Electromagnetic induction. Practical application of the phenomenon of electromagnetic induction

The law of electromagnetic induction underlies modern electrical engineering, as well as radio engineering, which, in turn, forms the core of modern industry, which has completely transformed our entire civilization. Practical use electromagnetic induction began only half a century after its discovery. At that time, technological progress was still relatively slow. The reason why electrical engineering plays so much important role throughout our modern life, is that electricity is the most convenient form energy and precisely thanks to the law of electromagnetic induction. The latter allows you to easily obtain electricity from mechanical (generators), flexibly distribute and transport energy (transformers) and convert it back into mechanical (electric motor) and other types of energy, and all this happens with very high efficiency. Just 50 years ago, the distribution of energy between machines in factories was carried out through complex system shafts and belt drives - the forest of transmissions constituted a characteristic detail of the industrial “interior” of that time. Modern machines are equipped with compact electric motors powered by a hidden electrical wiring system.

Modern industry uses a single power supply system covering the entire country, and sometimes several neighboring countries.

The power supply system begins with an electricity generator. The operation of the generator is based on the direct use of the law of electromagnetic induction. Schematically simple generator It is a stationary electromagnet (stator), in the field of which a coil (rotor) rotates. The alternating current excited in the rotor winding is removed using special movable contacts - brushes. Since it is difficult to pass large amounts of power through moving contacts, a reversed generator circuit is often used: a rotating electromagnet excites current in the stationary stator windings. Thus, the generator converts the mechanical energy of rotor rotation into electricity. The latter is driven by either thermal energy (steam or gas turbine), or mechanical (hydraulic turbine).

At the other end of the power supply system are various actuators that use electrical energy, the most important of which is the electric motor (electric motor). The most common, due to its simplicity, is the so-called asynchronous motor, invented independently in 1885-1887. the Italian physicist Ferraris and the famous Croatian engineer Tesla (USA). The stator of such a motor is a complex electromagnet that creates a rotating field. Field rotation is achieved using a system of windings in which the currents are out of phase. In the simplest case, it is enough to take a superposition of two fields in perpendicular directions, shifted in phase by 90° (Fig. VI.10).

Such a field can be written as a complex expression:

which represents a two-dimensional vector of constant length rotating counterclockwise with a frequency co. Although formula (53.1) is similar to the complex representation alternating current in § 52, her physical meaning other. In the case of alternating current, only the real part of the complex expression had a real value, but here the complex quantity represents a two-dimensional vector, and its phase is not only the phase of oscillations of the components of the alternating field, but also characterizes the direction of the field vector (see Fig. VI.10).

In technology, a little more is usually used complex circuit rotation of the field using the so-called three-phase current, i.e. three currents, the phases of which are shifted by 120° relative to each other. These currents create a magnetic field in three directions, rotated one relative to the other at an angle of 120° (Fig. VI.11). Note that such a three-phase current is automatically obtained in generators with a similar arrangement of windings. Three-phase current, which has become widespread in technology, was invented

Rice. VI.10. Scheme for obtaining a rotating magnetic field.

Rice. VI.11. Asynchronous motor diagram. For simplicity, the rotor is shown as a single turn.

in 1888 by the outstanding Russian electrical engineer Dolivo-Dobrovolsky, who built the world's first technical power transmission line in Germany on this basis.

The rotor winding of an asynchronous motor consists in the simplest case of short-circuited turns. An alternating magnetic field induces a current in the turns that causes the rotor to rotate in the same direction as the magnetic field. In accordance with Lenz's rule, the rotor tends to “catch up” with the rotating magnetic field. For a loaded motor, the rotor speed is always less than the field, since otherwise induced emf and the current in the rotor would become zero. Hence the name - asynchronous motor.

Task 1. Find the rotor speed of an asynchronous motor depending on the load.

The equation for the current in one turn of the rotor has the form

where is the angular velocity of the field sliding relative to the rotor, characterizes the orientation of the coil relative to the field, the location of the coil in the rotor (Fig. VI.12, a). Passing to complex quantities (see § 52), we obtain the solution (53.2)

The torque acting on the coil in the same magnetic field is

Rice. VI.12. To the problem of asynchronous motor. a - turn of the rotor winding in a “sliding” field; b - load characteristics of the engine.

