An alternating magnetic field generates induced electric field. If the magnetic field is constant, then there will be no induced electric field. Hence, the induced electric field is not associated with charges, as is the case in the case of an electrostatic field; its lines of force do not begin or end on charges, but are closed on themselves, similar to magnetic field lines. This means that induced electric field, like magnetic, is a vortex.

If a stationary conductor is placed in an alternating magnetic field, then an e is induced in it. d.s. The electrons are driven in directional motion by an electric field induced by an alternating magnetic field; an induced electric current occurs. In this case, the conductor is only an indicator of the induced electric field. The field sets in motion free electrons in the conductor and thereby reveals itself. Now we can say that even without a conductor this field exists, possessing a reserve of energy.

The essence of the phenomenon of electromagnetic induction lies not so much in the appearance of an induced current, but in the appearance of a vortex electric field.

This fundamental position of electrodynamics was established by Maxwell as a generalization of Faraday's law of electromagnetic induction.

Unlike the electrostatic field, the induced electric field is non-potential, since the work done in the induced electric field when moving a unit positive charge along a closed circuit is equal to e. d.s. induction, not zero.

The direction of the vortex electric field intensity vector is established in accordance with Faraday's law of electromagnetic induction and Lenz's rule. Direction of force lines of vortex electric. field coincides with the direction of the induction current.

Since the vortex electric field exists in the absence of a conductor, it can be used to accelerate charged particles to speeds comparable to the speed of light. It is on the use of this principle that the operation of electron accelerators - betatrons - is based.

An inductive electric field has completely different properties compared to an electrostatic field.

The difference between a vortex electric field and an electrostatic one

1) It is not associated with electric charges;
2) The lines of force of this field are always closed;
3) The work done by the vortex field forces to move charges along a closed trajectory is not zero.

electrostatic field	induction electric field (vortex electric field)
1. created by stationary electric. charges	1. caused by changes in the magnetic field
2. field lines are open - potential field	2. lines of force are closed - vortex field
3. The sources of the field are electric. charges	3. field sources cannot be specified
4. work done by field forces to move a test charge along a closed path = 0.	4. work of field forces to move a test charge along a closed path = induced emf

D. G. Evstafiev,
Municipal educational institution Pritokskaya secondary school, Romanovsky village, Aleksandrovsky district, Orenburg region.

Comparison of electric and magnetic fields. 11th grade

Lesson plan for repetition and generalization, 11th grade

Methodical recommendations . The lesson is conducted after studying the topic “Magnetic field”. The main methodological technique is highlighting the common and distinctive features of electric and magnetic fields and filling out the table. Sufficiently developed dialectical thinking is assumed, otherwise it will be necessary to make digressions of a philosophical nature. Comparing the electric and magnetic fields leads students to the conclusion about their relationship, on which the next topic is based - “Electromagnetic induction”.

Physics and philosophy consider matter as the basis of all things, which exists in different forms. It can be concentrated within a limited area of ​​space (localized), but it can, on the contrary, be delocalized. The first state can be associated with the concept substance, the second – the concept field. Along with specific physical characteristics, these conditions also have common ones. For example, there is the energy of a unit volume of matter and there is the energy of a unit volume of field. The properties of matter are inexhaustible, the process of cognition is endless. Therefore, all physical concepts must be considered in development. For example, modern physics, unlike classical physics, does not draw a strict boundary between field and matter. In modern physics, field and matter mutually transform: matter turns into field, and field turns into matter. But let’s not get ahead of ourselves, but let’s remember the classification of forms of matter. Let's look at the diagram on the board.

Using the diagram, try to compose a short story about the forms of existence of matter. ( After the students answer, the teacher reminds them that The consequence of this is the similarity of the characteristics of gravitational tion and electric fields, which was revealed lebut in previous lessons on the topic “Electric field” .) The conclusion suggests itself: if there is a similarity between the gravitational and electric fields, then there must be a similarity between the electric and magnetic fields. Let's let's compare the properties and characteristics of the fields in the form of a table similar to the one we did with comparison of gravitational and electric fields.

