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

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

IN 1820 Hans Christian Oersted showed that the electric current flowing through the circuit causes the magnetic needle to deflect. If electric current generates magnetism, then the appearance of electric current must be associated with magnetism. This thought captured the English scientist M. Faraday. “Convert magnetism into electricity,” he wrote in his diary in 1822. For many years he persistently carried out various experiments, but to no avail, and only August 29, 1831 triumph came: he discovered the phenomenon of electromagnetic induction. The setup in which Faraday made his discovery involved Faraday making a ring of soft iron about 2 cm wide and 15 cm in diameter and winding many turns of copper wire on each half of the ring. The circuit of one winding was closed by a wire, in its turns there was a magnetic needle, removed enough so that the effect of magnetism created in the ring did not affect. Current from a battery of galvanic cells was passed through the second winding. When the current was turned on, the magnetic needle made several oscillations and calmed down; when the current was interrupted, the needle oscillated again. It turned out that the needle deviated in one direction when the current was turned on and in the other when the current was interrupted. M. Faraday established that it is possible to “convert magnetism into electricity” using an ordinary magnet.

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FIELD LINES are lines drawn in any force field ( cm. FORCE FIELD) (electric, magnetic, gravitational), the tangents to which at each point of the field coincide in direction with the vector characterizing the given field (strength vector( cm. ELECTRIC FIELD STRENGTH) electric or gravitational fields, magnetic induction vector ( cm. MAGNETIC INDUCTION)). Lines of force are only a visual way of depicting force fields. For the first time, the concept of “lines of force” for electric and magnetic fields was introduced by M. Faraday ( cm. FARADAY Michael).
Since field strengths and magnetic induction are unambiguous functions of a point, only one field line can pass through each point in space. The density of the field lines is usually chosen so that the number of field lines crossing a unit area perpendicular to the field lines is proportional to the field strength (or magnetic induction) on this area. Thus, field lines provide a visual picture of the field distribution in space, characterizing the magnitude and direction of the field strength.
Electrostatic field lines ( cm. ELECTROSTATIC FIELD) are always open: they start on positive charges and end on negative charges (or go to infinity). The field lines do not intersect anywhere, since at each point of the field its intensity has one single value and a certain direction. The density of field lines is greater near charged bodies, where the field strength is greater.
The electric field lines in the space between two positive charges diverge; you can specify a neutral point at which the fields of repulsive forces of both charges cancel each other.
The field lines of a single charge are radial straight lines that diverge from the charge in rays, like the lines of force of the gravitational field of a point mass or a ball. The further away from the charge, the less dense the lines - this illustrates the weakening of the field with increasing distance.
Field lines emanating from a charged conductor of irregular shape become denser near any protrusion or tip; near concavities or cavities, the density of field lines decreases.
If the field lines emanate from a positively charged tip located near a negatively charged flat conductor, then they condense around the tip, where the field is very strong, and diverge into a large area near the plane on which they end, entering the plane perpendicularly.
The electric field in the space between parallel charged plates is uniform. Tension lines in a uniform electric field are parallel to each other.
If a particle, for example an electron, enters a force field, then under the influence of the force field it acquires acceleration, and the direction of its movement cannot exactly follow the direction of the lines of force, it will move in the direction of the momentum vector.
A magnetic field ( cm. A MAGNETIC FIELD) characterize magnetic induction lines, at any point of which the magnetic induction vector is directed tangentially.
The lines of magnetic induction of the magnetic field of a straight conductor with current are circles lying in planes perpendicular to the conductor. The centers of the circle are on the axis of the conductor. The field lines of the magnetic induction vector are always closed, i.e. the magnetic field is vortex. Iron filings placed in a magnetic field are aligned along the lines of force; Thanks to this, it is possible to experimentally determine the type of magnetic induction field lines. The vortex electric field generated by a changing magnetic field also has closed lines of force.

Maxwell laid the foundations of modern classical electrodynamics (Maxwell's equations), introduced the concepts into physics bias current And electromagnetic field, received a number of consequences from his theory (prediction electromagnetic waves, electromagnetic nature Sveta, light pressure and others). He is one of the founders kinetic theory of gases, established the distribution of gas molecules by speed ( Maxwell distribution). Maxwell was one of the first to introduce statistical concepts into physics and showed the statistical nature second law of thermodynamics(« Maxwell's demon"), obtained a number of important results in molecular physics And thermodynamics(Maxwell's thermodynamic relations, Maxwell's rule for the liquid-gas phase transition and others). He is a pioneer of quantitative color theory, the author of the principle color photography. Maxwell's other works include studies on sustainability Saturn's rings, elasticity theory and mechanics ( photoelasticity, Maxwell's theorem), optics, mathematics. He prepared manuscripts of works for publication Henry Cavendish, paid a lot of attention popularization of science, designed a number of scientific instruments.