Typically the rotor winding contains big number uniformly spaced turns, so summation over 9 can be replaced by integration, as a result we obtain for the total torque on the motor shaft

where is the number of rotor turns. The dependence graph is shown in Fig. VI.12, b. The maximum torque corresponds to the slip frequency. Note that the ohmic resistance of the rotor affects only the slip frequency, but not the maximum motor torque. A negative slip frequency (the rotor “overtakes” the field) corresponds to the generator mode. To maintain this mode, it is necessary to expend external energy, which is converted into electrical energy in the stator windings.

At a given torque, the slip frequency is ambiguous, but only the mode is stable

The main element of electricity conversion and transportation systems is a transformer that changes the alternating current voltage. For long-distance transmission of electricity, it is advantageous to use the maximum possible voltage, limited only by insulation breakdown. Currently, transmission lines operate with a voltage of about For a given transmitted power, the current in the line is inversely proportional to the voltage, and the losses in the line fall as the square of the voltage. On the other hand, significantly lower voltages are required to power electrical consumers, mainly for reasons of simplicity of design (insulation), as well as safety precautions. Hence the need for voltage transformation.

Typically, a transformer consists of two windings on a common iron core (Fig. VI. 13). An iron core is required in a transformer to reduce leakage flux and hence better flux linkage between the windings. Since iron is also a conductor, it transmits alternating

Rice. V1.13. AC transformer circuit.

Rice. VI.14. Diagram of the Rogowski belt. The dashed line conventionally shows the path of integration.

magnetic field only to a small depth (see § 87). Therefore, transformer cores have to be made laminated, that is, in the form of a set of thin plates electrically insulated from one another. For a power frequency of 50 Hz, the usual plate thickness is 0.5 mm. For transformers at high frequencies (in radio engineering) it is necessary to use very thin plates (mm) or ferrite cores.

Task 2. At what voltage should the transformer core plates be insulated?

If the number of plates in the core and the voltage per turn of the transformer winding, then the voltage between adjacent plates

In the simplest case of the absence of stray flux, the ratio of the emf in both windings is proportional to the number of their turns, since the induced emf per turn is determined by the same flux in the core. If, in addition, the losses in the transformer are small and the load resistance is large, then it is obvious that the ratio of the voltages on the primary and secondary windings is also proportional. This is the principle of operation of a transformer, which makes it possible to easily change the voltage many times over.

Task 3. Find the voltage transformation ratio at an arbitrary load.

Neglecting losses in the transformer and dissipation (ideal transformer), we write the equation for the currents in the windings in the form (in SI units)

where is the complex resistance of the load (see § 52) and expression (51.2) is used for the induced emf of a complex circuit. Using relation (51.6); you can find the voltage transformation coefficient without solving equations (53.6), but simply dividing them by one another:

The transformation coefficient turns out to be equal, therefore, simply to the ratio of the number of turns at any load. The sign depends on the choice of the beginning and end of the windings.

To find the current transformation ratio, you need to solve system (53.7), as a result of which we obtain

In the general case, the coefficient turns out to be some complex value, i.e., a phase shift appears between the currents in the windings. Of interest special case low load Then, that is, the ratio of currents becomes the inverse of the ratio of voltages.

This mode of operation of the transformer can be used to measure large currents (current transformer). It turns out that the same simple transformation of currents is preserved for an arbitrary dependence of the current on time with a special design of the current transformer. In this case, it is called a Rogowski belt (Fig. VI.14) and is a flexible closed solenoid of arbitrary shape with uniform winding. The operation of the belt is based on the law of conservation of magnetic field circulation (see § 33): where integration is carried out along the contour inside the belt (see Fig. VI.14), - the total measured current covered by the belt. Assuming that the transverse dimensions of the belt are sufficiently small, we can write the induced emf induced on the belt as follows:

where is the cross section of the belt, and is the winding density, both values are assumed to be constant along the belt; inside the belt, if the winding density of the belt and its cross-section 50 are constant along the length (53.9).

