Maxwell's basic theories for the electric field. Electromagnetic field

1. general characteristics Maxwell's theory for the electromagnetic field.

Bias current

2. Law of total current according to Maxwell

3. Maxwellian interpretation of the phenomenon of electromagnetic induction

4. Maxwell's system of equations in integral form for a magnetic field

1. General characteristics of Maxwell's theory for the electromagnetic field. Bias current

In previous lectures, we considered the basic laws of electrical and magnetic phenomena. These laws, as we have seen, are generalizations of experimental facts. At the same time, they described separately electrical and magnetic phenomena. In the 60s of the last century, Maxwell, based on Faraday's ideas about electric and magnetic fields, generalized these laws and developed a complete theory of a unified electromagnetic field.

Maxwell's theory is a macroscopic theory. It considers electric and magnetic fields created by macroscopic charges and currents without taking into account the internal mechanisms associated with vibrations of atoms or electrons.. Therefore, the distances from the sources of the fields to the considered points of space are assumed to be much larger compared to the sizes of the molecules. Besides,the frequency of oscillations of electric and magnetic fields in this theory is taken to be much lower than the frequency of intramolecular oscillations.In Maxwell's works, Faraday's idea of ​​a close connection between electrical and magnetic phenomena was finally formalized in the form of two main provisions and was expressed in strict form in the form of Maxwell's equations (1873).

The main achievements of Maxwell's theory are substantiation of the idea that:

An alternating electric field excites a vortex magnetic field;

An alternating magnetic field excites a vortex electric field.

Bias current

Analyzing various electromagnetic processes, Maxwell came to the conclusion that any change electric field should give rise to a magnetic field. This statement is one of the main provisions of Maxwell's theory and expresses the most important property of the electromagnetic field.

Consider the following experiment: we place a dielectric between the plates of a flat capacitor charged with a surface charge density.

The electric field inside the capacitor is uniform and the electric induction vector is equal to:

. (1)

Connect the capacitor plates with an external conductor. Since there is a potential difference between the capacitor plates, a current will flow through the conductor:. At the boundaries of the plates, the streamlines are perpendicular to their surfaces and the current density is equal to:

(2) if, then.

Taking into account formula (1), we obtain the formula for the conduction current density

. (3)

As the capacitor discharges, the electric field in it weakens. Therefore, the derivative of induction will have a negative sign, and the vector will be directed oppositely. Those. the direction of the vector will coincide with the direction of the current density vector. Therefore, formula (3) can be written in vector form:

. (4)

The left side of equation (4) characterizes the electric conduction current, and the right side characterizes the rate of change of the electric field in the dielectric. The equality of these two vectors at the metal dielectric boundary shows that the lines of the vector, as it were, continue the current lines through the dielectric and close the current. That's whythe derivative of electric induction with respect to time is called by Maxwell the displacement current density

. (5)

So, in the experimentthe conduction current passes in the dielectric into a displacement current(i.e. into a changing electric field).

If we use the formula for the relationship between induction, intensity and polarization R substance, then the following formula can be obtained for the displacement current density:

. (6)

The first term on the right side of formula (6) determines the variable field of free charges (an alternating electric field in vacuum). The second term is the rate of change in the polarization of the dielectric with time, associated with the displacement of its charges when the field strength changes. The movement of charges in an electric field within molecular dimensions is ordered and is called the polarization component of the displacement current. This explains the origin of the termdisplacement current current due to the displacement of charges in a dielectric placed in an alternating electric field.

When the polarization is reversed, the molecules "turn" behind the changing field and collide with neighboring molecules. As a result of such collisions, the dielectric heats up. That.displacement current can be registered by its thermal action. In addition, like any current, currentdisplacement creates a magnetic field. Direct observation of the magnetic field generated by the displacement current was carried out by the Russian scientist Eichenwald.

In his experiment, a dielectric disk was placed between the plates of two flat capacitors, and rotated around an axis. The capacitor plates were connected to a voltage source so that the halves of the dielectric were polarized in opposite directions. With each revolution of the disk, the direction of polarization of each of the parts is reversed. As a result of such repolarization of the dielectric during its rotation, a polarization current arises in it, directed parallel to the axis of rotation. The magnetic field of this current was detected from the deflection of a magnetic needle placed near the axis of the disk.

2. Law of total current for a magnetic field according to Maxwell

In general, conduction currents and displacement current are not separated in space, as is the case in a capacitor. All types of currents can exist in the same volume and one can speak of a total current equal to the sum of the conduction currents (macrocurrents) and the displacement current. In integral form for the total current, one can write

. (7)

Depending on the electrical conductivity of the medium and the frequency of electric field oscillations, both terms in formula (7) make different contributions to the value of the total current. In highly conductive substances (metals) and at low frequencies, the bias current can be neglected in comparison with the conduction current. In conductors, the displacement current appears at high frequencies. On the contrary, in poorly conducting media (dielectrics), the displacement current plays a major role. Here it should be noted the practical use of the bias current for induction hardening of materials.

Both terms in formula (7) can have either the same or opposite signs. So that the total current can be either greater or less than the conduction current.

Taking into account the presence of a bias current in the medium,the total current law for a magnetic field in a substance according to Maxwell is written in the following form

. (8)

Formula (8) of the law of the total current according to Maxwell differs from the formulas obtained earlier in that it allows one to proceed to the description of alternating electric and magnetic fields.

3. Faraday and Maxwellian interpretations of the phenomenon of electromagnetic induction

If a conducting circuit is placed in an alternating magnetic field, then an emf will appear in it. This phenomenon is called electromagnetic induction and is described by Faraday's law

. (9)

Taking into account that and we write the law of electromagnetic induction in a different form

Or. (10)

Explaining the phenomenon of electromagnetic induction, Faraday assumed that an alternating magnetic field createsin a conductive circuitvortex electric field.

Maxwell generalized this result and gave his interpretation of electromagnetic induction:

an alternating magnetic field creates a vortex electric field at any point in space, regardless of the presence of a conductor in it.

4. Maxwell's equations for the electromagnetic field in integral form

Generalizing the previously obtained relations to the case of variable fields, Maxwell obtained a system of equations

Law of electromagnetic induction

Full current law

Gauss's theorem for electric field

Gauss theorem for magnetic field

Relationship of electrical induction with tension

Relationship of magnetic induction with intensity

Ohm's law in differential form

5. Consequences from Maxwell's equations

A number of important consequences follow from Maxwell's equations.

1. It follows from the first equation that the source of the electric field can be not only electric charges, but also an alternating magnetic field.

An alternating magnetic field can generate a vortex electric field notonly in a conductor, but also in a vacuum.

2. It follows from the second equation that the magnetic field can be excited both by macrocurrent (electrical conduction current) and by displacement current. Excitation occurs according to the same law. Therefore, these two factors are indistinguishable. In this case, in the field region where there are no macrocurrents, the equation has the form

Those. the magnetic field can only be generated by a displacement current. Moreover, in the absence of the polarization component of the bias currenta magnetic field can be generated by an alternating electric field in a vacuum.The latter is one of the most important consequences of Maxwell's theory. Based on this, Maxwell theoretically predicted the existence of electromagnetic waves. Qualitatively, the appearance of a wave can be explained with the help of a figure. An alternating electric field that has arisen in one place generates a magnetic field, which in turn generates an electric field, and so on. Thus, an alternating electromagnetic field arises, which propagates in space in the form of an electromagnetic wave at the speed of light. Further theoretical studies of the properties of electromagnetic waves led Maxwell to the creation of an electromagnetic theory of light. In an electromagnetic wave, the vectors E and H oscillate in the same phase.

Questions for self-examination:

1. What is displacement current? What is displacement current?
2. What is the form of the total current law for a magnetic field according to Maxwell?
3. What is the difference between Maxwell's interpretation of the phenomenon of electromagnetic induction and Faraday's interpretation?
4. List the main consequences of Maxwell's equations.

+σ

- σ

The nature of the movement of electrons

The directions of the vectors follow the rule

Lenz

Having generalized the basic experimental laws of electricity and magnetism, Maxwell created a unified theory of the electromagnetic field. In electrodynamics, Maxwell's theory plays the same role as Newton's laws in classical mechanics. She allowed not only to explain with unified positions already known facts, but also to predict the existence of electromagnetic waves.