Hertz's experimental confirmation of Maxwell's theory
The first experimental confirmation of Maxwell's electromagnetic theory was given in the experiments of G. Hertz in 1887, eight years after Maxwell's death. To produce electromagnetic waves, Hertz used a device consisting of two rods separated by a spark gap (Hertz vibrator). At a certain potential difference, a spark appeared in the gap between them - a high-frequency discharge, current oscillations were excited and an electromagnetic wave was emitted. To receive the waves, Hertz used a resonator - a rectangular circuit with a gap, at the ends of which small copper balls were attached.
Experimentally, it was also possible to measure the speed of electromagnetic waves, which turned out to be equal to the speed of light in a vacuum. These results are one of the strongest proofs of the correctness of Maxwell's electromagnetic theory, according to which light is an electromagnetic wave.

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1 Einstein's postulate or principle of relativity: all laws of nature are invariant with respect to all inertial frames of reference. All physical, chemical, biological phenomena occur equally in all inertial frames of reference.

Postulate or principle of the constancy of the speed of light: the speed of light in a vacuum is constant and the same in relation to any inertial frame of reference. It does not depend either on the speed of the light source or on the speed of its receiver. No material object can move faster than the speed of light in a vacuum. Moreover, pi one particle of matter, i.e. a particle with a rest mass different from zero cannot reach the speed of light in a vacuum; only field particles can move at such a speed, i.e. particles with rest mass equal to zero.

Space-time (space-time continuum) is a physical model that complements space with an equal time dimension and, thus, creates a theoretical-physical construct called the space-time continuum.

According to the theory of relativity, the Universe has three spatial dimensions and one time dimension, and all four dimensions are organically connected into a single whole, being almost equal and (within certain limits, see notes below) capable of transforming into each other when the observer changes system countdown.

Within the framework of the general theory of relativity, space-time has a single dynamic nature, and its interaction with all other physical objects (bodies, fields) is gravity. Thus, the theory of gravity within the framework of General Relativity is a theory of space-time (which is assumed in it not to be flat, but capable of dynamically changing its curvature).

Spacetime is continuous and, from a mathematical point of view, a manifold, which is usually endowed with a Lorentz metric.

The phenomenon of the occurrence of electric current in a closed conducting circuit when the magnetic flux covered by this circuit changes is called electromagnetic induction.

It was discovered by Joseph Henry (observations made in 1830, results published in 1832) and Michael Faraday (observations made and results published in 1831).

Faraday's experiments were carried out with two coils inserted into each other (the outer coil is constantly connected to the ammeter, and the inner one, through a key, to the battery). The induction current in the outer coil is observed:

A

V

b

When closing and opening the circuit of the internal coil, motionless relative to the external one (Fig. a);

When moving the internal coil with direct current relative to the external one (Fig. b);

When moving relative to the outer coil of a permanent magnet (Fig. c).

Faraday showed that in all cases of the occurrence of an induced current in the external coil, the magnetic flux through it changes. In Fig. The outer coil is shown as one turn. In the first case (Fig. a), when the circuit is closed, a current flows through the internal coil, a magnetic field arises (changes) and, accordingly, a magnetic flux through the external coil. In the second (Fig. b) and third (Fig. c) cases, the magnetic flux through the external coil changes due to a change in the distance from it to the internal coil with current, or to the permanent magnet, during the movement.

A

V

b

I

I

I

In 1834, Emilius Christianovich Lenz experimentally established a rule that allows one to determine the direction of the induction current: the induction current is always directed so as to counteract the cause that causes it; the induced current always has such a direction that the increment in the magnetic flux it creates and the increment in the magnetic flux that caused this induced current are opposite in sign. This rule is called Lenz's rule.

Law of Electromagnetic Induction can be formulated in the following form: the emf of electromagnetic induction in a circuit is equal to the rate of change with time of the magnetic flux through the surface bounded by this circuit, taken with a minus sign

Here dФ = is the scalar product of the magnetic induction vector and the vector of the surface area. Vector , where is the unit vector () of the normal to an infinitesimal surface area of ​​area .

The minus sign in the expression is associated with the rule for choosing the direction of the normal to the contour that bounds the surface, and the positive direction of traversing along it. In accordance with the definition, magnetic flux Ф through a surface of area S

depends on time if the following changes over time: surface area S;

magnetic induction vector module B; angle between vectors and normal .

If a closed loop (coil) consists of turns, then the total flux through the surface bounded by such a complex contour is called flux linkage and is defined as

where Ф i is the magnetic flux through the i turn. If all the turns are the same, then

where Ф is the magnetic flux through any turn. In this case

I

I

I

N turns

1 turn

2 turns

The expression allows you to determine not only the magnitude, but also the direction of the induction current. If the values ​​of the emf and, therefore, the induced current are positive values, then the current is directed along the positive direction of the circuit, if negative - in the opposite direction (the direction of the positive circuit is determined by choosing the normal to the surface bounded by the circuit)

First of all, it is worth finding out what electric current is. Electric current is the ordered movement of charged particles in a conductor. For it to arise, an electric field must first be created, under the influence of which the above-mentioned charged particles will begin to move.

The first knowledge of electricity, many centuries ago, related to electrical “charges” produced through friction. Already in ancient times, people knew that amber, rubbed with wool, acquired the ability to attract light objects. But only at the end of the 16th century, the English physician Gilbert studied this phenomenon in detail and found out that many other substances had exactly the same properties. Bodies that, like amber, after rubbing, can attract light objects, he called electrified. This word is derived from the Greek electron - “amber”. Currently, we say that bodies in this state have electrical charges, and the bodies themselves are called “charged.”

