In the theory of the electromagnetic field of Maxwell, the variable electric. Basics of Maxwell theory for electromagnetic field

In the 60s of the last century (around 1860), Maxwell, based on the ideas of Faraday, summarized the laws of electrostatics and electromagnetism: Theorem of Gauss - Ostrogradsky for the electrostatic field and for the magnetic field; Full current law ; The law of electromagnetic induction, and as a result, developed the completed theory of the electromagnetic field.

The theory of Maxwell was the greatest contribution to the development of classical physics. It allowed from a single point of view to understand the wide cool phenomena, ranging from the electrostatic field of fixed charges and ending with the electromagnetic nature of the world.

Mathematical expression of Maxwell's theory serve four Maxwell Equations. which is customary to record in two forms: integral and differential. Differential equations are obtained from integral using two vector analyzing theorems - Gauss theorems and the Stokes theorem. Gauss Theorem:

(1)

(2)

- vector projections on the axis; V - surface limited S.

Stokes Theorem: . (3)

here rot - Rotor vector which is a vector and is expressed in the Cartesian coordinates as follows: rot. , (4)

S - Square limited by contour L.

The Maxwell equations in the integral form express the ratios that are valid for mentally spent in the electromagnetic field of fixed closed contours and surfaces.

The Maxwell 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 interconnected.

12.1. The first equation Maxwell

It is a generalization of the law of electromagnetic induction ,

and in integrated form has the following (5)

and approves. With a variable magnetic field, a vortex electrical field is inextricably linked, which does not depend on the extension 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. Current mix. The second equation Maxwell

Maxwell summarized the full current law Suppose that an alternating electric field, as well as an electric current, is a source of magnetic field. For the quantitative characteristic of the "magnetic action" of an alternating electric field Maxwell introduced the concept shift current.

According to the Gaussian Theorem - Ostrogradsky stream of electrical mixing through the closed surface

Differentizing this expression in time, we get for a fixed and non-deformormorm surface S. (8)

The left part of this formula has a current dimension, which is known, is expressed through the current density vector . (9)

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

. (10)

Shift current . (11)

Of all the physical properties inherent in the actual current (current conductivity) associated with the transfer of charges, the mixing current is paying only one: the ability to create a magnetic field. With the "flow" of the bias current in a vacuum or a dielectric, heat is not highlighted. An example of a bias current can be alternating current through the condenser. In general, the conductivity and displacement currents are not divided into space and can be mentioned about a complete current equal to the amount of conductivity currents and offset: (12)

With this in mind, Maxwell summarized the law of the total current by adding the mixing current to the right side. (thirteen)

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

. (14)

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. The third and fourth Maxwell equation

Maxwell summarized the Gaussian theorem - Ostrogradsky for the electrostatic field. He suggested that this theorem is valid for any electric field, both inpatient and alternating. Accordingly, the third equation of Maxwell in the integral form has the form :. (I7) or . (18)

where - Volumetric density of free charges, \u003d CL / m 3

From (1) it follows that . (19)

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

The fourth Maxwell equation in integral and differential forms has

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

12.4. Complete system of Maxwell equations in differential form

. (23)

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

, , . (24)

So, after opening the relationship between electric and magnetic fields, it became clear that these fields do not exist separately, independently one of the other. You can not create a variable magnetic field without the electrical field simultaneously in the space.

Note that the electrical charge resting in some reference system creates only the electrostatic field in this reference system, but it will create a magnetic field in the reference systems relative to which it moves. The same applies to a fixed magnet. We also note that Maxwell equations are invariant to Lorentz transforms: and for inertial reference systems TO and TO' The following ratios are performed: , . (25)

Based on the above, it can be concluded that the electrical and magnetic fields are a manifestation of a single field, which is called the electromagnetic field. It extends in the form of electromagnetic waves.

8) Boundary conditions on the surface of the media section. The perfect conductor in the electrostatic field. Surface charges. Electric field near island.

Boundary conditions on the surface of the media section

On the surface of the separation of two dielectrics with various absolute dielectric permeals E 1 and E 2, equal among themselves tangential components of the field strength

Here, index 1 refers to the first dielectric, and the index 2 is the second.

Conditions can be represented in this form

From these boundary conditions, it is possible to obtain another condition - the refractive condition for the field lines when moving them from one dielectric to another:

q 1 and Q 2 - angles between the tension vector (or offset) and normal to the interface boundary.

At the same time, if the vector of tension is perpendicular to the interface, the field strength changes jump.