A fundamentally new idea put forward by Maxwell was the idea of ​​mutual transformations of electric and magnetic fields. Generalizing Faraday's law for electromagnetic induction, Maxwell suggested that the changing magnetic field generates a vortex electric field, the circulation of the intensity vector of which is determined by the equation

. (3.1)

In turn, one should expect that a time-varying electric field should create an alternating magnetic field. To establish a quantitative relationship between the changing electric and magnetic fields caused by it, Maxwell introduced the concept of displacement current. Considering a capacitor in an alternating current circuit, he suggested that the conduction current is closed in the capacitor by a bias current. The displacement current is a changing electric field and is not accompanied by movement electric charges, but it is capable of creating a magnetic field, like a conduction current. The bias current density is

, (3.2)

Where is the electric displacement vector.

The sum of the conduction current and the displacement current is called full current, its density is

. (3.3)

The introduction of the total current makes it possible to generalize the theorem on the circulation of the magnetic field strength, presenting it in the form

(3.4)

From given equation It follows that a magnetic field can be excited not only by moving charges, but also by changes in the electric field, just as an electric field can be excited not only by electric charges, but also by changes in the magnetic field.

To the considered equations (3.1 and 3.4) Maxwell added two more equations expressing the Gauss theorem for the vectors and electromagnetic field

(3.5)

. (3.6)

In the 60s of the last century (around 1860), Maxwell, based on the ideas of Faraday, generalized the laws of electrostatics and electromagnetism: the Gauss–Ostrogradsky theorem for an electrostatic field and for a magnetic field; total current law; the law of electromagnetic induction, and as a result developed a complete theory of the electromagnetic field.

Maxwell's theory was the greatest contribution to the development of classical physics. It made it possible to understand a wide range of phenomena from a unified point of view, ranging from the electrostatic field of stationary charges to the electromagnetic nature of light.

Maxwell's four equations serve as a mathematical expression of Maxwell's theory. which are usually written in two forms: integral and differential. Differential equations are obtained from integral equations using two theorems of vector analysis - the Gauss theorem and the Stokes theorem. Gauss theorem:

- vector projections on the axes; V- volume bounded by a surface S.

Stokes' theorem: . (3)

Here rot- vector rotor , which is a vector and is expressed in Cartesian coordinates as follows: , (4)

S- area bounded by a contour L.

Maxwell's equations in integral form express relationships that are valid for immobile closed contours and surfaces mentally drawn in an electromagnetic field.

Maxwell's equations in differential form show how the characteristics of the electromagnetic field and the density of charges and currents at each point of this field are related.

12.1. Maxwell's first equation

It is a generalization of the law of electromagnetic induction ,

and in integral form has the following form (5)

and claims that a vortex electric field is inextricably linked with an alternating magnetic field, which does not depend on whether there are conductors in it or not. From (3) it follows that . (6)

From comparison (5) and (6) we find that (7)

This is the first Maxwell equation in differential form.

12.2. bias current. Maxwell's second equation

Maxwell generalized the total current law by assuming that an alternating electric field, like an electric current, is a source of a magnetic field. For quantitative characteristics"magnetic action" of an alternating electric field Maxwell introduced the concept bias current.

According to the Gauss-Ostrogradsky theorem, the electric displacement flux through a closed surface

Differentiating this expression with respect to time, we obtain for a fixed and non-deformable surface S (8)

The left side of this formula has the dimension of current, which, as is known, is expressed in terms of the current density vector . (9)

From comparison (8) and (9) it follows that has the dimension of current density: A /m 2 . Maxwell proposed to call the displacement current density:

Bias current . (11)

Of all the physical properties inherent in the real current (conduction current) associated with the transfer of charges, the displacement current has only one: the ability to create a magnetic field. When the bias current "flows" in a vacuum or dielectric, no heat is generated. An example of a bias current is an alternating current through a capacitor. In the general case, conduction and displacement currents are not separated in space, and we can speak of a total current equal to the sum of conduction and displacement currents: (12)

With this in mind, Maxwell generalized the total current law by adding the displacement current to the right side of it. (13)

So, the second Maxwell equation in integral form has the form:

From (3) it follows that . (15)

From comparison (14) and (15) we find that . (16)

This is the second Maxwell equation in differential form.

12.3. Third and fourth Maxwell equations

Maxwell generalized the Gauss-Ostrogradsky theorem for the electrostatic field. He suggested that this theorem is valid for any electric field, both stationary and variable. Accordingly, the third Maxwell equation in integral form has the form: . (I7) or . (18)

Where - bulk density of free charges, \u003d C / m 3

From (1) it follows that . (19)

From comparison (18) and (19) we find that . (20)

Maxwell's fourth equation in integral and differential forms has

the following form: , (21) . (22)

12.4. Complete system of Maxwell's equations in differential form

This system of equations must be supplemented with material equations characterizing the electrical and magnetic properties of the medium:

, , . (24)

So, after the discovery of the relationship between electric and magnetic fields, it became clear that these fields do not exist in isolation, independently of each other. It is impossible to create an alternating magnetic field without simultaneously generating an electric field in space.

Note that an electric charge at rest in a certain frame of reference creates only an electrostatic field in this frame of reference, but it will create a magnetic field in the frames of reference with respect to which it moves. The same applies to a fixed magnet. Note also that Maxwell's equations are invariant to Lorentz transformations: moreover, for inertial frames of reference TO And TO' the following relations hold: , . (25)

Based on the foregoing, we can conclude that electric and magnetic fields are a manifestation of a single field, which is called the electromagnetic field. It propagates in the form of electromagnetic waves.

When writing the lecture notes, well-known textbooks on physics were used, published in the period from 1923 (Khvolson O.D. "Course of Physics") to the present day (Detlaf A.A., Yavorsky B.M., Savelyev I.V., Sivukhin D.V., Trofimova T.I., Sukhanov A.D., etc.)

PHYSICS EXAM PREPARATION QUESTIONS

1. Electric charge. charge discreteness. The law of conservation of charge. Coulomb's law (1.1, 1.2)*.

2. Electric field. Electric field strength of a point charge (1.3).

3. The principle of superposition of electric fields. Field lines (1.4).

4. Electric dipole. Electric dipole field (1.5).

5. Moment of force acting on a dipole in an electric field. Dipole energy in an electric field (1.5).

6. The flow of the intensity vector. Gauss-Ostrogradsky theorem for an electrostatic field in vacuum (2.1, 2.2).

7. The field of a uniformly charged, infinitely extended field. Field between two infinitely extended oppositely charged parallel planes (2.2.1, 2.2.2).

8. The field of a charged cylinder. The field of a charged sphere (2.2.3, 2.2.4).

9. The work of the forces of the electrostatic field. Circulation of the electric field strength vector (3.1).

10. Potential nature of the electrostatic field. Potential (conclusion 3.1, 3.2).

11. Potential of the field of a point charge and the field created by the system point charges. Potential difference (3.2).

12. Equipotential surfaces (3.3).

13. Relationship between electric field strength and potential (3.4).

14. Electric field in dielectrics. Polar and non-polar dielectrics. Dipole moment of dielectric (4, 4.1).

15. Polarization of dielectrics: orientational and ionic. Polarization vector (4.2).

17. The Gauss-Ostrogradsky theorem for a field in a dielectric. Relationship of the vectors - displacement, - intensity and - polarization (4.4).

18. Conductors in an electrostatic field (5.5.1).

19. Electric capacitance of a solitary conductor. The electrical capacitance of the capacitor. Flat capacitor (5.2).

20. Energy of a charged conductor, a system of charged conductors and a capacitor (5.3).

21. Electric field energy. Volume energy density of the electric field in dielectric and vacuum (5.4).

22. Electric current. Electric current characteristics: current strength, current density vector (6.1).

23. Electromotive force of the current source. Voltage (6.2).

24. Ohm's law for a homogeneous section of the chain. Electrical resistance, resistivity. The dependence of the resistance of conductors on temperature (6.3.1).

25. Ohm's law in differential form. Electrical conductivity (6.3.2).

26. Ohm's law for an inhomogeneous section of the chain. Ohm's law for a closed circuit (6.4).

27. Joule-Lenz law. Work and current power. Source efficiency (6.5).

28. Joule-Lenz law in differential form (6.6).

29. Magnetic field in vacuum. Magnetic moment of a circuit with current. Magnetic induction vector. Force lines of the magnetic field (8.1).