Electric charges always arise when different substances come into close contact. If the bodies are solid, then their close contact is prevented by microscopic protrusions and irregularities that are present on their surface. By squeezing such bodies and rubbing them against each other, we bring together their surfaces, which without pressure would only touch at a few points. In some bodies, electrical charges can move freely between different parts, but in others this is impossible. In the first case, the bodies are called “conductors”, and in the second - “dielectrics, or insulators”. Conductors are all metals, aqueous solutions of salts and acids, etc. Examples of insulators are amber, quartz, ebonite and all gases found under normal conditions.

Nevertheless, it should be noted that the division of bodies into conductors and dielectrics is very arbitrary. All substances conduct electricity to a greater or lesser extent. Electric charges are positive and negative. This kind of current will not last long, because the electrified body will run out of charge. For the continued existence of an electric current in a conductor, it is necessary to maintain an electric field. For these purposes, electric current sources are used. The simplest case of the occurrence of electric current is when one end of the wire is connected to an electrified body, and the other to the ground.

Electrical circuits supplying current to light bulbs and electric motors did not appear until the invention of batteries, which dates back to around 1800. After this, the development of the doctrine of electricity went so quickly that in less than a century it became not just a part of physics, but formed the basis of a new electrical civilization.

Basic quantities of electric current

Amount of electricity and current. The effects of electric current can be strong or weak. The strength of the electric current depends on the amount of charge that flows through the circuit in a certain unit of time. The more electrons moved from one pole of the source to the other, the greater the total charge transferred by the electrons. This net charge is called the amount of electricity passing through a conductor.

In particular, the chemical effect of electric current depends on the amount of electricity, i.e., the greater the charge passed through the electrolyte solution, the more substance will be deposited on the cathode and anode. In this regard, the amount of electricity can be calculated by weighing the mass of the substance deposited on the electrode and knowing the mass and charge of one ion of this substance.

Current strength is a quantity that is equal to the ratio of the electric charge passing through the cross section of the conductor to the time of its flow. The unit of charge is the coulomb (C), time is measured in seconds (s). In this case, the unit of current is expressed in C/s. This unit is called ampere (A). In order to measure the current in a circuit, an electrical measuring device called an ammeter is used. For inclusion in the circuit, the ammeter is equipped with two terminals. It is connected in series to the circuit.

Electrical voltage. We already know that electric current is the ordered movement of charged particles - electrons. This movement is created using an electric field, which does a certain amount of work. This phenomenon is called the work of electric current. In order to move more charge through an electrical circuit in 1 s, the electric field must do more work. Based on this, it turns out that the work of electric current should depend on the strength of the current. But there is one more value on which the work of the current depends. This quantity is called voltage.

Voltage is the ratio of the work done by the current in a certain section of an electrical circuit to the charge flowing through the same section of the circuit. Current work is measured in joules (J), charge - in coulombs (C). In this regard, the unit of measurement for voltage will become 1 J/C. This unit was called the volt (V).

In order for voltage to arise in an electrical circuit, a current source is needed. When the circuit is open, voltage is present only at the terminals of the current source. If this current source is included in the circuit, voltage will also arise in individual sections of the circuit. In this regard, a current will appear in the circuit. That is, we can briefly say the following: if there is no voltage in the circuit, there is no current. In order to measure voltage, an electrical measuring instrument called a voltmeter is used. In its appearance, it resembles the previously mentioned ammeter, with the only difference being that the letter V is written on the voltmeter scale (instead of A on the ammeter). The voltmeter has two terminals, with the help of which it is connected in parallel to the electrical circuit.

Electrical resistance. After connecting various conductors and an ammeter to the electrical circuit, you can notice that when using different conductors, the ammeter gives different readings, i.e. in this case, the current strength available in the electrical circuit is different. This phenomenon can be explained by the fact that different conductors have different electrical resistance, which is a physical quantity. It was named Ohm in honor of the German physicist. As a rule, larger units are used in physics: kilo-ohm, mega-ohm, etc. The resistance of a conductor is usually denoted by the letter R, the length of the conductor is L, and the cross-sectional area is S. In this case, the resistance can be written as a formula:

R = r * L/S

where the coefficient p is called resistivity. This coefficient expresses the resistance of a conductor 1 m long with a cross-sectional area equal to 1 m2. Resistivity is expressed in Ohms x m. Since wires, as a rule, have a fairly small cross-section, their areas are usually expressed in square millimeters. In this case, the unit of resistivity will be Ohm x mm2/m. In the table below. Figure 1 shows the resistivities of some materials.

Table 1. Electrical resistivity of some materials
Material	p, Ohm x m2/m	Material	p, Ohm x m2/m
Copper	0,017	Platinum-iridium alloy	0,25
Gold	0,024	Graphite	13
Brass	0,071	Coal	40
Tin	0,12	Porcelain	1019
Lead	0,21	Ebonite	1020
Metal or alloy
Silver	0,016	Manganin (alloy)	0,43
Aluminum	0,028	Constantan (alloy)	0,50
Tungsten	0,055	Mercury	0,96
Iron	0,1	Nichrome (alloy)	1,1
Nickelin (alloy)	0,40	Fechral (alloy)	1,3
		Chromel (alloy)	1,5

According to the table. 1 it becomes clear that copper has the lowest electrical resistivity, and metal alloy has the highest. In addition, dielectrics (insulators) have high resistivity.