Simple conversion electrical voltage possible only for alternating current. This determines his a vital role in modern industry. In cases where direct current is required, significant difficulties arise. For example, in ultra-long-distance power transmission lines, the use of direct current provides significant advantages: heat losses are reduced, since there is no skin effect (see § 87) and there are no resonant

(wave) transient processes when turning on - off a transmission line, the length of which is about the wavelength of alternating current (6000 km for an industrial frequency of 50 Hz). The difficulty lies in rectifying the alternating current high voltage at one end of the transmission line and reverse conversion at the other.

Today we will talk about the phenomenon of electromagnetic induction. Let us reveal why this phenomenon was discovered and what benefits it brought.

Silk

People have always strived to live better. Some might think that this is a reason to accuse humanity of greed. But often we're talking about about acquiring basic household conveniences.

IN medieval Europe knew how to make wool, cotton and linen fabrics. And even at that time, people suffered from an excess of fleas and lice. At the same time, Chinese civilization has already learned how to masterfully weave silk. Clothes made from it kept bloodsuckers away from human skin. The insects' legs slid along smooth fabric, and the lice fell off. Therefore, the Europeans wanted to dress in silk at all costs. And the merchants thought that this was another opportunity to get rich. Therefore, the Great Silk Road was built.

This was the only way to deliver the desired fabric to suffering Europe. And so many people were involved in the process that cities arose as a result, empires fought over the right to levy taxes, and some parts of the path are still the most convenient way get to the right place.

Compass and star

Mountains and deserts stood in the way of caravans with silk. It happened that the character of the area remained the same for weeks and months. Steppe dunes gave way to similar hills, one pass followed another. And people had to somehow navigate in order to deliver their valuable cargo.

The stars were the first to come to the rescue. Knowing what day it was today and what constellations to expect, an experienced traveler could always determine where south was, where east was, and where to go. But there were always not enough people with sufficient knowledge. And they didn’t know how to count time accurately back then. Sunset, sunrise - that's all the landmarks. And a snow or sandstorm, cloudy weather excluded even the possibility of seeing the polar star.

Then people (probably the ancient Chinese, but scientists are still arguing about this) realized that one mineral is always located in a certain way in relation to the cardinal points. This property was used to create the first compass. The discovery of the phenomenon of electromagnetic induction was a long way off, but a start had been made.

From compass to magnet

The name “magnet” itself goes back to the toponym. The first compasses were probably made from ore mined in the hills of Magnesia. This region is located in Asia Minor. And the magnets looked like black stones.

The first compasses were very primitive. Water was poured into a bowl or other container, and a thin disk of floating material was placed on top. And a magnetized arrow was placed in the center of the disk. One end always pointed to the north, the other to the south.

It's hard to imagine that the caravan saved water for the compass while people were dying of thirst. But do not lose direction and allow people, animals and goods to reach safe place was more important than several separate lives.

The compasses made many journeys and encountered various natural phenomena. It is not surprising that the phenomenon of electromagnetic induction was discovered in Europe, although magnetic ore was originally mined in Asia. In this intricate way, the desire of Europeans to sleep more comfortably led to a major discovery in physics.

Magnetic or electric?

In the early nineteenth century, scientists figured out how to produce direct current. The first primitive battery was created. It was enough to send a stream of electrons through metal conductors. Thanks to the first source of electricity, a number of discoveries were made.

In 1820, the Danish scientist Hans Christian Oersted found out that the magnetic needle deviates near a conductor connected to the network. The positive pole of the compass is always located in a certain way in relation to the direction of the current. The scientist carried out experiments in all possible geometries: the conductor was above or below the arrow, they were located parallel or perpendicular. The result was always the same: the switched on current set the magnet in motion. This was how the discovery of the phenomenon of electromagnetic induction was anticipated.