30. Law of Biot-Savart-Laplace. Principle of superposition of magnetic fields (8.3).

31. Direct current magnetic field (8.3.1).

32. Magnetic field of circular current (8.3.2).

33. The theorem on the circulation of the vector of magnetic induction. Vortex character of the magnetic field (9.1).

34. Magnetic field of the solenoid (9.1.1).

35. Magnetic flux. Gauss theorem for magnetic field (9.2).

36. Work of moving a conductor with current in a constant magnetic field (9.3).

37. Action of a magnetic field on a moving charge. Lorentz forces (8.2, 9.4).

38. Magnetic field in matter. Magnetic moments of atoms. Magnetization vector. Magnetic field strength. Magnetic permeability of matter (10.1, 10.2).

39. The theorem on the circulation of the magnetic field vector (10.3).

40. Types of magnets: diamagnets, paramagnets, ferromagnets. Magnetic permeability and magnetic field of magnets (10.4).

41. The law of electromagnetic induction. Lenz's law (11.1).

42. The phenomenon of self-induction. Inductance. Electromotive force of self-induction (11.2).

43. Currents when opening and closing the circuit (11.3).

44. Energy of the magnetic field. Volumetric energy density of the magnetic field (11.4).

45. Maxwell's first equation (12.1).

46. ​​Bias current. The second Maxwell equation (12.2).

47. Third and fourth Maxwell equations (12.3).

48. Complete system of Maxwell's equations in differential form. Material equations (12.4).

* In the designation (1.1., 1.2), the first digit means the number of the lecture, and the second - the number of the paragraph in this lecture, where the material on this issue is presented.

By about 1860, thanks to the work of Neumann, Weber, Helmholtz and Felici (see § 11), electrodynamics was already considered a science finally systematized, with clearly defined boundaries. The main research now seemed to have to follow the path of finding and deriving all the consequences from the established principles and their practical application, which the inventive techniques had already embarked on.

However, the prospect of such a quiet work was violated by the young Scottish physicist James Clark Maxwell (1831-1879), pointing to a much wider area of ​​application of electrodynamics. With good reason, Duhem wrote:

“No logical necessity pushed Maxwell to invent a new electrodynamics; he was guided only by some analogies and the desire to complete the work of Faraday in the same spirit as the works of Coulomb and Poisson were completed by Ampère's electrodynamics, and also, perhaps, by an intuitive sense of the electromagnetic nature of light " (P. Duhem, Les theories electriques de J. Clerk Maxwell, Paris, 1902, p. 8).

Perhaps the main motivation that made Maxwell take up work that was not at all required by the science of those years was admiration for Faraday's new ideas, so original that the scientists of that time were not able to perceive and assimilate them. To a generation of theoretical physicists, brought up on the concepts and mathematical elegance of the works of Laplace, Poisson and Ampère, Faraday's thoughts seemed too vague, and to experimental physicists - too sophisticated and abstract. A strange thing happened: Faraday, who was not a mathematician by training (he started his career as a peddler in a bookshop and then joined Davy's laboratory as a half-assistant-half-service), felt an urgent need to develop some theoretical method as effective as and mathematical equations. Maxwell guessed it.

“Having begun to study the work of Faraday,” Maxwell wrote in the preface to his famous Treatise, “I found that his method of understanding phenomena was also mathematical, although not presented in the form of ordinary mathematical symbols. I have also found that this method1 can be expressed in the usual mathematical form and thus compared with the methods of professional mathematicians. So, for example, Faraday saw lines of force penetrating all space, where mathematicians saw centers of forces attracting at a distance; Faraday saw the medium where they saw nothing but distance; Faraday assumed the source and cause of phenomena in real actions occurring in a medium, but they were satisfied that they found them in the force of action at a distance attributed to electric fluids.

When I translated what I considered Faraday's ideas into mathematical form, I found that in most cases the results of both methods coincided, so that they explained the same phenomena and derived the same laws of action, but that Faraday's methods were like those in which we start from the whole and arrive at the particular by analysis, while the ordinary mathematical methods are based on the principle of moving from particulars and building the whole by synthesis.

I also found that many of the fruitful methods of investigation discovered by mathematicians could be expressed much better with the help of ideas arising from the works of Faraday than in their original form ”( J. Clerk Maxwell, A Treatise on Electricity and Magnetism, London, 1873; 2nd ed., Oxford, 1881.).

As for mathematical method Faraday, Maxwell notes elsewhere that mathematicians, who considered Faraday's method devoid of scientific precision, themselves did not come up with anything better than using hypotheses about the interaction of things that do not have physical reality, such as current elements, “which arise from nothing, pass through a section of wire and then again turn into nothing.

To give Faraday's ideas a mathematical form, Maxwell began by creating the electrodynamics of dielectrics. Maxwell's theory is directly related to Mossotti's theory. While Faraday, in his theory of dielectric polarization, deliberately left open the question of the nature of electricity, Mossotti, a supporter of Franklin's ideas, imagines electricity as a single fluid, which he calls ether and which, in his opinion, is present with a certain degree of density in all molecules. . When a molecule is under the action of an inductive force, the ether is concentrated at one end of the molecule and rarefied at the other; because of this, a positive force arises at the first end and an equal negative force at the second. Maxwell fully accepts this concept. In his Treatise, he writes:

“The electric polarization of a dielectric is a state of deformation into which the body comes under the action of an electromotive force and which disappears simultaneously with the termination of this force. We can think of it as something that can be called an electrical displacement produced by an electromotive force. When an electromotive force acts in a conducting medium, it induces a current there, but if the medium is non-conductive or dielectric, then the current cannot pass through this medium. Electricity, however, is displaced in it in the direction of the electromotive force, and the magnitude of this displacement depends on the magnitude of the electromotive force. If the electromotive force increases or decreases, then the electric displacement increases or decreases correspondingly in the same proportion.

The amount of displacement is measured by the amount of electricity that crosses a unit area as the displacement increases from zero to a maximum value. Such, therefore, is the measure of electric polarization.

If a polarized dielectric consists of a collection of conducting particles scattered in an insulating medium, on which electricity is distributed in a certain way, then any change in the state of polarization must be accompanied by a change in the distribution of electricity in each particle, i.e., a real electric current, though limited only by the volume of the conducting particle. In other words, each change in the state of polarization is accompanied by a bias current. In the same Treatise, Maxwell says:

“Changes in electrical displacement obviously cause electrical currents. But these currents can only exist during a change in displacement, and since the displacement cannot exceed a certain amount without causing a destructive discharge, these currents cannot continue indefinitely in the same direction, like currents in conductors..

After Maxwell introduces the concept of field strength, which is a mathematical interpretation of the Faraday concept of the field of forces, he writes down the mathematical relationship for the mentioned concepts of electric displacement and displacement current. He concludes that the so-called charge of a conductor is surface charge surrounding dielectric, that energy is stored in the dielectric in the form of a state of voltage, that the movement of electricity is subject to the same conditions as the movement of an incompressible fluid. Maxwell himself summarizes his theory thus:

“The energy of electrization is concentrated in a dielectric medium, whether it be a solid, liquid or gas, a dense medium, or rarefied, or completely devoid of weighty matter, so long as it is able to transmit electrical action.

Energy is contained in each point of the medium in the form of a state of deformation, called electric polarization, the magnitude of which depends on the electromotive force acting at that point ...

In dielectric liquids, electric polarization is accompanied by tension in the direction of the induction lines and an equal pressure in all directions perpendicular to the induction lines; the magnitude of this tension or pressure per unit area is numerically equal to the energy per unit volume at that point.”

It is difficult to express more clearly the main idea of ​​this approach, which is the idea of ​​Faraday: the place in which electrical phenomena occur is the environment. As if to emphasize that this is the main thing in his treatise, Maxwell ends it with the following words:

“If we accept this environment as a hypothesis, I believe that it should occupy a prominent place in our studies and that we should try to construct a rational idea of ​​all the details of its operation, which was my constant goal in this treatise”.

Having substantiated the theory of dielectrics, Maxwell transferred its concepts with the necessary corrections to magnetism and created the theory of electromagnetic induction. He summarizes his entire theoretical construction in several equations that have now become famous: in Maxwell's six equations.