Electrical capacity. We already know that two conductors isolated from each other can accumulate electrical charges. This phenomenon is characterized by a physical quantity called electrical capacitance. The electrical capacitance of two conductors is nothing more than the ratio of the charge of one of them to the potential difference between this conductor and the neighboring one. The lower the voltage when the conductors receive a charge, the greater their capacity. The unit of electrical capacitance is the farad (F). In practice, fractions of this unit are used: microfarad (μF) and picofarad (pF).

If you take two conductors isolated from each other and place them at a short distance from one another, you will get a capacitor. The capacitance of a capacitor depends on the thickness of its plates and the thickness of the dielectric and its permeability. By reducing the thickness of the dielectric between the plates of the capacitor, the capacitance of the latter can be significantly increased. On all capacitors, in addition to their capacity, the voltage for which these devices are designed must be indicated.

Work and power of electric current. From the above it is clear that electric current does some work. When connecting electric motors, the electric current makes all kinds of equipment work, moves trains along the rails, illuminates the streets, heats the home, and also produces a chemical effect, i.e., allows electrolysis, etc. We can say that the work done by the current on a certain section of the circuit is equal to the product current, voltage and time during which the work was performed. Work is measured in joules, voltage in volts, current in amperes, time in seconds. In this regard, 1 J = 1B x 1A x 1s. From this it turns out that in order to measure the work of electric current, three instruments should be used at once: an ammeter, a voltmeter and a clock. But this is cumbersome and ineffective. Therefore, usually, the work of electric current is measured with electric meters. This device contains all of the above devices.

The power of the electric current is equal to the ratio of the work of the current to the time during which it was performed. Power is designated by the letter “P” and is expressed in watts (W). In practice, kilowatts, megawatts, hectowatts, etc. are used. In order to measure the power of the circuit, you need to take a wattmeter. Electrical engineers express the work of current in kilowatt-hours (kWh).

Basic laws of electric current

Ohm's law. Voltage and current are considered the most useful characteristics of electrical circuits. One of the main features of the use of electricity is the rapid transportation of energy from one place to another and its transfer to the consumer in the required form. The product of the potential difference and the current gives power, i.e., the amount of energy given off in the circuit per unit time. As mentioned above, to measure the power in an electrical circuit, 3 devices would be needed. Is it possible to get by with just one and calculate the power from its readings and some characteristic of the circuit, such as its resistance? Many people liked this idea and found it fruitful.

So what is the resistance of a wire or circuit as a whole? Does a wire, like water pipes or vacuum system pipes, have a permanent property that could be called resistance? For example, in pipes, the ratio of the pressure difference producing flow divided by the flow rate is usually a constant characteristic of the pipe. Similarly, heat flow in a wire is governed by a simple relationship involving the temperature difference, the cross-sectional area of ​​the wire, and its length. The discovery of such a relationship for electrical circuits was the result of a successful search.

In the 1820s, the German schoolteacher Georg Ohm was the first to begin searching for the above relationship. First of all, he strived for fame and fame, which would allow him to teach at the university. That is why he chose an area of ​​research that promised special advantages.

Om was the son of a mechanic, so he knew how to draw metal wire of different thicknesses, which he needed for experiments. Since it was impossible to buy suitable wire in those days, Om made it himself. During his experiments, he tried different lengths, different thicknesses, different metals and even different temperatures. He varied all these factors one by one. In Ohm's time, batteries were still weak and produced inconsistent current. In this regard, the researcher used a thermocouple as a generator, the hot junction of which was placed in a flame. In addition, he used a crude magnetic ammeter, and measured potential differences (Ohm called them “voltages”) by changing the temperature or the number of thermal junctions.

The study of electrical circuits has just begun to develop. After batteries were invented around 1800, it began to develop much faster. Various devices were designed and manufactured (quite often by hand), new laws were discovered, concepts and terms appeared, etc. All this led to a deeper understanding of electrical phenomena and factors.

Updating knowledge about electricity, on the one hand, became the reason for the emergence of a new field of physics, on the other hand, it was the basis for the rapid development of electrical engineering, i.e. batteries, generators, power supply systems for lighting and electric drive, electric furnaces, electric motors, etc. were invented , other.

Ohm's discoveries were of great importance both for the development of the study of electricity and for the development of applied electrical engineering. They made it possible to easily predict the properties of electrical circuits for direct current, and subsequently for alternating current. In 1826, Ohm published a book in which he outlined theoretical conclusions and experimental results. But his hopes were not justified; the book was greeted with ridicule. This happened because the method of crude experimentation seemed unattractive in an era when many were interested in philosophy.

He had no choice but to leave his teaching position. He did not achieve an appointment to the university for the same reason. For 6 years, the scientist lived in poverty, without confidence in the future, experiencing a feeling of bitter disappointment.

But gradually his works gained fame, first outside Germany. Om was respected abroad and benefited from his research. In this regard, his compatriots were forced to recognize him in his homeland. In 1849 he received a professorship at the University of Munich.