But the idea of scientists must be confirmed by experiment. Immediately after Oersted's experiment, the English physicist Michael Faraday asked the question: “Magnetic and electric field Do they just influence each other, or are they more closely related? The scientist was the first to test the assumption that if an electric field causes a magnetized object to deviate, then the magnet should generate a current.

The experimental design is simple. Now any schoolchild can repeat it. A thin metal wire was coiled into the shape of a spring. Its ends were connected to a device that recorded the current. When a magnet moved near the coil, the device's arrow showed the voltage of the electric field. Thus, Faraday's law of electromagnetic induction was derived.

Continuation of experiments

But that's not all the scientist did. Since the magnetic and electric fields are closely related, it was necessary to find out how much.

To do this, Faraday supplied current to one winding and pushed it inside another similar winding with a radius larger than the first. Once again electricity was induced. Thus, the scientist proved: a moving charge generates both electric and magnetic fields at the same time.

It is worth emphasizing that we are talking about the movement of a magnet or magnetic field inside a closed loop of a spring. That is, the flow must change all the time. If this does not happen, no current is generated.

Formula

Faraday's law for electromagnetic induction is expressed by the formula

Let's decipher the symbols.

ε stands for emf or electromotive force. This quantity is scalar (that is, not vector), and it shows the work that certain forces or laws of nature apply to create a current. It should be noted that the work must necessarily be performed by non-electrical phenomena.

Φ is the magnetic flux through a closed loop. This value is the product of two others: the magnitude of the magnetic induction vector B and the area of the closed loop. If the magnetic field does not act strictly perpendicular to the contour, then the cosine of the angle between vector B and the normal to the surface is added to the product.

Consequences of the discovery

This law was followed by others. Subsequent scientists established the dependence of electric current intensity on power and resistance on conductor material. New properties were studied and incredible alloys were created. Finally, humanity deciphered the structure of the atom, delved into the mystery of the birth and death of stars, and revealed the genome of living beings.

And all these achievements required a huge amount of resources, and, above all, electricity. Any production or large Scientific research were carried out where three components were available: qualified personnel, the material itself with which to work, and cheap electricity.

And this was possible where the forces of nature could give big moment rotation of the rotor: rivers with large elevation differences, valleys with strong winds, faults with excess geomagnetic energy.

I wonder what modern way obtaining electricity is not fundamentally different from Faraday's experiments. The magnetic rotor spins very quickly inside a large spool of wire. The magnetic field in the winding changes all the time and an electric current is generated.

Of course, selected and best material for magnet and conductors, and the technology of the whole process is completely different. But the point is one thing: the principle discovered in the simplest system is used.

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INTRODUCTION

It is no coincidence that the first and most important step in the discovery of this new side of electromagnetic interactions was taken by the founder of the concept of the electromagnetic field - one of the greatest scientists in the world - Michael Faraday (1791-1867). Faraday was absolutely confident in the unity of electrical and magnetic phenomena. Soon after Oersted's discovery, he wrote in his diary (1821): "Convert magnetism into electricity." From then on, Faraday never stopped thinking 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 design of all power plant generators in the world, which convert mechanical energy into electrical 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 place an iron bar inside the coil. Couldn't a magnet, in turn, cause an electric current to appear or change its magnitude? For a long time nothing could be found.

HISTORY OF THE DISCOVERY OF ELECTROMAGNETIC INDUCTION

Statements by Signors Nobili and Antinori from the magazine "Antologia"

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

This message prompted the Cavalier 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 have known value, and therefore we are in a hurry to publish them, without having anypreviousmaterials, except for the note that served starting point in our research.»

“Mr. Faraday’s memoir,” as the note says, “is divided into four parts.

In the first, entitled "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 exciting current is removed, a current appears in the wire under its influence that is 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 talks about electric currents caused by a magnet. By bringing coils closer to the magnets, Mr. Faraday produced electric currents; When the coils were removed, currents of the opposite direction arose. These currents act strongly on the galvanometer and pass, albeit weakly, through brine and other solutions. It follows that this scientist, using a magnet, excited electric currents discovered by Mr. Ampere.

The third part of the memoir concerns the fundamental electrical state, which Mr. Faraday calls the electromonic state.