Electric field	Magnetic field
Field sources
Electrically charged bodies	Moving electrically charged bodies (electric currents)
Field indicators
Small pieces of paper. Electric sleeve. Electric "sultan"	Metal filings. Closed circuit with current. Magnetic needle
Experienced Facts
Coulomb's experiments on the interaction of electrically charged bodies	Ampere's experiments on the interaction of conductors with current
Graphic characteristics
Electric field strength lines in the case of stationary charges have a beginning and an end (potential field); can be visualized (quinine crystals in oil)	The magnetic field lines are always closed (vortex field); can be visualized (metal filings)
Power characteristic
Electric field strength vector E. Size: Direction:	Magnetic field induction vector B. Size: . Direction is determined by the left hand rule
Energy characteristics
The work done by the electric field of stationary charges (Coulomb force) is zero when going around a closed trajectory	The work done by the magnetic field (Lorentz force) is always zero
Action of a field on a charged particle
The force is always non-zero: F = qE	The force depends on the speed of the particle: it does not act if the particle is at rest, and also if
Matter and field
.

Conclusion

1. When discussing field sources, it is good to compare two natural stones to increase interest in the subject: amber and magnet.

Amber - a warm stone of amazing beauty - has an unusual property that is conducive to philosophical constructions: it can attract! Being rubbed, it attracts dust particles, threads, pieces of paper (papyrus). It was for this property that they were given names in ancient times. That's what the Greeks called itelectron – attractive; Romans – harpax – robber, and the Persians - cowboy, i.e. capable of attracting chaff . It was considered magical, medicinal, cosmetic...

Another stone known for thousands of years, a magnet, was considered just as mysterious and useful. In different countries the magnet was called differently, but most of these names are translated as loving. This is how the ancients poetically noted the property of pieces of a magnet to attract iron.

From my point of view, these two special stones can be considered as the first natural sources of electric and magnetic fields to be studied.

2. When discussing field indicators, it is useful to simultaneously demonstrate with the help of students the interaction of an electrified ebonite rod with an electric sleeve and a permanent magnet with a closed loop carrying current.

3. Visualization of power lines is best demonstrated using screen projection.

4. Division of dielectrics into electrets and ferroelectrics - additional material. Electrets are dielectrics that maintain polarization for a long time in the absence of an external electric field and create their own electric field. In this sense, electrets are similar to permanent magnets that create a magnetic field. But this is another similarity with hard ferromagnets!

Ferroelectrics are crystals that have (in a certain temperature range) spontaneous polarization. As the external field strength decreases, the induced polarization is partially retained. They are characterized by the presence of a limiting temperature - the Curie point, at which the ferroelectric becomes an ordinary dielectric. Again similarities with ferromagnets!

After working with the table, the discovered similarities and differences are collectively discussed. Similarity underlies a single picture of the world; differences are explained so far at the level of different organization of matter, or better to say, the degree of organization of matter. The mere fact that a magnetic field is detected only near moving electric charges (as opposed to an electric one) makes it possible to predict more complex methods for describing the field, a more complex mathematical apparatus used to characterize the field.

Dmitry Georgievich Evstafiev – hereditary physics teacher (father, Georgy Sevostyanovich, a participant in the Great Patriotic War, worked for many years at the Dobrinsky secondary school, combining teaching with the duties of a school director), graduated in 1978 Physics and Mathematics of the Orenburg State Pedagogical Institute named after. V.P. Chkalova, majoring in Physics, teaching experience 41 years. Since 1965 he has been working at the municipal educational institution Pritokskaya Secondary School, and was its director for several years. He was awarded three times with certificates of honor from the Orenburg Regional District. Pedagogical credo: “Do not be satisfied with what has been achieved!” Many of its graduates graduated from technical universities. Together with his wife, they raised five children, three work in schools in the Orenburg region, two study at the history and philological faculties of the Orenburg State Pedagogical University. Son Sergei is the winner of the All-Russian competition “The Best Teachers of Russia” in 2006, a computer science teacher, works in the regional center - the village of Novosergievka. Hobby: beekeeping.