These equations are very different from the usual equations of mechanics - they determine the structure of the electromagnetic field. While the laws of mechanics apply to areas of space in which matter is present, Maxwell's equations apply to all of space, whether or not bodies or electric charges are present. They determine the changes in the field, while the laws of mechanics determine the changes in material particles. In addition, Newtonian mechanics refused, as we said in Chap. 6, from the continuity of action in space and time, while Maxwell's equations establish the continuity of phenomena. They connect events that are adjacent in space and time: given the state of the field "here" and "now" we can deduce the state of the field in close proximity at close times. Such an understanding of the field is absolutely consistent with Faraday's idea. but is in insurmountable contradiction with the two-century tradition. Therefore, it is not surprising that it met with resistance.

The objections that were put forward against Maxwell's theory of electricity were numerous and were treated as fundamental concepts underlying theory, and, perhaps even more so, to the too free manner that Maxwell uses in deriving consequences from it. Maxwell builds his theory step by step with the help of "sleight of fingers", as Poincaré aptly put it, referring to the theological stretches that scientists sometimes allow themselves to formulate new theories. When, in the course of an analytic construction, Maxwell encounters an obvious contradiction, he does not hesitate to overcome the era with the help of discouraging liberties. For example, it doesn't cost him anything to exclude a member, replace an inappropriate sign of an expression with a reverse, change the meaning of a letter. For those who admired the infallible logic of Ampère's electrodynamics, Maxwell's theory must have made an unpleasant impression. Physicists failed to bring it into order, that is, to free it from logical errors and inconsistencies. But. on the other hand, they could not abandon the theory, which, as we shall see later, organically connected optics with electricity. Therefore, at the end of the last century, the leading physicists adhered to the thesis put forward in 1890 by Hertz: since the reasoning and calculations by which Maxwell arrived at his theory of electromagnetism are full of errors that we cannot correct, let us accept Maxwell's six equations as the initial hypothesis, as postulates on which the whole theory of electromagnetism will be based. "The main thing in Maxwell's theory is Maxwell's equations," Hertz says.

21. ELECTROMAGNETIC THEORY OF LIGHT

The formula found by Weber for the force of interaction of two electric charges moving relative to each other includes a coefficient that has the meaning of a certain speed. Weber himself and Kohlrausch determined the value of this speed experimentally in the work of 1856, which became a classic; this value turned out to be somewhat more speed Sveta. The following year, Kirchhoff "from Weber's theory derived the law of propagation of electrodynamic induction along a wire: if the resistance is zero, then the speed of propagation of an electric wave does not depend on the cross section of the wire, on its nature and the density of electricity and is almost equal to the speed of propagation of light in a vacuum. Weber, in one of his theoretical and experimental works in 1864, confirmed the results of Kirchhoff, showing that the Kirchhoff constant is quantitatively equal to the number of electrostatic units contained in an electromagnetic unit, and noted that the coincidence of the propagation velocity of electric waves and the speed of light can be considered as an indication of there is a close connection between the two phenomena. However, before talking about this, one should first find out exactly what is the true meaning of the concept of the speed of propagation of electricity: "and this meaning," Weber concludes melancholy, "is not at all such as to arouse great hopes."

Maxwell did not have any doubts, perhaps because he found support in Faraday's ideas regarding the nature of light (see § 17).

“In various places of this treatise,” writes Maxwell, starting in Chapter XX of the fourth part to present the electromagnetic theory of light, “an attempt was made to explain electromagnetic phenomena by means of a mechanical action transmitted from one body to another through a medium that occupies the space between these bodies. The wave theory of light also allows for the existence of some kind of medium. We must now show that the properties of the electromagnetic medium are identical with those of the luminiferous medium...

We can obtain a numerical value for certain properties of a medium, such as the speed with which a disturbance propagates through it, which can be calculated from electromagnetic experiments and also observed directly in the case of light. If it were found that the speed of propagation of electromagnetic disturbances is the same as the speed of light, not only in air, but also in other transparent media, we would get a good reason to consider light as an electromagnetic phenomenon, and then the combination of optical and electrical evidence will give the same proof of the reality of the environment, which we receive in the case of other forms of matter on the basis of the totality of evidence from our senses" ( Ibid. pp. 550-551 of the Russian edition).

As in the first work of 1864, Maxwell proceeds from his equations and, after a series of transformations, comes to the conclusion that in vacuum, transverse displacement currents propagate at the same speed as light, which "represents a confirmation of the electromagnetic theory of light" - Maxwell confidently states.

Then Maxwell studies the properties of electromagnetic disturbances in more detail and comes to conclusions that are already well known today: an oscillating electric charge creates an alternating electric field, inextricably linked with an alternating magnetic field; this is a generalization of Oersted's experience. Maxwell's equations make it possible to trace the changes in the field over time at any point in space. The result of such a study shows that electric and magnetic oscillations arise at each point in space, i.e., the intensity of the electric and magnetic fields changes periodically; these fields are inseparable from each other and polarized mutually perpendicular. These oscillations propagate in space at a certain speed and form a transverse electromagnetic wave: electrical and magnetic oscillations at each point occur perpendicular to the direction of wave propagation.

Among the many particular consequences arising from Maxwell's theory, we mention the following: the statement that the dielectric constant is equal to the square of the refractive index of optical rays in a given medium, which has been especially often criticized; the presence of light pressure in the direction of light propagation; orthogonality of two polarized waves - electric and magnetic.

22. ELECTROMAGNETIC WAVES

In § 11 we have already said that the oscillatory nature of the discharge of the Leyden jar has been established. This phenomenon from 1858 to 1862 was again subjected to careful analysis by Wilhelm Feddersen (1832-1918). He noticed that if two capacitor plates are connected by a small resistance, then the discharge is oscillatory in nature and the duration of the oscillation period is proportional to the square root of the capacitance of the capacitor. In 1855, Thomson deduced from potential theory that the period of oscillation of an oscillating discharge is proportional to the square root of the product of the capacitance of a capacitor and its coefficient of self-induction. Finally, in 1864, Kirchhoff gave the theory of an oscillatory discharge, and in 1869, Helmholtz showed that similar oscillations can also be obtained in an induction coil, the ends of which are connected to the capacitor plates.

In 1884, Heinrich Hertz (1857-1894), a former student and assistant of Helmholtz, began to study Maxwell's theory (see Ch. 12). In 1887 he repeated Helmholtz's experiments with two induction coils. After several attempts, he managed to stage his classical experiments, which are now well known. With the help of a “generator” and a “resonator”, Hertz experimentally proved (in a way that is described in all textbooks today) that an oscillatory discharge causes waves in space, consisting of two oscillations - electric and magnetic, polarized perpendicular to each other. Hertz also established the reflection, refraction and interference of these waves, showing that all his experiments are fully explainable by Maxwell's theory.

Many experimenters rushed along the path discovered by Hertz, but they did not manage to add much to understanding the similarity of light and electric waves, because, using the same wavelength that Hertz took (about 66 cm), they came across diffraction phenomena that obscured all others. effects. To avoid this, installations of such large sizes were needed, which were practically unrealizable at that time. A big step forward was made by Augusto Righi (1850-1920), who, with the help of a new type of generator he created, managed to excite waves several centimeters long (most often he worked with waves 10.6 cm long). Thus, Righi managed to reproduce all optical phenomena with the help of devices that are basically analogues of the corresponding optical instruments. In particular, Rigi was the first to obtain double refraction of electromagnetic waves. The works of Riga, begun in 1893 and described from time to time in notes and articles published in scientific journals, were then combined and supplemented in the now classic book"Ottica delle oscillazioni elettriche" ("Optics of electrical oscillations"), published in 1897, whose title alone expresses the content of an entire era in the history of physics.

The ability of a metal powder placed in a tube to become conductive under the action of a discharge from a nearby electrostatic machine was studied by Snez (1853-1922) in 1884, and ten years later this ability was used by Dodge a.d. and many others to indicate electromagnetic waves. Combining the Riga generator and the Demolish indicator with the ingenious ideas of "antenna" and "grounding", at the end of 1895 Guglielmo Marconi (1874-1937) successfully carried out the first practical experiments ( As you know, the priority in the invention of radio belongs to the Russian scientist A.S. Popov, who read on May 7, 1895 at a meeting of the Physics Department of the Russian Physical and Chemical Society) in the field of radiotelegraphy, the rapid development and amazing results of which truly border on a miracle.