The fourth part talks about an experience as curious as it is unusual, belonging to Mr. Arago; As is known, this experiment consists in the fact that a 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 quantities sufficient to make a new electric machine from the disk.

MODERN THEORY OF ELECTROMAGNETIC INDUCTION

Electric currents create a magnetic field around themselves. Couldn't a magnetic field cause an electric field to appear? Faraday experimentally discovered that when changing magnetic flux piercing a closed circuit, an electric current arises in it. This phenomenon was called electromagnetic induction. The current arising from the phenomenon of electromagnetic induction is called induction. Strictly speaking, when a circuit moves in a magnetic field, it is not a certain current that is generated, but a certain EMF. A more detailed study of electromagnetic induction showed that the induced emf arising 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.

Electromotive force in a 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 influence of which charges are separated, as a result of which a potential difference appears at the ends of the conductor. The induced emf in a conductor characterizes the work of moving a unit positive charge along the conductor.

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

EXPERIMENTAL STUDY OF THE PHENOMENON OF ELECTROMAGNETIC INDUCTION

Let's consider Faraday's classical experiments, with the help of which the phenomenon of electromagnetic induction was discovered:

When a permanent magnet moves, it power lines intersect the turns of the coil, which causes induced current, so the galvanometer needle is deflected. The readings of the device depend on the speed of movement of the magnet and the number of turns of the coil.

In this experiment, we pass a current through the first coil, which creates a magnetic flux and when the second coil moves inside the first, an intersection occurs magnetic lines, therefore an induced current occurs.

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 EMF value, 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 EMF value, then returned to its original position. When the switch is turned on, the current increases, but some force arises that prevents the current from increasing. This force induces itself, which is why it is called self-induced emf. At the moment of shutdown, the same thing happens, only the direction of the EMF has changed, so the arrow of the device deviates in the opposite direction.

This experience shows that the EMF of electromagnetic induction occurs when the magnitude and direction of the current changes. This proves that the induced emf, 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. All that remained was to give the law a strict quantitative form and completely reveal physical nature phenomena. Faraday himself already grasped the general thing on which the appearance of an induction current depends in experiments that outwardly look different.

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

This may be a change in the number of lines of magnetic induction piercing a stationary conductor due to a change in the current strength in a neighboring coil, or a change in the number of lines due to the movement of the circuit in a non-uniform magnetic field, the density of the lines of which varies in space.

LENZ'S RULE

The induction current generated 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 induced current with its magnetic field necessarily repels the magnet (coil). To bring the magnet and coil closer together, work must be done. 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 automatically rush inside it. In this case, the law of conservation of energy would be violated. 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, since 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. That is why, to rotate the armature, work must be done, the greater the more strength current. Due to this work, an induced current arises. It is interesting to note that if the magnetic field of our planet were very large and highly inhomogeneous, then rapid 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 if in a dense viscous medium and would become very hot. Neither planes nor rockets could fly. A person could not quickly move either his arms or legs, since the human body is 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 changes in the current in the primary winding.

The repulsion or attraction of a magnet by a coil depends on the direction of the induced 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: bringing a magnet closer to the coil and moving it away? In the first case, the magnetic flux (or the number of lines of magnetic induction piercing the turns of the coil) increases (Fig. a), and in the second case it decreases (Fig. b). Moreover, in the first case, the induction lines B" of the magnetic field created by the induced current arising in the coil come out of 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 depicted with a dash .

Now we come to the main thing: with an increase in the magnetic flux through the turns of the coil, the induced current has such a direction that the magnetic field it creates prevents the increase in 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 induced current creates a magnetic field with induction, increasing the magnetic flux through the turns of the coil.

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

According to Lenz's rule, the induced current arising in a closed circuit has such a direction that the magnetic flux it creates through the surface bounded by the circuit tends to prevent the change in flux that this current generates. Or, the induced current has such a direction that it interferes with the cause that causes it.

In the case of superconductors, 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 over time under any conditions.