Purpose of the lesson: form the concept that induced emf can occur either in a stationary conductor placed in a changing magnetic field, or in a moving conductor located in a constant magnetic field; the law of electromagnetic induction is valid in both cases, but the origin of the emf is different.

Lesson progress

Checking homework using the method of frontal questioning and problem solving

1. What quantity changes proportionally to the rate of change of magnetic flux?

2. Work, what forces does the induced emf create?

3. Formulate and write down the formula for the law of electromagnetic induction.

4. The law of electromagnetic induction has a minus sign. Why?

5. What is the induced emf in a closed turn of wire, the resistance of which is 0.02 Ohm, and the induced current is 5 A.

Solution. Ii = ξi /R; ξi= Ii·R; ξi= 5 0.02= 0.1 V

Learning new material

Let us consider how induced emf occurs in A stationary conductor, located in an alternating magnetic field. The easiest way to understand this is by looking at the operation of a transformer.

One coil is closed to the alternating current network; if the second coil is closed, then a current arises in it. The electrons in the wires of the secondary winding will begin to move. What forces move free electrons? A magnetic field cannot do this, since it only acts on moving electric charges.

Free electrons move under the influence of an electric field that was created by an alternating magnetic field.

Thus, we come to the concept of a new fundamental property of fields: Changing over time, the magnetic field generates an electric field. This conclusion was made by J. Maxwell.

Thus, the main thing in the phenomenon of electromagnetic induction is the creation of an electric field by a magnetic field. This field sets free charges in motion.

The structure of this field is different from that of the electrostatic one. It is not associated with electric charges. Tension lines do not start at positive charges and do not end at negative charges. Such lines have no beginning or end - they are closed lines similar to magnetic field induction lines. This is a vortex electric field.

The induced emf in a stationary conductor placed in an alternating magnetic field is equal to the work of the vortex electric field moving charges along this conductor.

Toki Foucault (French physicist)

The benefits and harms of induction currents in massive conductors.

Where are ferrites used? Why don't eddy currents arise in them?

Reinforcing the material learned

- Explain the nature of external forces acting in stationary conductors.

Difference between electrostatic and vortex electric fields.

Pros and cons of Foucault currents.

Why don't eddy currents occur in ferrite cores?

Calculate the induced emf in the conductor circuit if the magnetic flux changed by 0.06 Wb in 0.3 s.

The following can occur through a circuit: 1) in the case of a stationary conducting circuit placed in a time-varying field; 2) in the case of a conductor moving in a magnetic field, which may not change over time. The value of the induced emf in both cases is determined by the law (2.1), but the origin of this emf is different.

Let us first consider the first case of the occurrence of an induction current. Let's place a circular wire coil of radius r in a time-varying uniform magnetic field (Fig. 2.8). Let the magnetic field induction increase, then the magnetic flux through the surface limited by the coil will increase with time. According to the law of electromagnetic induction, an induced current will appear in the coil. When the magnetic field induction changes according to a linear law, the induction current will be constant.

What forces make the charges in the coil move? The magnetic field itself, penetrating the coil, cannot do this, since the magnetic field acts exclusively on moving charges (this is how it differs from the electric one), and the conductor with the electrons in it is motionless.

In addition to the magnetic field, charges, both moving and stationary, are also affected by an electric field. But those fields that have been discussed so far (electrostatic or stationary) are created by electric charges, and the induced current appears as a result of the action of a changing magnetic field. Therefore, we can assume that electrons in a stationary conductor are driven by an electric field, and this field is directly generated by a changing magnetic field. This establishes a new fundamental property of the field: changing over time, the magnetic field generates an electric field . This conclusion was first reached by J. Maxwell.

Now the phenomenon of electromagnetic induction appears before us in a new light. The main thing in it is the process of generating an electric field by a magnetic field. In this case, the presence of a conducting circuit, for example a coil, does not change the essence of the process. A conductor with a supply of free electrons (or other particles) plays the role of a device: it only allows one to detect the emerging electric field.