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As a result of studying this chapter, the student should:

know

• empirical and theoretical foundations of the electromagnetic field theory;
• the history of the creation of the theory of the electromagnetic field, the history of the discovery of light pressure and electromagnetic waves;
• physical essence of Maxwell's equations (in integral and differential forms);
• the main stages of the biography of J. K. Maxwell;
• the main directions in the development of electrodynamics after J.K. Maxwell;
• J.K. Maxwell's achievements in molecular physics and thermodynamics;

be able to

• evaluate the role of Maxwell in the development of the theory of electricity and magnetism, the fundamental significance of Maxwell's equations, the place of the book "Treatise on Electricity and Magnetism" in the history of science, the historical experiments of G. Hertz and P. N. Lebedev;
• discuss the biographies of the leading scientists working in the field of electromagnetism;

own

Skills of operating with the basic concepts of the theory of the electromagnetic field.

Key terms: electromagnetic field, Maxwell's equations, electromagnetic waves, light pressure.

Faraday's discoveries revolutionized the science of electricity. With his light hand, electricity began to gain new positions in technology. Earned an electromagnetic telegraph. In the early 70s. XIX century, it already connected Europe with the USA, India and South America, the first electric current generators and electric motors appeared, electricity began to be widely used in chemistry. Electromagnetic processes invaded science ever deeper. An era has come when the electromagnetic picture of the world was ready to replace the mechanical one. A man of genius was needed who could, like Newton in his time, combine the facts and knowledge accumulated by that time and, on their basis, create a new theory describing the foundations of the new world. J.K. Maxwell became such a person.

James Clerk Maxwell(Fig. 10.1) was born in 1831. His father, John Clerk Maxwell, was clearly an outstanding man. A lawyer by profession, he, nevertheless, devoted considerable time to other things that were more interesting to him: he traveled, designed cars, set up physical experiments, and even published several scientific articles. When Maxwell was 10 years old, his father sent him to study at the Edinburgh Academy, where he stayed for six years - until entering the university. At the age of 14, Maxwell wrote the first scientific paper on the geometry of oval curves. A summary of it was published in Proceedings of the Royal Society of Edinburgh, 1846.

In 1847, Maxwell entered the University of Edinburgh, where he began to study mathematics in depth. At this time, two more scientific work gifted student were published in Proceedings of the Royal Society of Edinburgh. The content of one of them (about rolling curves) was introduced to the society by Professor Kelland, the other (about the elastic properties of solids) was first presented by the author himself.

In 1850, Maxwell continued his education at Peterhouse - St. Peter's College, Cambridge University, and from there moved to the Holy Trinity College - Trinity College, which gave the world I. Newton, and later V. V. Nabokov, B. Russell and others. In 1854 Mr. Maxwell passes the exam and receives a bachelor's degree. Then he was left at Trinity College as a teacher. However, he was more concerned with scientific problems. At Cambridge, Maxwell began to study color and color vision. In 1852, he came to the conclusion that the mixing of spectral colors does not coincide with the mixing of colors. Maxwell develops the theory of color vision, designs a color top (Fig. 10.2).

Rice. 10.1.

Rice. 10.2.

In addition to his old hobbies - geometry and color problems, Maxwell became interested in electricity. In 1854, on February 20, he wrote a letter from Cambridge to W. Thomson in Glasgow. Here is the beginning of that famous letter:

"Dear Thomson! Now that I've entered the unholy undergraduate class, I've begun to think about reading. It is very pleasant sometimes to be among deservedly recognized books that I have not yet read, but must read. But we have a strong desire to return to physical things, and some of us here want to attack electricity.”

After completing the course, Maxwell became a member of Trinity College, Cambridge University, and in 1855 became a member of the Royal Society of Edinburgh. However, he soon left Cambridge and returned to his native Scotland. Professor Forbes informed him that a vacancy for a professor of physics had opened up in Aberdeen, at Marishall College, and he had every chance of filling it. Maxwell accepted the offer and in April 1856 (at the age of 24!) took up a new position. In Aberdeen, Maxwell continued to work on the problems of electrodynamics. In 1857, he sent M. Faraday his work "On Faraday's lines of force."

Of Maxwell's other work at Aberdeen, his work on the stability of Saturn's rings was widely known. From the study of the mechanics of the rings of Saturn, it was quite natural to move on to the consideration of the motions of gas molecules. In 1859, Maxwell spoke at a meeting of the British Association for the Advancement of Sciences with a report "On the dynamical theory of gases." This report marked the beginning of his fruitful research in the field of the kinetic theory of gases and statistical physics.

In 1860, Maxwell accepted an invitation from King's College London and worked there as a professor for five years. He was not a brilliant lecturer and did not particularly enjoy lecturing. Therefore, the ensuing break in teaching was more desirable than annoying for him, and allowed him to completely immerse himself in solving fascinating problems of theoretical physics.

According to A. Einstein, Faraday and Maxwell played the same roles in the science of electricity that Galileo and Newton played in mechanics. Just as Newton gave the mechanical effects discovered by Galileo a mathematical form and physical justification, so Maxwell did the same with respect to Faraday's discoveries. Maxwell gave Faraday's ideas a rigorous mathematical form, introduced the term "electromagnetic field", and formulated mathematical laws describing this field. Galileo and Newton laid the foundations for the mechanical picture of the world, Faraday and Maxwell for the electromagnetic one.

Maxwell began to think about his ideas about electromagnetism in 1857, when the already mentioned article "On Faraday's lines of force" was written. Here he makes extensive use of hydrodynamic and mechanical analogies. This allowed Maxwell to apply the mathematical apparatus of the Irish mathematician W. Hamilton and thus express the electrodynamic relations in mathematical language. In the future, hydrodynamic analogies are replaced by methods of the theory of elasticity: the concepts of deformation, pressure, vortices, etc. Proceeding from this, Maxwell comes to the field equations, which at this stage have not yet been reduced to a single system. Investigating dielectrics, Maxwell expresses the idea of ​​"displacement current", as well as, as yet vaguely, the idea of ​​the connection between light and the electromagnetic field ("electrotonic state") in the Faraday formulation that Maxwell then used.

These ideas are set forth in the articles "On the physical lines of forces" (1861-1862). They were written during the most prolific London period (1860-1865). At the same time, Maxwell's famous articles "Dynamical Theory of the Electromagnetic Field" (1864-1865) were published, where thoughts were expressed about the unified nature of electromagnetic waves.

From 1866 to 1871 Maxwell lived at his family estate, Middleby, leaving occasionally for exams in Cambridge. Being engaged in economic affairs, Maxwell did not leave scientific studies. He worked hard on the main work of his life, "Treatise on Electricity and Magnetism", wrote the book "Theory of Heat", a number of articles on the kinetic theory of gases.

In 1871 an important event took place. At the expense of the descendants of G. Cavendish, the Department of Experimental Physics was established in Cambridge and the construction of the experimental laboratory building began, which in the history of physics is known as the Cavendish Laboratory (Fig. 10.3). Maxwell was invited to become the first professor of the department and head of the laboratory. In October 1871 he delivered an inaugural lecture on the trends and significance of experimental research in university education. This lecture became a program for teaching experimental physics for many years to come. On June 16, 1874, the Cavendish Laboratory was opened.

Since then, the laboratory has become the center of world physical science for many decades, and it is the same now. For more than a hundred years, thousands of scientists have passed through it, among them many of those who have made the glory of world physical science. After Maxwell, the Cavendish Laboratory was headed by many outstanding scientists: J. J. Thomson, E. Rutherford, L. Bragg, N. F. Mott, A. B. Pippard, and others.

Rice. 10.3.

After the publication of the "Treatise on Electricity and Magnetism", in which the theory of the electromagnetic field was formulated, Maxwell decides to write the book "Electricity in an Elementary Presentation" in order to popularize and disseminate his ideas. Maxwell worked on the book, but his health was getting worse. He died on November 5, 1879, without witnessing the triumph of his theory.

Let us dwell on the creative heritage of the scientist. Maxwell left a deep mark in all areas of physical science. Not without reason a whole series physical theories bear his name. He proposed a thermodynamic paradox that haunted physicists for many years - "Maxwell's demon". In the kinetic theory, he introduced the concepts known as: "Maxwell distribution" and "Maxwell-Boltzmann statistics". He also wrote an elegant study of the stability of Saturn's rings. In addition, Maxwell created many small scientific masterpieces in a wide variety of fields - from the implementation of the world's first color photograph to the development of a method for radically removing grease stains from clothes.