When moving across the border of the section of two dielectrics, the electric potential does not undergo jumps.

Perfect conductor in the electrostatic field

Near the surface of the charged conductor, the power lines are perpendicular to its surface, and therefore work on the movement of the charge along any line on the surface of the conductor .

For electrostatic phenomena, the field inside the conductor is zero

Surface charges

Density charge - This is the amount of charge per unit length, area or volume.

If the conductor report redundant charge, then this charge distributed over the surface of the conductor.

The field strength on the surface of the conductor should be aimed at the normal surface to the surface, otherwise, the component appears directed along the surface, which will lead to the movement of charges until the component disappears. Consequently, in the event of equilibrium charges, the surface of the conductor will be equipotential. If a conductive body inform some charge Q, then it will be distributed so that the equilibrium conditions are respected. Imagine an arbitrary closed surface, fully concluded within the body. Since, with equilibrium of charges, the field at each point inside the conductor is absent, the flow of the electrical displacement vector through the surface is zero. According to the Gauss Theorem, the algebraic amount of charges inside the surface will also be zero.

Electric field near the island

Thread lines near the island are thickened, in the depressions are discharged.

9) Capacity coefficients and mutual capacities of conductors. Capacitors. Capacitance capacitors.

Capacity coefficients and mutual capacity conductors. Condencators

Capacitor (from lat. cONDENSARE - "Seal", "thicken") - a two-solid, with a certain value of tank and low ohmic conductivity; Device for the accumulation of charge and energy of the electric field

Capacitance capacitors

The main characteristic of the capacitor is its capacitycharacterizing the ability of the capacitor to accumulate an electrical charge.

The container of a flat capacitor consisting of two parallel metal plates with an area of \u200b\u200beach, located at a distance from each other, in the system SI is expressed by the formula: where ε is the relative dielectric permeability of the medium that fills the space between the plates (in vacuo is equal to one), ε 0 - electric constant, numerically equal to the F / M

10) Energy of interaction of electrical charges. Energy of the system of charged conductors. Energy charged condenser. Electrostatic field energy density

Electrical charge interaction energy

Two point charges in vacuum act on each other with the forces that are proportional to the product of the modules of these charges, inversely proportional to the square of the distance between them and are directed along the straight line connecting these charges. These forces are called electrostatic (Coulomb).

Energy of the system of charged conductors

A charged conductor can be represented as a set of interacting point charges. It has one characteristic for conductors feature - the entire volume of the conductor is equipotential, i.e., for all charged charges, there are the same potential. Therefore, to find the energy of the charged conductor, you can use the formula (5.10).

, (5.11)

where - the charge of the conductor; - Conductor potential. Using the determination of the container of a secluded conductor, formula (5.11) can be rewritten in the form:

.(5.12)

It follows from formula (5.12) that the energy of the charged conductor (regardless of the charge sign) is always positive.

The scope of formula (5.10), taking into account the expression (5.11), it can be changed: instead of determining the energy of the interaction of point charges, it is possible to calculate the energy of the interaction of charged conductors. In this case, instead of the parameters of point charges in (5.10), the parameters of charged conductors will appear.

Relying on the results obtained above, you can consider the overall task - definition energy of the system of charged conductors.

The simplest example of the system of charged conductors is a condenser. The capacitor has one conductor (label), which is charged, has the potential, and the potential of the plated on which the charge is located is equal to. According to the formula (5.10), the energy of such charges is defined as

where is the potential difference between the capacitor plates. Using the determination of the capacitor capacity (5.3), the formula for the energy of the charged condenser can be represented as:

Energy charged condenser

If on the plates of the capacitor with electrical capacity WITH There are electrical charges + Q. and - q, then according to formula (20.1), the voltage between the capacitor plates is equal

Electrostatic field energy density

This is a physical quantity, numerically equal to the ratio of the potential energy of the field concluded in the volume element, to this volume. For a homogeneous field, the volumetric energy density is equal. For a flat capacitor, the volume of which is SD, where S is the plates area, D - the distance between the plates, we have

Considering that

11) Dielectrics in the electric field. Polarization of dielectric. Polarization and electrical induction vectors (electric mixing). Dielectric permeability and susceptibility

Dielectrics in the electric field

Unlike conductors, there are no free charges in dielectrics. All charges are associated: electrons belong to their atoms, and the ions of solid dielectrics oscillate

near the crystal lattice nodes.