LAW OF ELECTROMAGNETIC INDUCTION

electromagnetic induction faraday lenz

Faraday's experiments showed that the strength of the induction 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. This statement can be formulated more precisely using the concept of magnetic flux.

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

Therefore, the statement, which 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:

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

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

According to the law of electromagnetic induction (EMF), the induced emf in a closed loop is equal in magnitude 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 induced current (or the sign of the induced emf) in the law of electromagnetic induction in accordance with Lenz’s rule?

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

If these directions coincide, then E i > 0 and accordingly I i > 0. Otherwise, the emf and current 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 induced current creates a magnetic flux F" < 0. Линии индукции B"magnetic field of the induction current are shown in the figure with a dashed line. Therefore, the induction current I i is directed clockwise (against the positive direction of the bypass) and the induced emf is negative. Therefore, the law of electromagnetic induction must have a minus sign:

IN International system units, the law of electromagnetic induction is used to establish the unit of magnetic flux. This unit is called Weber (Wb).

Since the induced emf E i is expressed in volts, and time in seconds, then from Weber’s EMR law can be determined as follows:

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

PRACTICAL APPLICATION OF THE PHENOMENON 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, etc. Mutually generating each other, these fields form a single alternating electromagnetic field - 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

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

Synchrophasotrons

Currently, a magnetic field is understood as special shape 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 rule " right hand"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 through it.

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

TRANSFORMERS

Transformer (from Latin transformo - transform) - a static electromagnetic device having two or more inductively coupled windings and designed to transform, through electromagnetic induction, 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 induction coil with two windings as a transformer to power the electric candles he invented. Yablochkov's transformer had an open core. Closed-core transformers, similar to those used today, appeared much later, in 1884. With the invention of the transformer, technical interest arose in alternating current, which had not been used 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.

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.

Ualignment of an ideal transformer

An ideal transformer is a transformer that has no energy losses due to heating of the windings and no leakage fluxes from the windings. In an ideal transformer, all lines of force pass through all turns of both windings, and since the changing magnetic field produces 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 coming 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 the voltages at the ends of the windings, we obtain the equation of an ideal transformer:

Thus, we find that as the voltage at the ends of the secondary winding U2 increases, the secondary circuit current 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, resistance Z2 is connected to the ends of the secondary winding, its reduced value to the primary circuit will be

This rule also applies to the secondary circuit:

Designation on diagrams

In the diagrams, the transformer is designated as follows:

The central thick line corresponds to the core, 1 is the primary winding (usually on the left), 2,3 are 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).

APPLICATION OF TRANSFORMERS

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

1. For the transmission and distribution of electrical energy.

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

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

2. To ensure the required circuit for switching on valves in converter devices and matching the voltage at the output and input of the converter. Transformers used for these purposes are called converters.

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

4. For powering various circuits of radio equipment, electronic equipment, communication and automation devices, electrical household appliances, for separating electrical circuits various elements specified 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 transformers.

CONCLUSION

The phenomenon of electromagnetic induction and its special cases are widely used in electrical engineering. To convert mechanical energy into electrical energy, they are used synchronous generators . Transformers are used to increase or decrease the 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 circuit theory, G.I. Atabekov, Lan, St. Petersburg, M., Krasnodar, 2006.

3. Electric cars, L.M. Piotrovsky, L., “Energy”, 1972.

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

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

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

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

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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.

main sources 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 The 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, network filters and so on.). 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 industries 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). By 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. Main elements of the system cellular communication 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.

Radiation intensity base station determined by the load, that is, the presence of owners cell phones 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 the functions they perform. 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.

Inspection equipment Used by intelligence services, customs officers and security officers of various organizations to search for metal objects (weapons, precious metals, wires of explosive devices, 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. main feature arched metal detectors - high sensitivity (adjustable) and high speed of processing the flow of people.

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

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 in a closed conducting circuit electrical circuit When the magnetic field changes, an electric current occurs. 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 movement electric charges, and, accordingly, no induced current is generated. More detailed consideration the phenomena 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 an external source through the circuit, then the magnet located inside the circuit will begin to move under the influence of the magnetic field formed electric shock. 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.