Let's move on to the discussion electromagnetic field theory- the quintessence of Maxwell's scientific creativity.

It is noteworthy that James Clerk Maxwell was born in the same year that Michael Faraday discovered the phenomenon of electromagnetic induction. Maxwell was particularly impressed by Faraday's book Experimental Investigations in Electricity.

In Maxwell's time, there were two alternative theories of electricity: Faraday's theory of "lines of force" and the theory developed by the French scientists Coulomb, Ampère, Biot, Savart, Arago and Laplace. The initial position of the latter is the idea of ​​long-range action - the instantaneous transfer of interaction from one body to another without the help of any intermediate medium. Realistically thinking Faraday could not reconcile himself with such a theory. He was absolutely convinced that "matter cannot act where it does not exist." The medium through which the action is transmitted, Faraday called the "field". The field, he believed, was permeated with magnetic and electrical "lines of force."

In 1857 Maxwell's article "On Faraday's lines of force" appeared in the Proceedings of the Cambridge Philosophical Society. It contained the entire program of research on electricity. Note that Maxwell's equations have already been written in this article, but so far without a bias current. The article "On Faraday's lines of force" required continuation. Electrohydraulic analogies have given a lot. With their help, useful differential equations. But not everything could be subordinated to electrohydraulic analogies. The most important law of electromagnetic induction did not fit into their framework. It was necessary to come up with a new auxiliary mechanism that would facilitate the understanding of the process, reflecting at the same time and forward movement currents, and the rotational, vortex nature of the magnetic field.

Maxwell proposed a special medium in which the vortices are so small that they fit inside the molecules. Rotating "molecular vortices" produce a magnetic field. The direction of the axes of the vortices of molecules coincides with their lines of force, and they themselves can be represented as thin rotating cylinders. But the external, touching parts of the vortices must move in opposite directions, i.e. prevent mutual movement. How can two adjacent gears rotate in the same direction? Maxwell suggested that between the rows of molecular vortices a layer of tiny spherical particles ("idle wheels") capable of rotation is placed. Now the vortices could rotate in the same direction and interact with each other.

Maxwell also began to study the behavior of his mechanical model in the case of conductors and dielectrics and came to the conclusion that electrical phenomena can also occur in a medium that prevents the passage of current - in a dielectric. Suppose that the “idle wheels” could not move forward in these media under the action of an electric field, but when the electric field is applied and removed, they are displaced from their positions. It took Maxwell great scientific courage to identify this displacement of bound charges with electric current. After all, this current - bias current- no one has watched yet. After that, Maxwell inevitably had to take the next step - to recognize behind this current the ability to create its own magnetic field.

Thus, Maxwell's mechanical model made it possible to draw the following conclusion: a change in the electric field leads to the appearance of a magnetic field, i.e. to the phenomenon opposite to Faraday, when a change in the magnetic field leads to the appearance of an electric field.

Maxwell's next article on electricity and magnetism is "On Physical Lines of Force". Electrical phenomena demanded an ether as hard as steel for their explanation. Maxwell unexpectedly found himself in the role of O. Fresnel, forced to "invent" his own "optical" ether to explain polarization phenomena, as hard as steel and as permeable as air. Maxwell notes the similarity of two media: "luminiferous" and "electric". He is gradually approaching his great discovery of the "single nature" of light and electromagnetic waves.

In the next article - "Dynamical theory of the electromagnetic field" - Maxwell used the term "electromagnetic field" for the first time. “The theory that I propose may be called the theory of the electromagnetic field, because it deals with the space surrounding electric or magnetic bodies, and it may also be called the dynamical theory, since it assumes that there is matter in this space, which is in movement, by means of which the observed electromagnetic phenomena are produced.

When Maxwell deduced his equations in the Dynamic Theory of the Electromagnetic Field, one of them seemed to indicate exactly what Faraday was talking about: magnetic influences really propagated in the form of transverse waves. Maxwell did not notice then that more follows from his equations: along with the magnetic action, an electrical disturbance propagates in all directions. An electromagnetic wave in the full sense of the word, including both electrical and magnetic perturbations, appeared in Maxwell later, already in Middleby, in 1868, in the article “On the method of direct comparison of the electrostatic force with the electromagnetic one with a note on the electromagnetic theory of light” .

In Middleby, Maxwell completed the main work of his life - "A Treatise on Electricity and Magnetism", first published in 1873 and subsequently reprinted several times. The content of this book, of course, was primarily articles on electromagnetism. In the "Treatise" the basics of vector calculus are systematically given. Then there are four parts: electrostatics, electrokinematics, magnetism, electromagnetism.

Note that Maxwell's research method differs sharply from the methods of other researchers. Not only every mathematical quantity, but also every mathematical operation is endowed with a deep physical meaning. At the same time each physical quantity corresponds to a clear mathematical characteristic. One of the chapters of the "Treatise" is called "Basic Equations of the Electromagnetic Field". Here are the basic equations of the electromagnetic field from this Treatise. Thus, with the help of vector calculus, Maxwell did more simply what he had done earlier with the help of mechanical models - he derived the equations of the electromagnetic field.

Consider physical meaning Maxwell's equations. The first equation says that the sources of the magnetic field are currents and an electric field that changes with time. Maxwell's brilliant conjecture was his introduction of a fundamentally new concept - displacement current - as a separate term in the generalized Ampère - Maxwell law:

Where H- vector of magnetic field strength; j is the electric current density vector, to which the displacement current has been added by Maxwell; D- electric induction vector; c is some constant.

This equation expresses the magnetoelectric induction, discovered by Maxwell and based on the concepts of displacement currents.

Another idea that immediately won Maxwell's recognition was Faraday's idea of ​​the nature of electromagnetic induction - the occurrence of an induction current in a circuit, the number of magnetic lines of force in which changes either due to the relative motion of the circuit and the magnet, or due to a change in the magnetic field. Maxwell wrote the following equation:

Where Yo- electric field strength vector; IN- century-

torus of magnetic field strength and, respectively: - -

change of the magnetic field in time, s - some constant.

This equation reflects Faraday's law of electromagnetic induction.

It is necessary to take into account one more important property of the vectors of electric and magnetic induction Yo and B. While electric lines of force begin and end on the charges that are the sources of the field, the lines of force of the magnetic field are closed on themselves.

In mathematics, to denote the characteristics of a vector field, the operator of "divergence" (differentiation of the field flow) - div is used. Using this, Maxwell adds to the two existing equations two more:

where p is the density of electric charges.

Maxwell's third equation expresses the law of conservation of the amount of electricity, the fourth - the vortex nature of the magnetic field (or the absence of magnetic charges in nature).

The vectors of electric and magnetic induction and the vectors of electric and magnetic fields included in the considered equations are connected by simple relations and can be written in the form of the following equations:

where e is the dielectric constant; p is the magnetic permeability of the medium.

In addition, one more relation can be written that relates the intensity vector Yo and specific conductivity at:

To represent the complete system of Maxwell's equations, it is also necessary to write down the boundary conditions. These conditions must be satisfied by the electromagnetic field at the interface between two media.

Where O- surface density of electric charges; i is the surface conduction current density at the considered interface. In the particular case when there are no surface currents, the last condition turns into:

Thus, J. Maxwell comes to the definition of the electromagnetic field as a type of matter, expressing all its manifestations in the form of a system of equations. Note that Maxwell did not use vector notation and wrote his equations in rather cumbersome component form. The modern form of Maxwell's equations appeared around 1884 after the work of O. Heaviside and G. Hertz.

Maxwell's equations are one of the greatest achievements not only of physics, but of civilization in general. They combine the strict logic of the natural sciences with the beauty and proportion that characterize the arts and the humanities. Equations with the maximum possible accuracy reflect the essence of natural phenomena. The potential of Maxwell's equations is far from being exhausted; on their basis, all new works, explanations latest discoveries V various areas physics - from superconductivity to astrophysics. Maxwell's system of equations is the basis of modern physics, and so far there is not a single experimental fact that would contradict these equations. Knowledge of Maxwell's equations, at least their physical essence, is mandatory for any educated person, not only a physicist.

Maxwell's equations were the forerunner of a new non-classical physics. Although Maxwell himself, according to his scientific convictions, was a “classical” person to the marrow of his bones, the equations he wrote belonged to a different science, different from the one that was known and close to the scientist. This is evidenced at least by the fact that Maxwell's equations are not invariant under the Galilean transformations, but they are invariant under the Lorentz transformations, which, in turn, underlie relativistic physics.