Ohm discovered a simple law establishing the relationship between current and voltage for a piece of wire (for part of a circuit, for the entire circuit). In addition, he compiled rules that allow you to determine what will change if you take a wire of a different size. Ohm's law is formulated as follows: the current strength in a section of a circuit is directly proportional to the voltage in this section and inversely proportional to the resistance of the section.

Joule-Lenz law. Electric current in any part of the circuit does some work. For example, let's take any section of the circuit between the ends of which there is a voltage (U). By definition of electric voltage, the work done when moving a unit of charge between two points is equal to U. If the current strength in a given section of the circuit is equal to i, then in time t the charge it will pass, and therefore the work of the electric current in this section will be:

A = Uit

This expression is valid for direct current in any case, for any section of the circuit, which may contain conductors, electric motors, etc. The current power, i.e. work per unit time, is equal to:

P = A/t = Ui

This formula is used in the SI system to determine the unit of voltage.

Let us assume that the section of the circuit is a stationary conductor. In this case, all the work will turn into heat, which will be released in this conductor. If the conductor is homogeneous and obeys Ohm’s law (this includes all metals and electrolytes), then:

U = ir

where r is the conductor resistance. In this case:

A = rt2i

This law was first experimentally deduced by E. Lenz and, independently of him, by Joule.

It should be noted that heating conductors has numerous applications in technology. The most common and important among them are incandescent lighting lamps.

Law of Electromagnetic Induction. In the first half of the 19th century, the English physicist M. Faraday discovered the phenomenon of magnetic induction. This fact, having become the property of many researchers, gave a powerful impetus to the development of electrical and radio engineering.

In the course of experiments, Faraday found out that when the number of magnetic induction lines penetrating a surface bounded by a closed loop changes, an electric current arises in it. This is the basis of perhaps the most important law of physics - the law of electromagnetic induction. The current that occurs in the circuit is called induction. Due to the fact that an electric current arises in a circuit only when free charges are exposed to external forces, then with a changing magnetic flux passing along the surface of a closed circuit, these same external forces appear in it. The action of external forces in physics is called electromotive force or induced emf.

Electromagnetic induction also appears in open conductors. When a conductor crosses magnetic lines of force, voltage appears at its ends. The reason for the appearance of such voltage is the induced emf. If the magnetic flux passing through a closed loop does not change, no induced current appears.

Using the concept of “induction emf,” we can talk about the law of electromagnetic induction, i.e., the induction 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.

Lenz's rule. As we already know, an induced current arises in a conductor. Depending on the conditions of its appearance, it has a different direction. On this occasion, the Russian physicist Lenz formulated the following rule: the induced current arising in a closed circuit always has such a direction that the magnetic field it creates does not allow the magnetic flux to change. All this causes the occurrence of an induction current.

Induction current, like any other, has energy. This means that in the event of an induction current, electrical energy appears. According to the law of conservation and transformation of energy, the above-mentioned energy can only arise due to the amount of energy of some other type of energy. Thus, Lenz's rule fully corresponds to the law of conservation and transformation of energy.

In addition to induction, so-called self-induction can appear in the coil. Its essence is as follows. If a current arises in the coil or its strength changes, a changing magnetic field appears. And if the magnetic flux passing through the coil changes, then an electromotive force appears in it, which is called self-induction emf.

According to Lenz's rule, the self-inductive emf when closing a circuit interferes with the current strength and prevents it from increasing. When the circuit is turned off, the self-inductive emf reduces the current strength. In the case when the current strength in the coil reaches a certain value, the magnetic field stops changing and the self-induction emf becomes zero.

Test 11-1(electromagnetic induction)

Option 1

1. Who discovered the phenomenon of electromagnetic induction?

A. X. Oersted. B. Sh. Pendant. V. A. Volta. G. A. Ampere. D. M. Faraday. E . D. Maxwell.

2. The leads of the copper wire coil are connected to a sensitive galvanometer. In which of the following experiments will the galvanometer detect the occurrence of an emf of electromagnetic induction in the coil?

A permanent magnet is removed from the coil.

A permanent magnet rotates around its longitudinal axis inside the coil.

A. Only in case 1. B. Only in case 2. C. Only in case 3. D. In cases 1 and 2. E. In cases 1, 2 and 3.

3.What is the name of the physical quantity equal to the product of the module B of the magnetic field induction by the area S of the surface penetrated by the magnetic field and the cosine
angle a between the vector B of induction and the normal n to this surface?

A. Inductance. B. Magnetic flux. B. Magnetic induction. D. Self-induction. D. Magnetic field energy.

4. Which of the following expressions determines the induced emf in a closed loop?

A. B. IN. G. D.

5. When a strip magnet is pushed into and out of a metal ring, an induced current occurs in the ring. This current creates a magnetic field. Which pole faces the magnetic field of the current in the ring towards: 1) the retractable north pole of the magnet and 2) the retractable north pole of the magnet.

6. What is the name of the unit of measurement of magnetic flux?

7. The unit of measurement of what physical quantity is 1 Henry?

A. Magnetic field induction. B. Electrical capacitances. B. Self-induction. D. Magnetic flux. D. Inductance.

8. What expression determines the connection between the magnetic flux through a circuit and inductance L circuit and current strength I in the circuit?

