraday's discovery, the following hypothesis was proved: electric current appears only when the magnetic field changes. It has also been proven that changing the number of turns in the coil changes the value of the current (increasing the coils increases the current). Moreover, an induced electric current can appear in a closed circuit only in the presence of an alternating magnetic field.

What determines the inductive electric current?

Based on all of the above, it can be noted that even if there is a magnetic field, it will not lead to the appearance of an electric current, if this field is not alternating.

So what does the magnitude of the induction field depend on?

The number of turns on the coil;
The rate of change of the magnetic field;
The speed of the magnet.

Magnetic flux is a quantity that characterizes a magnetic field. Changing, the magnetic flux leads to a change in the induced electric current.

Fig. 2 Change in current strength when moving a) the coil in which the solenoid is located; b) a permanent magnet by inserting it into the coil

Faraday's Law

Based on the experiments, Michael Faraday formulated the law of electromagnetic induction. The law is that, when a magnetic field changes, it leads to the appearance of an electric current, while the current indicates the presence of an electromotive force of electromagnetic induction (EMF).

Changing the speed of the magnetic current entails a change in the speed of the current and the EMF.

Faraday's Law: The EMF of electromagnetic induction is numerically equal and opposite in sign to the rate of change of magnetic flux that passes through a surface bounded by a contour

Loop inductance. Self-induction.

A magnetic field is created when current flows in a closed circuit. In this case, the current strength affects the magnetic flux and induces an EMF.

Self-induction is a phenomenon in which the induction emf occurs when the current strength in the circuit changes.

Self-induction varies depending on the features of the shape of the circuit, its dimensions and the environment containing it.

As the electric current increases, the self-inductive current of the loop can slow it down. When it decreases, the self-induction current, on the contrary, does not allow it to decrease so quickly. Thus, the circuit begins to have its electrical inertia, slowing down any change in current.

Application of induced emf

The phenomenon of electromagnetic induction has a practical application in generators, transformers and motors running on electricity.

In this case, the current for these purposes is obtained in the following ways:

Change of current in the coil;
The movement of the magnetic field through permanent magnets and electromagnets;
The rotation of coils or coils in a constant magnetic field.

The discovery of electromagnetic induction by Michael Faraday made a great contribution to science and to our everyday life. This discovery served as an impetus for further discoveries in the field of studying electromagnetic fields and is widely used in modern life of people.

Practical application of electromagnetic induction

The phenomenon of electromagnetic induction is used primarily to convert mechanical energy into electric current energy. For this purpose, apply alternators(induction generators).

sin

BUT

With

Rice. 4.6

For industrial production electricity at power plants are used synchronous generators(turbo generators, if the station is thermal or nuclear, and hydro generators, if the station is hydraulic). The stationary part of a synchronous generator is called stator, and rotating - rotor(Fig. 4.6). The generator rotor has a DC winding (excitation winding) and is a powerful electromagnet. D.C submitted to
the excitation winding through the brush-contact apparatus, magnetizes the rotor, and in this case an electromagnet with north and south poles is formed.

On the stator of the generator there are three windings of alternating current, which are offset one relative to the other by 120 0 and are interconnected according to a certain switching circuit.

When an excited rotor rotates with the help of a steam or hydraulic turbine, its poles pass under the stator windings, and an electromotive force that changes according to a harmonic law is induced in them. Next, the generator according to a certain scheme electrical network connected to power consumption nodes.

If you transfer electricity from generators of stations to consumers via power lines directly (at the generator voltage, which is relatively small), then large losses of energy and voltage will occur in the network (pay attention to the ratios , ). Therefore, for economical transportation of electricity, it is necessary to reduce the current strength. However, since the transmitted power remains unchanged, the voltage must
increase by the same factor as the current decreases.