Based on the equations obtained, Maxwell solved specific problems: he determined the coefficients of electrical permeability of a number of dielectrics, calculated the coefficients of self-induction, mutual induction of coils, etc.

Maxwell's equations allow us to draw a number of important conclusions. Maybe the main one is the existence of transverse electromagnetic waves propagating at a speed c.

Maxwell found that the unknown number c turned out to be approximately equal to the ratio of electromagnetic and electrostatic units of charge, which is approximately 300,000 kilometers per second. Convinced of the universality of his equations, he shows that "light is an electromagnetic disturbance." Recognition of the finite, albeit very high, speed of propagation of the electromagnetic field of stone on stone did not leave the supporters of "instantaneous long-range action" from theories.

The most important consequence of the electromagnetic theory of light was the prediction by Maxwell light pressure. He was able to calculate that in the case when, in clear weather, sunlight absorbed by a plane of one square meter gives 123.1 kilogram meters of energy per second. This means that it presses on this surface in the direction of its fall with a force of 0.41 milligrams. Thus, Maxwell's theory was strengthened or collapsed depending on the results of experiments not yet carried out. Are there electromagnetic waves in nature with properties similar to light? Is there light pressure? Already after the death of Maxwell, Heinrich Hertz answered the first question, and Pyotr Nikolaevich Lebedev answered the second.

J.K. Maxwell is a giant figure in physical science and as a person. Maxwell will live in people's memory for as long as humanity exists. Maxwell's name is immortalized in the name of a crater on the Moon. The highest mountains on Venus are named after the great scientist (Maxwell's mountains). They rise 11.5 km above the average surface level. Also, his name is the world's largest telescope that can operate in the submillimeter range (0.3-2 mm) - the telescope named after. J.C. Maxwell (JCMT). It is located in the Hawaiian Islands (USA), in the highlands of Mauna Kea (4200 m). The JCMT's 15-meter main mirror is made from 276 individual pieces of aluminum, tightly butted together. Maxwell telescope used to study solar system, interstellar dust and gas, as well as distant galaxies.

After Maxwell, electrodynamics became fundamentally different. How did she develop? We note the most important direction of development - experimental confirmation of the main provisions of the theory. But the theory itself also required some interpretation. In this regard, it is necessary to note the merits of the Russian scientist Nikolai Alekseevich Umov, who headed the Department of Physics at Moscow University from 1896 to 1911.

Nikolai Alekseevich Umov (1846-1915) - Russian physicist, born in Simbirsk (now Ulyanovsk), graduated from Moscow University. He taught at Novorossiysk University (Odessa), and then at Moscow University, where from 1896, after the death of A. G. Stoletov, he headed the Department of Physics.

Umov's works are devoted to various problems of physics. The main one was the creation of the doctrine of the movement of energy (the Umov vector), which he outlined in 1874 in his doctoral dissertation. Umov was endowed with high civic responsibility. Together with other professors (V. I. Vernadsky, K. A. Timiryazev,

N. D. Zelinsky, P. N. Lebedev), he left Moscow University in 1911 in protest against the actions of the reactionary Minister of Education L. A. Kasso.

Umov was an active propagandist of science, popularizer of scientific knowledge. Almost the first of the physicists, he realized the need for serious and targeted research on the methods of teaching physics. Most of the Methodist scholars of the older generation are his students and followers.

The main merit of Umov - development of the doctrine of the movement of energy. In 1874 he received general expression for the energy flux density vector as applied to elastic media and viscous liquids (the Umov vector). After 11 years, an English scientist John Henry Poynting(1852-1914) did the same for the flow of electromagnetic energy. Thus, in the theory of electromagnetism, the well-known Umov vector - Pointing.

Poynting was one of those scientists who immediately accepted Maxwell's theory. It cannot be said that there were many such scientists, which Maxwell himself understood. Maxwell's theory was not immediately understood even in the Cavendish Laboratory he created. Nevertheless, with the advent of the theory of electromagnetism, the knowledge of nature has risen to a qualitatively different level, which, as always happens, increasingly removes us from direct sensory representations. This is normal natural process accompanying the entire development of physics. The history of physics provides many such examples. It is enough to recall the provisions of quantum mechanics, the special theory of relativity, and other modern theories. So the electromagnetic field at the time of Maxwell was hardly accessible to the understanding of people, including the scientific community, and even more so not accessible to their sensory perception. Nevertheless, after the experimental work of Hertz, ideas arose about creating wireless communications using electromagnetic waves, which culminated in the invention of radio. Thus, the emergence and development of radio communication technology has turned the electromagnetic field into a well-known and familiar concept for everyone.

The German physicist played a decisive role in the victory of Maxwell's theory of electromagnetic field Heinrich Rudolf Hertz. Hertz's interest in electrodynamics was stimulated by G. L. Helmholtz, who, considering it necessary to "order" this area of ​​physics, suggested that Hertz study processes in open electrical circuits. At first, Hertz abandoned the topic, but then, while working in Karlsruhe, he discovered devices there that could be used for such studies. This predetermined his choice, especially since Hertz himself, knowing Maxwell's theory well, was fully prepared for such studies.

Heinrich Rudolf Hertz (1857-1894) - German physicist, was born in 1857 in Hamburg in the family of a lawyer. He studied at the University of Munich, and then - in Berlin with G. Helmholtz. Since 1885, Hertz has been working at the Technische Hochschule in Karlsruhe, where he began his research, which led to the discovery of electromagnetic waves. They were continued in 1890 in Bonn, where Hertz moved, replacing R. Clausius as professor of experimental physics. Here he continues to study electrodynamics, but gradually his interests shift to mechanics. Hertz died on January 1, 1894 in the prime of his talent at the age of 36.

By the beginning of Hertz's work, electrical oscillations had already been studied in some detail. William Thomson (Lord Kelvin) received an expression that is now known to every schoolchild:

Where T- period of electrical oscillations; A- inductance, which Thomson called the "electrodynamic capacitance" of the conductor; C is the capacitance of the capacitor. The formula has been confirmed in experiments Berend Wilhelm Feddersen(1832-1918), who studied the oscillations of the spark discharge of a Leyden jar.

In the article "On very fast electrical oscillations" (1887), Hertz gives a description of his experiments. Figure 10.4 explains their essence. In its final form, the oscillatory circuit used by Hertz consisted of two conductors CuC ", located at a distance of about 3 m from each other and connected by a copper wire, in the middle of which there was a spark gap IN induction coil. The receiver was a circuit acdb with dimensions 80 x 120 cm, with spark gap M on one of the short sides. Detection was determined by the presence of a weak spark in the spark gap M. The conductors with which Hertz experimented are, saying modern language, antenna with detector. They are now named vibrator And Hertz resonator.

Rice. 10.4.

The essence of the results obtained was that the electric spark in the spark gap IN caused a spark in the discharger M. At first, Hertz, in explaining the experiments, does not speak of Maxwellian waves. He speaks only of the "interaction of conductors" and tries to find an explanation in the theory of long-range interaction. While conducting experiments, Hertz discovered that at short distances the nature of the propagation of the "electric force" is similar to the field of a dipole, and then it decreases more slowly and has an angular dependence. We would now say that the spark gap has an anisotropic radiation pattern. This, of course, fundamentally contradicts the theory of long-range action.

After analyzing the results of experiments and conducting his own theoretical research, Hertz accepts Maxwell's theory. He comes to the conclusion about the existence of electromagnetic waves propagating with a finite speed. Now Maxwell's equations are no longer an abstract mathematical system and they should be brought to such a form that they are convenient to use.

Hertz received electromagnetic waves experimentally predicted by Maxwell's theory and, no less important, proved their identity with light. To do this, it was necessary to prove that with the help of electromagnetic waves one can observe the known effects of optics: refraction and reflection, polarization, etc. Hertz carried out these studies, which required virtuoso experimental skill: he conducted experiments on the propagation, reflection, refraction, and polarization of electromagnetic waves discovered by him. He built mirrors for experiments with these waves (Hertz mirrors), an asphalt prism, and so on. Hertz mirrors are shown in fig. 10.5. The experiments showed the complete identity of the observed effects with those that were well known for light waves.

Rice. 10.5.