A. LI . B. . IN. LI ‘ . G. LI 2 . D.

9. What expression determines the relationship between the self-induction emf and the current strength in the coil?

A. B . IN . LI . G . . D. LI ‘ .

10. Properties of various fields are listed below. Which of them has an electrostatic field?

Tension lines are not associated with electric charges.

The field has energy.

The field has no energy.

A. 1, 4, 6. B. 1, 3, 5. IN. 1, 3, 6. G. 2, 3, 5. D. 2, 3, 6. E. 2, 4, 6.

11. A circuit with an area of ​​1000 cm 2 is in a uniform magnetic field with an induction of 0.5 T, the angle between the vector IN

A. 250Wb. B. 1000 Wb. IN. 0.1 Wb. G. 2,5 · 10 -2 Wb. D. 2.5 Wb.

12. What current strength in a circuit with an inductance of 5 mH creates a magnetic flux 2· 10 -2 Wb?

A. 4 mA. B. 4 A. C. 250 A. D. 250 mA. D. 0.1 A. E. 0.1 mA.

13. The magnetic flux through the circuit in 5 · 10 -2 s uniformly decreased from 10 mWb to 0 mWb. What is the value of the EMF in the circuit at this time?

A. 5 · 10 -4 V.B. 0.1 V.V. 0.2 V.G. 0.4 V.D. 1 V.E. 2 V.

14. What is the value of the energy of the magnetic field of a coil with an inductance of 5 H when the current in it is 400 mA?

A. 2 J. B. 1 J. B. 0.8 J. G. 0.4 J. D. 1000 J. E. 4 10 5 J.

15. A coil containing n turns of wire is connected to a direct current source with voltage U at the exit. What is the maximum value of the self-inductive emf in the coil when the voltage at its ends increases from 0 V to U IN?

A, U V, B. nU V.V. U /P U ,

16. Two identical lamps are connected to a DC source circuit, the first in series with a resistor, the second in series with a coil. In which of the lamps (Fig. 1) will the current strength, when switch K is closed, reach its maximum value later than the other?

A. In the first one. B. In the second. B. In the first and second at the same time. D. In the first, if the resistance of the resistor is greater than the resistance of the coil. D. In the second, if the coil resistance is greater than the resistor resistance.

17. A coil with an inductance of 2 H is connected in parallel with a resistor with an electrical resistance of 900 Ohms, the current in the coil is 0.5 A, the electrical resistance of the coil is 100 Ohms. What electric charge will flow in the circuit of the coil and resistor when they are disconnected from the current source (Fig. 2)?

A. 4000 Cl. B. 1000 Cl. V. 250 Cl. G. 1 10 -2 Cl. D. 1.1 10 -3 Cl. E. 1 10 -3 Cl.

18. An airplane flies at a speed of 900 km/h, the module of the vertical component of the induction vector of the Earth’s magnetic field is 4 10 5 Tesla. What is the potential difference between the ends of the airplane's wings if the wingspan is 50 m?

A. 1.8 B. B. 0.9 C. C. 0.5 C. D. 0.25 C.

19. What should be the current strength in the armature winding of an electric motor in order for a force of 120 N to act on a section of the winding of 20 turns 10 cm long, located perpendicular to the induction vector in a magnetic field with an induction of 1.5 Tesla?

A. 90 A. B. 40 A. C. 0.9 A. D. 0.4 A.

20. What force must be applied to a metal jumper to move it uniformly at a speed of 8 m/s along two parallel conductors located at a distance of 25 cm from each other in a uniform magnetic field with an induction of 2 Tesla? The induction vector is perpendicular to the plane in which the rails are located. The conductors are closed by a resistor with an electrical resistance of 2 Ohms.

A. 10000 N. B. 400 N. C. 200 N. G. 4 N. D. 2 N. E. 1 N.

Test 11-1(electromagnetic induction)

Option 2

1. What is the name of the phenomenon of the occurrence of electric current in a closed circuit when the magnetic flux through the circuit changes?

A. Electrostatic induction. B. The phenomenon of magnetization. B. Ampere force. D. Lorentz force. D. Electrolysis. E. Electromagnetic induction.

2. The leads of the copper wire coil are connected to a sensitive galvanometer. In which of the following experiments will the galvanometer detect the occurrence of an emf of electromagnetic induction in the coil?

A permanent magnet is inserted into the coil.

The coil is placed on a magnet.

3) The coil rotates around a magnet located
inside her.

A. In cases 1, 2 and 3. B. In cases 1 and 2. C. Only in case 1. D. Only in case 2. E. Only in case 3.

3. Which of the following expressions determines magnetic flux?

A. BScosα. B. . IN. qvBsinα. G. qvBI. D. IBlsina .

4. What does the following statement express: the induced emf in a closed loop is proportional to the rate of change of the magnetic flux through the surface bounded by the loop?

A. The law of electromagnetic induction. B. Lenz's rule. B. Ohm's law for a complete circuit. D. The phenomenon of self-induction. D. Law of electrolysis.

5. When a strip magnet is pushed into and out of a metal ring, an induced current occurs in the ring. This current creates a magnetic field. Which pole faces the magnetic field of the current in the ring towards: 1) the retractable south pole of the magnet and 2) the retractable south pole of the magnet.