At the consumer of electricity, in turn, the voltage must be reduced to the required level. Electrical devices in which the voltage is increased or decreased by a given number of times are called transformers. The work of the transformer is also based on the law of electromagnetic induction.

sin

Then

In powerful transformers, the coil resistances are very small,
therefore, the voltages at the terminals of the primary and secondary windings are approximately equal to the EMF:

where k- transformation ratio. At k<1 () the transformer is raising, at k>1 () the transformer is lowering.

When connected to the secondary winding of a load transformer, current will flow in it. With an increase in electricity consumption according to the law
energy conservation, the energy given off by the generators of the station should increase, that is

This means that by increasing the voltage with a transformer
in k times, it is possible to reduce the current strength in the circuit by the same amount (in this case, the Joule losses decrease by k 2 times).

Topic 17. Fundamentals of Maxwell's theory for the electromagnetic field. Electromagnetic waves

In the 60s. 19th century English scientist J. Maxwell (1831-1879) summarized the experimentally established laws of electric and magnetic fields and created a complete unified electromagnetic field theory. It allows you to decide the main task of electrodynamics: find the characteristics of the electromagnetic field of a given system of electric charges and currents.

Maxwell hypothesized that any alternating magnetic field excites a vortex electric field in the surrounding space, the circulation of which is the cause of the emf of electromagnetic induction in the circuit:

(5.1)

Equation (5.1) is called Maxwell's second equation. The meaning of this equation is that a changing magnetic field generates a vortex electric field, and the latter, in turn, causes a changing magnetic field in the surrounding dielectric or vacuum. Since the magnetic field is created by an electric current, then, according to Maxwell, the vortex electric field should be considered as a certain current,
which flows both in a dielectric and in a vacuum. Maxwell called this current bias current.

Displacement current, as follows from Maxwell's theory
and Eichenwald's experiments, creates the same magnetic field as the conduction current.

In his theory, Maxwell introduced the concept full current equal to the sum
conduction and displacement currents. Therefore, the total current density

According to Maxwell, the total current in the circuit is always closed, that is, only the conduction current breaks at the ends of the conductors, and in the dielectric (vacuum) between the ends of the conductor there is a displacement current that closes the conduction current.

Introducing the concept of total current, Maxwell generalized the vector circulation theorem (or ):

(5.6)

Equation (5.6) is called Maxwell's first equation in integral form. It is a generalized law of the total current and expresses the main position of the electromagnetic theory: displacement currents create the same magnetic fields as conduction currents.

The unified macroscopic theory of the electromagnetic field created by Maxwell made it possible, from a unified point of view, not only to explain electrical and magnetic phenomena, but to predict new ones, the existence of which was subsequently confirmed in practice (for example, the discovery of electromagnetic waves).

Summarizing the provisions discussed above, we present the equations that form the basis of Maxwell's electromagnetic theory.

1. Theorem on the circulation of the magnetic field vector:

This equation shows that magnetic fields can be created either by moving charges (electric currents) or by alternating electric fields.

2. Electric field can be both potential () and vortex (), so the total field strength . Since the circulation of the vector is equal to zero, then the circulation of the vector of the total electric field strength

This equation shows that the sources of the electric field can be not only electric charges, but also time-varying magnetic fields.

3. ,

where is the volume charge density inside the closed surface; is the specific conductivity of the substance.

For stationary fields ( E= const , B= const) Maxwell's equations take the form

that is, the sources of the magnetic field in this case are only
conduction currents, and the sources of the electric field are only electric charges. In this particular case, the electric and magnetic fields are independent of each other, which makes it possible to study separately permanent electric and magnetic fields.

Using known from vector analysis Stokes and Gauss theorems, one can imagine the complete system of Maxwell's equations in differential form(characterizing the field at each point in space):

(5.7)

Obviously, Maxwell's equations not symmetrical regarding electric and magnetic fields. This is due to the fact that nature
There are electric charges, but there are no magnetic charges.