In 1887, in his work “On the Influence of Ultraviolet Light on an Electric Discharge,” Hertz describes a phenomenon that later became known as external photoelectric effect. He found that when high-voltage electrodes are irradiated with ultraviolet rays, the discharge occurs at a greater distance between the electrodes than without irradiation.

This effect was then comprehensively investigated by the Russian scientist Alexander Grigorievich Stoletov (1839-1896).

In 1889, at a congress of German natural scientists and physicians, Hertz read a report "On the relationship between light and electricity", in which he expressed his opinion on the great importance of Maxwell's theory, now confirmed by experiments.

Hertz's experiments made a splash in the scientific world. They have been repeated and modified many times. One of those who did this was Petr Nikolaevich Lebedev. He received the shortest electromagnetic waves at that time and in 1895 made experiments with them on birefringence. In his work, Lebedev set the task of gradually reducing the wavelength of electromagnetic radiation in order to finally connect them with long infrared waves. Lebedev himself failed to do this, but it was carried out in the 20s of the XX century by Russian scientists Alexandra Andreevna Glagoleva-Arkadieva(1884-1945) and Maria Afanasievna Levitskaya (1883-1963).

Petr Nikolaevich Lebedev (1866-1912) - Russian physicist, born in 1866 in Moscow, graduated from the University of Strasbourg and in 1891 began working at Moscow University. Lebedev remained in the history of physics as a virtuoso experimenter, the author of research carried out with modest means on the verge of the technical capabilities of that time, and also as the founder of a generally recognized scientific school in Moscow, from where the famous Russian scientists P. P. Lazarev, S. I. Vavilov, A. R. Colley et al.

Lebedev died in 1912 shortly after he, along with other professors, left Moscow University in protest against the actions of the reactionary minister of education L. A. Kasso.

However, Lebedev's main contribution to physics is that he experimentally measured the light pressure predicted by Maxwell's theory. Lebedev devoted his whole life to studying this effect: in 1899, an experiment was set up that proved the presence of light pressure on solid bodies(Fig. 10.6), and in 1907 - for gases. Lebedev's works on light pressure have become classics, they are one of the pinnacles of the experiment late XIX- beginning of XX century.

Lebedev's experiments on light pressure brought him worldwide fame. On this occasion, W. Thomson said, "All my life I fought with Maxwell, not recognizing his light motion, but ... Lebedev forced me to surrender to his experiments."

Rice. 10.6.

The experiments of Hertz and Lebedev finally confirmed the priority of Maxwell's theory. As for practice, i.e. practical application of the laws of electromagnetism, then by the beginning of the 20th century. humanity already lived in a world in which electricity began to play a huge role. This was facilitated by vigorous inventive activity in the field of application of electrical and magnetic phenomena discovered by physicists. Let's take a look at some of these inventions.

One of the first applications of electromagnetism found in communications technology. The telegraph had already existed since 1831. In 1876, an American physicist, inventor and businessman Alexander Bell(1847-1922) invented the telephone, which was further improved by the famous American inventor Thomas Alva Edison (1847-1931).

In 1892 an English physicist William Crooks(1832-1912) formulated the principles of radio communication. Russian physicist Alexander Stepanovich Popov(1859-1906) and Italian scientist Guglielmo Marconi(1874-1937) actually put them into practice at the same time. The question usually arises as to the priority of the present invention. Popov demonstrated the capabilities of the device he created a little earlier, but did not patent it, as Marconi did. The latter determined the tradition prevailing in the West to consider Marconi the "father" of radio. This was facilitated by the awarding of the Nobel Prize to him in 1909. Popov, apparently, would also have been among the laureates, but by that time he was no longer alive, and the Nobel Prize is awarded only to living scientists. More about the history of the invention of the radio will be told in part VI of the book.

They tried to use electrical phenomena for lighting as early as the 18th century. (voltaic arc), later this device was improved Pavel Nikolaevich Yablochkov(1847-1894), who in 1876 invented the first practical electric light source (Yablochkov's candle). However, it did not find wide application, primarily because in 1879 T. Edison created an incandescent lamp of a sufficiently durable design and convenient for industrial production. Note that the incandescent lamp was invented back in 1872 by a Russian electrical engineer Alexander Nikolaevich Lodygin (1847- 1923).

Control questions

• 1. What research did Maxwell do while working at Marischal College? What role did Maxwell play in the development of the theory of electricity and magnetism?
• 2. When was the Cavendish Laboratory organized? Who became its first director?
• 3. What law could not be described using electrohydraulic analogies?
• 4. With what model did Maxwell come to the conclusion about the existence of a displacement current and the phenomenon of magnetoelectric induction?
• 5. In which article did Maxwell first use the term "electromagnetic field"?
• 6. How is the system of equations compiled by Maxwell written?
• 7. Why are Maxwell's equations considered one of the triumphant achievements of human civilization?
• 8. What conclusions did Maxwell draw from the theory of the electromagnetic field?
• 9. How did electrodynamics develop after Maxwell?
• 10. How did Hertz come to the conclusion about the existence of electromagnetic waves?
• 11. What is Lebedev's main contribution to physics?
• 12. How is the electromagnetic field theory used in engineering?

Tasks for independent work

• 1. J. K. Maxwell. Biography and scientific achievements in electrodynamics and other fields of physics.
• 2. Empirical and theoretical foundations of Maxwell's electromagnetic field theory.
• 3. The history of the creation of Maxwell's equations.
• 4. Physical essence of Maxwell's equations.
• 5. J. K. Maxwell - first director of the Cavendish Laboratory.
• 6. How is Maxwell's system of equations currently written: a) in integral form; b) in differential form?
• 7. G. Hertz. Biography and scientific achievements.
• 8. History of detection of electromagnetic waves and their identification with light.
• 9. P. N. Lebedev’s Experiments on the Detection of Light Pressure: Scheme, Problems, Difficulties, and Significance.
• 10. Works by A. A. Glagoleva-Arkadyeva and M. A. Levitskaya on the generation of short electromagnetic waves.
• 11. History of the discovery and study of the photoelectric effect.
• 12. Development of Maxwell's electromagnetic theory. Works by J. G. Poynting, N. A. Umov, O. Heaviside.
• 13. How was the electric telegraph invented and improved?
• 14. Historical stages in the development of electrical and radio engineering.
• 15. The history of the creation of lighting devices.

• 1. Kudryavtsev, P. S. Course in the history of physics. - 2nd ed. - M.: Enlightenment, 1982.
• 2. Kudryavtsev, P. S. History of physics: in 3 volumes - M.: Education, 1956-1971.
• 3. Spassky, B. I. History of Physics: in 2 volumes - M.: Higher School, 1977.
• 4. Dorfman, Ya. G. World history of physics: in 2 volumes - M .: Nauka, 1974-1979.
• 5. Golin, G. M. Classics of physical science (from ancient times to the beginning of the 20th century) / G. M. Golin, S. R. Filonovich. - M.: Higher school, 1989.
• 6. Khramov, Yu. A. Physicists: a biographical guide. - M.: Nauka, 1983.
• 7. Virginsky, V. S. Essays on the history of science and technology in 1870-1917. / V. S. Virginsky, V. F. Khoteenkov. - M.: Enlightenment, 1988.
• 8. Witkowski, N. A sentimental history of science. - M.: Hummingbird, 2007.
• 9. Maxwell, J.K. Selected works on the theory of the electromagnetic field. - M.: GITTL, 1952.
• 10. Kuznetsova, O. V. Maxwell and the Development of Physics in the 19th-20th Centuries: Sat. articles / resp. ed. L. S. POLAK. - M.: Nauka, 1985.
• 11. Maxwell, J.K. Treatise on electricity and magnetism: in 2 volumes - M .: Nauka, 1989.
• 12. Kartsev, V.P. Maxwell. - M.: Young Guard, 1974.
• 13. Niven, W. Life and scientific activity J. K. Maxwell: a short essay (1890) // J. K. Maxwell. Matter and motion. - M.: Izhevsk: RHD, 2001.
• 14. Harman, R. M. The natural philosophy of James Clerk Maxwell. - Cambridge: University Press, 2001.
• 15. Bolotovsky, B. M. Oliver Heaviside. - M.: Nauka, 1985.
• 16. Gorokhov, V. G. The formation of radio engineering theory: from theory to practice on the example of technical consequences from the discovery of G. Hertz // VIET. - 2006. - No. 2.
• 17. Book series "ZhZL": "People of science", "Creators of science and technology".