A. 1 - northern, 2 - northern. B. 1 - southern, 2 - southern.

B. 1 - southern, 2 - northern. G. 1 - northern, 2 - southern.

6. The unit of measurement of what physical quantity is 1 Weber?

A. Magnetic field induction. B. Electrical capacitances. B. Self-induction. D. Magnetic flux. D. Inductance.

7. What is the name of the unit of measurement of inductance?

A. Tesla. B. Weber. V. Gauss. G. Farad. D. Henry.

8. What expression determines the relationship between the energy of the magnetic flux in the circuit and the inductance L circuit and current strength I in the circuit?

A . . B . . IN . LI 2 , G . LI ‘ . D . LI.

9.What is the physical quantity X is determined by the expression x= for a coil of P turns .

A. Induction emf. B. Magnetic flux. B. Inductance. D. EMF of self-induction. D. Magnetic field energy. E. Magnetic induction.

10. Properties of various fields are listed below. Which of them does a vortex induction electric field have?

Tension lines are necessarily associated with electric charges.

Tension lines are not associated with electric charges.

The field has energy.

The field has no energy.

The work done by forces to move an electric charge along a closed path may not be equal to zero.

The work done by forces to move an electric charge along any closed path is zero.

A. 1, 4, 6. B. 1, 3, 5. C. 1, 3, c. G. 2, 3, 5. D. 2, 3, 6. E. 2, 4, 6.

11. A circuit with an area of ​​200 cm 2 is in a uniform magnetic field with an induction of 0.5 T, the angle between the vector IN induction and a normal to the contour surface of 60°. What is the magnetic flux through the loop?

A. 50 Wb. B. 2 · 10 -2 Wb. V. 5 · 10 -3 Wb. G. 200 Wb. D. 5 Wb.

12. A current of 4 A creates a magnetic flux of 20 mWb in the circuit. What is the inductance of the circuit?

A. 5 Gn. B. 5 mH. V. 80 Gn. G. 80 mH. D. 0.2 Gn. E. 200 Gn.

13. The magnetic flux through the circuit in 0.5 s uniformly decreased from 10 mWb to 0 mWb. What is the value of the EMF in the circuit at this time?

A. 5 10 -3 B. B. 5 C. C. 10 C. D. 20 V. D. 0.02 V. E. 0.01 V.

14. What is the value of the energy of the magnetic field of a coil with an inductance of 500 mH when the current in it is 4 A?

A. 2 J. B. 1 J. C. 8 J. D. 4 J. D. 1000 J. E. 4000 J.

15. Coil containing P turns of wire, connected to a DC source with voltage U on the way out. What is the maximum value of the self-inductive emf in the coil when the voltage at its ends decreases from U V to 0 V?

A. U V.B. nU V.V. U / n V.G. Maybe many times more U , depends on the rate of change of current and on the inductance of the coil.

16. In the electrical circuit shown in Figure 1, there are four keys 1, 2, 3 And 4 closed. Opening which of the four will provide the best opportunity to detect the phenomenon of self-induction?

A. 1. B. 2. V. 3. G. 4. D. Any of the four.

17. A coil with an inductance of 2 H is connected in parallel with a resistor with an electrical resistance of 100 Ohms, the current in the coil is 0.5 A, the electrical resistance of the coil is 900 Ohms. What electric charge will flow in the circuit of the coil and resistor when they are disconnected from the current source (Fig. 2)?

A. 4000 Cl. B. 1000 Cl. V. 250 Cl. G. 1 10 -2 Cl. D. 1.1 10 -3 Cl. E. 1 10 -3 Cl.

18. An airplane flies at a speed of 1800 km/h, the module of the vertical component of the induction vector of the Earth’s magnetic field is 4 10 -5 Tesla. What is the potential difference between the ends of the airplane's wings if the wingspan is 25 m?

A. 1.8 B. B. 0.5 B. C. 0.9 V. D. 0.25 V.

19. Rectangular frame with areaS With electric shockI placed in magnetic induction fieldIN . What is the moment of force acting on the frame if the angle between the vectorIN and the normal to the frame is a?

A. IBS sin a. B. IBS. IN. IBS cos a. G. I 2 B.S. sin a. D. I 2 B.S. cos a.

Option 2

.

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

Magnetic flux In a uniform magnetic field, the magnitude of the induction vector is equal to B, a flat closed loop of area S is placed. The normal n to the contour plane makes an angle a with the direction of the magnetic induction vector B (see Fig. 1). The magnetic flux through the surface is the quantity Ф, determined by the relation: Ф = В·S·cos a. The unit of measurement of magnetic flux in the SI system is 1 Weber (1 Wb).

Induction emf in a moving conductor Let a conductor of length L move with speed V in a uniform magnetic field, crossing lines of force. The charges in the conductor move along with the conductor. A charge moving in a magnetic field is acted upon by the Lorentz force. Free electrons are displaced to one end of the conductor, and uncompensated positive charges remain at the other. A potential difference arises, which is the induced emf ei. Its value can be determined by calculating the work done by the Lorentz force when moving a charge along a conductor: ei = A/q = F·L/q. It follows that ei = B·V·L·sin a.