Maxwell's equations are the most general equations for electrical
and magnetic fields in media at rest. They play the same role in the theory of electromagnetism as Newton's laws in mechanics.

electromagnetic wave called an alternating electromagnetic field propagating in space with a finite speed.

The existence of electromagnetic waves follows from Maxwell's equations, formulated in 1865 on the basis of a generalization of the empirical laws of electrical and magnetic phenomena. An electromagnetic wave is formed due to the interconnection of alternating electric and magnetic fields - a change in one field leads to a change in the other, that is, the faster the magnetic field induction changes in time, the greater the electric field strength, and vice versa. Thus, for the formation of intense electromagnetic waves, it is necessary to excite electromagnetic oscillations of a sufficiently high frequency. Phase speed electromagnetic waves is determined
electrical and magnetic properties of the medium:

In a vacuum ( ) the speed of propagation of electromagnetic waves coincides with the speed of light; in matter , That's why the speed of propagation of electromagnetic waves in matter is always less than in vacuum.

Electromagnetic waves are shear waves –
oscillations of the vectors and occur in mutually perpendicular planes, and the vectors , and form a right-handed system. It also follows from Maxwell's equations that in an electromagnetic wave the vectors and always oscillate in the same phases, and the instantaneous values E and H at any point are related by the relation

plane equations electromagnetic wave in vector form:

(6.66)

Rice. 6.21

On fig. 6.21 shows a "snapshot" of a plane electromagnetic wave. It can be seen from it that the vectors and form a right-handed system with the direction of wave propagation. At a fixed point in space, the vectors of the electric and magnetic fields change with time according to a harmonic law.

To characterize the transfer of energy by any wave in physics, a vector quantity called energy flux density. It is numerically equal to the amount of energy transferred per unit time through a unit area perpendicular to the direction in which
the wave propagates. The direction of the vector coincides with the direction of energy transfer. The value of the energy flux density can be obtained by multiplying the energy density by the wave speed

The energy density of the electromagnetic field is the sum of the energy density of the electric field and the energy density of the magnetic field:

(6.67)

Multiplying the energy density of an electromagnetic wave by its phase velocity, we obtain the energy flux density

(6.68)

The vectors and are mutually perpendicular and form a right-handed system with the direction of wave propagation. Therefore the direction
vector coincides with the direction of energy transfer, and the modulus of this vector is determined by relation (6.68). Therefore, the energy flux density vector of an electromagnetic wave can be represented as a vector product

(6.69)

Vector call Umov-Poynting vector.

Vibrations and waves

Topic 18. Loose harmonic vibrations

Movements that have some degree of repetition are called fluctuations.

If the values of physical quantities that change in the process of movement are repeated at regular intervals, then such a movement is called periodical (the movement of planets around the Sun, the movement of a piston in the cylinder of an internal combustion engine, etc.). An oscillatory system, regardless of its physical nature, is called oscillator. An example of an oscillator is an oscillating weight suspended on a spring or thread.

Full swingone complete cycle of oscillatory motion is called, after which it is repeated in the same order.

According to the method of excitation, vibrations are divided into:

· free(intrinsic) occurring in the system presented to itself near the equilibrium position after some initial impact;

· forced occurring under periodic external action;

· parametric, occurring when changing any parameter of the oscillatory system;

· self-oscillations occurring in systems that independently regulate the flow of external influences.

Any oscillatory movement is characterized amplitude A - the maximum deviation of the oscillating point from the equilibrium position.

Oscillations of a point occurring with a constant amplitude are called undamped, and fluctuations with gradually decreasing amplitude – fading.

The time it takes for a complete oscillation to take place is called period(T).

Frequency periodic oscillations is the number of complete oscillations per unit of time. Oscillation frequency unit - hertz(Hz). Hertz is the frequency of oscillations, the period of which is equal to 1 s: 1 Hz = 1 s -1 .

cyclicor circular frequency periodic oscillations is the number of complete oscillations that occur in a time 2p with: . \u003d rad / s.