The field sets electrons in motion in the conductor and thereby reveals itself. The essence of the phenomenon of electromagnetic induction in a stationary conductor is not so much the appearance of an induction current, but rather the appearance of an electric field that sets electric charges in motion.

The electric field that arises when the magnetic field changes has a completely different nature than the electrostatic one.

It is not directly connected with electric charges, and its lines of tension cannot begin and end on them. They do not begin or end anywhere at all, but are closed lines, similar to magnetic field induction lines. This is the so called vortex electric field (Fig. 2.9).

The faster the magnetic induction changes, the greater the electric field strength. According to Lenz's rule, with increasing magnetic induction, the direction of the electric field intensity vector forms a left screw with the direction of the vector. This means that when a screw with a left-hand thread rotates in the direction of the electric field strength lines, the translational movement of the screw coincides with the direction of the magnetic induction vector. On the contrary, when the magnetic induction decreases, the direction of the intensity vector forms a right screw with the direction of the vector.

The direction of the tension lines coincides with the direction of the induction current. The force acting from the vortex electric field on the charge q (external force) is still equal to = q. But in contrast to the case of a stationary electric field, the work of the vortex field in moving the charge q along a closed path is not zero. Indeed, when a charge moves along a closed line of electric field strength, the work on all sections of the path has the same sign, since the force and movement coincide in direction. The work of a vortex electric field when moving a single positive charge along a closed stationary conductor is numerically equal to the induced emf in this conductor.

Induction currents in massive conductors. Induction currents reach a particularly large numerical value in massive conductors, due to the fact that their resistance is low.

Such currents, called Foucault currents after the French physicist who studied them, can be used to heat conductors. The design of induction furnaces, such as microwave ovens used in everyday life, is based on this principle. This principle is also used for melting metals. In addition, the phenomenon of electromagnetic induction is used in metal detectors installed at the entrances to airport terminal buildings, theaters, etc.

However, in many devices the occurrence of Foucault currents leads to useless and even unwanted energy losses due to heat generation. Therefore, the iron cores of transformers, electric motors, generators, etc. are not made solid, but consist of separate plates isolated from each other. The surfaces of the plates must be perpendicular to the direction of the vortex electric field strength vector. The resistance to electric current of the plates will be maximum, and the heat generation will be minimal.

Application of ferrites. Electronic equipment operates in the region of very high frequencies (millions of vibrations per second). Here, the use of coil cores from separate plates no longer gives the desired effect, since large Foucault currents arise in the calede plate.

In § 7 it was noted that there are magnetic insulators - ferrites. During magnetization reversal, eddy currents do not arise in ferrites. As a result, energy losses due to heat generation in them are minimized. Therefore, cores of high-frequency transformers, magnetic antennas of transistors, etc. are made from ferrites. Ferrite cores are made from a mixture of powders of starting substances. The mixture is pressed and subjected to significant heat treatment.

With a rapid change in the magnetic field in an ordinary ferromagnet, induction currents arise, the magnetic field of which, in accordance with Lenz's rule, prevents a change in the magnetic flux in the coil core. Because of this, the magnetic induction flux remains virtually unchanged and the core does not remagnetize. In ferrites, eddy currents are very small, so they can be quickly remagnetized.

Along with the potential Coulomb electric field, there is a vortex electric field. The intensity lines of this field are closed. The vortex field is generated by a changing magnetic field.

1. What is the nature of external forces that cause the appearance of induced current in a stationary conductor!
2. What is the difference between a vortex electric field and an electrostatic or stationary one!
3. What are Foucault currents!
4. What are the advantages of ferrites compared to conventional ferromagnets!

Myakishev G. Ya., Physics. 11th grade: educational. for general education institutions: basic and profile. levels / G. Ya. Myakishev, B. V. Bukhovtsev, V. M. Charugin; edited by V. I. Nikolaeva, N. A. Parfentieva. - 17th ed., revised. and additional - M.: Education, 2008. - 399 p.: ill.

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