Self-induction Self-induction is a special case of various manifestations of electromagnetic induction. Let's consider a circuit connected to a current source (Fig. 6). Electric current I flows along the circuit. This current creates a magnetic field in the surrounding space. As a result, the circuit is penetrated by its own magnetic flux F. Obviously, the own magnetic flux is proportional to the current in the circuit that created the magnetic field: Ф = L·I. The proportionality factor L is called the loop inductance. Inductance depends on the size, shape of the conductor, and the magnetic properties of the medium. The SI unit of inductance is 1 Henry (H). If the current in the circuit changes, then the intrinsic magnetic flux Fs also changes. A change in the value of Fs leads to the appearance of an induction emf in the circuit. This phenomenon is called self-induction, and the corresponding value is the self-induction emf eiс. From the law of electromagnetic induction it follows that eiс = dФс/dt. If L = const, then eiс= - L·dI/dt.

Transformer A transformer is a static electromagnetic device with two (or more) windings, most often designed to convert alternating current of one voltage into alternating current of another voltage. Energy conversion in a transformer is carried out by an alternating magnetic field. Transformers are widely used in transmitting electrical energy over long distances, distributing it between receivers, as well as in various rectifying, amplifying, signaling and other devices.

Power transformers Power transformers convert alternating current of one voltage into alternating current of another voltage to supply consumers with electricity. Depending on the purpose, they can be increasing or decreasing. In distribution networks, as a rule, three-phase two-winding step-down transformers are used, converting voltages of 6 and 10 kV to a voltage of 0.4 kV.

Current Transformer A current transformer is an auxiliary device in which the secondary current is practically proportional to the primary current and is designed to connect measuring instruments and relays to alternating current electrical circuits. Current transformers are used to convert current of any value and voltage into a current convenient for measuring with standard instruments (5 A), powering current windings of relays, disconnecting devices, as well as isolating devices and their operating personnel from high voltage.

Instrument voltage transformers Instrument voltage transformers are intermediate transformers through which measuring instruments are switched on at high voltages. Thanks to this, the measuring instruments are isolated from the network, which makes it possible to use standard instruments (with their scale re-graded) and thereby expands the limits of the measured voltages. Voltage transformers are used both for measuring voltage, power, energy, and for powering automation circuits, alarms and relay protection of power lines from ground faults. In some cases, voltage transformers can be used as low-power step-down power transformers or as step-up test transformers (for testing the insulation of electrical devices)

Classification of voltage transformers Voltage transformers differ: a) by the number of phases - single-phase and three-phase; b) according to the number of windings, two-winding and three-winding; c) according to the accuracy class, i.e. according to the permissible error values; d) by cooling method, transformers with oil cooling (oil), with natural air cooling (dry and with cast insulation); e) by type of installation for indoor installation, for outdoor installation and for complete switchgear (switchgear)

Classification of current transformers Current transformers are classified according to various criteria: 1. According to their purpose, current transformers can be divided into measuring, protective, intermediate (for including measuring instruments in relay protection current circuits, for equalizing currents in differential protection circuits, etc.) and laboratory (high accuracy, as well as with many transformation ratios). 2. According to the type of installation, current transformers are distinguished: a) for outdoor installation (in open switchgears); b) for indoor installation; c) built into electrical devices and machines: switches, transformers, generators, etc.; d) overhead covers placed on top of the bushing (for example, on the high-voltage input of a power transformer); e) portable (for control measurements and laboratory tests). 3. According to the design of the primary winding, current transformers are divided into: a) multi-turn (coil, loop-winding and figure-of-eight winding); b) single-turn (rod); c) tires.

4. According to the installation method, current transformers for indoor and outdoor installation are divided into: a) feed-through; b) supporting. 5. Based on insulation, current transformers can be divided into groups: a) with dry insulation (porcelain, bakelite, cast epoxy insulation, etc.); b) with paper-oil insulation and with capacitor paper-oil insulation; c) filled with compound. 6. According to the number of transformation stages, there are current transformers: a) single-stage; b) two-stage (cascade). 7. Transformers are distinguished by operating voltage: a) for rated voltage above 1000 V; b) for rated voltage up to 1000 V.

Electrical energy generators Electrical current is generated in generators - devices that convert energy of one kind or another into electrical energy. Generators include galvanic cells, electrostatic machines, thermopiles, solar panels, etc. The scope of application of each of the listed types of electricity generators is determined by their characteristics. Thus, electrostatic machines create a high potential difference, but are unable to create any significant current in the circuit. Galvanic cells can produce a large current, but their duration of action is short. The predominant role in our time is played by electromechanical induction alternating current generators. In these generators, mechanical energy is converted into electrical energy. Their action is based on the phenomenon of electromagnetic induction. Such generators have a relatively simple design and make it possible to obtain large currents at a sufficiently high voltage

Alternating Current Generator An alternating current generator (alternator) is an electromechanical device that converts mechanical energy into alternating current electrical energy. Generators include galvanic cells, electrostatic machines, thermopiles, solar panels, etc. The scope of application of each of the listed types of electricity generators is determined by their characteristics. Thus, electrostatic machines create a high potential difference, but are unable to create any significant current in the circuit.