Accordingly, when placing a dielectric in the electric field does not arise the directional movement of charges. Therefore, for dielectrics, our evidence of the properties of the conductors does not pass - after all, all these reasoning relied on the possibility of current appearance. Indeed, none of the four properties of conductors formulated in the previous article does not apply to dielectrics.

2. The volumetric charge density in the dielectric can be different from zero.

3. Voltage lines may not be perpendicular to the surface of the dielectric.

4. Different dielectric points may have different potential. Became to talk about

The "dielectric potential" does not have.

Nevertheless, one most important general property has dielectrics, and it is known to you

(Remember the dot charge field strength in the dielectric!). Tension

the fields decrease inside the dielectric for some number "times compared with vacuum.

The value is given in the tables and is called dielectric permeability of the dielectric.

Polarization of dielectric

Polarization of dielectrics - The phenomenon associated with a limited displacement of associated charges in a dielectric or turning electric dipoles is usually under the influence of an external electric field, sometimes under the action of other external strength or spontaneously.

Polarization of dielectrics characterizes vector of electric polarization. The physical meaning of the electric polarization vector is a dipole moment, referred to a unit volume of a dielectric. Sometimes the polarization vector is briefly called simply polarization.

Polarization vector is applicable to describing the macroscopic state of polarization not only conventional dielectrics, but also ferroelectrics, and, in principle, any media with similar properties. It is applicable not only to describe induced polarization, but also spontaneous polarization (in ferroelectrics).

Polarization is a dielectric state, which is characterized by the presence of an electrical dipole moment in any (or almost anyone) element of its volume.

There are polarization induced in a dielectric under the action of an external electric field, and spontaneous (spontaneous) polarization, which occurs in ferroelectrics in the absence of an external field. In some cases, the polarization of the dielectric (ferroelectric) occurs under the action of mechanical stresses, friction forces or due to temperature change.

Polarization does not change the total charge in any macroscopic volume inside a homogeneous dielectric. However, it is accompanied by the appearance of connected electrical charges on its surface with some surface density σ. These associated charges are created in dielectric an additional macroscopic field with e 1 tension, directed against the external field with e 0 tension. The resulting intensity of the field e inside the dielectric e \u003d e 0 -e 1.

Polarization and electrical induction vectors (electric mixing)

Vector polarization - Vector physical value reduced by an external electric field of the dipole moment unit volume of the substance, quantitatively characteristics of dielectric polarization.

Denoted by the letter, in Xi is measured in a / m.

Electrical induction (electrical displacement) - vector magnitude equal to the sum of the voltage vector of the electric field and polarization vector.

Dielectric permeability and susceptibility

Absolute dielectric constant - Physical value showing the dependence of electrical induction from the tension of the electric field. In foreign literature, the letter ε is denoted by the letter ε, in the domestic (where it usually denotes the relative dielectric constant) is preferably a combination of where -electric constant. This article uses.

Relative dielectric constant The medium ε is a dimensionless physical value that characterizes the properties of an insulating (dielectric) medium. It is associated with the effect of polarization of dielectrics under the action of the electric field (and with the characterizing this effect of dielectric susceptibility of the medium). The value of ε shows how many times the strength of the interaction of two electrical charges in the medium is less than in vacuum. The relative dielectric permeability of air and most other gases under normal conditions is close to one (due to their low density). For most solid or liquid dielectrics, the relative dielectric constant lies in the range from 2 to 8 (for a static field). The dielectric constant of water in the static field is sufficiently high - about 80. It is large for its values \u200b\u200bfor substances with molecules with a large electric dipole. The relative dielectric permeability of ferroelectrics is tens and hundreds of thousands.

Relative dielectric permeability of the substance ε R. It can be determined by comparing the tank capacitor capacity with this dielectric (C x) and the capacitance of the same capacitor in vacuum (C O):

Dielectric susceptibility (or polarizability) Substances - physical value, measure of the ability of a substance to polarize under the action of an electric field. Dielectric susceptibility χ. E. - Linear communication coefficient between the polarization of the dielectric P. and external electric field E. In sufficiently small fields:

In the SI system:

where ε 0 is electrical constant; Production ε 0 χ E. called in system si absolute dielectric susceptibility.

In case of Vacuum

Dielectrics, as a rule, the dielectric susceptibility is positive. Dielectric susceptibility is a dimensionless value.

Polarizability is associated with dielectric constant ε by the ratio:

ε \u003d 1 + 4πχ (SGS)

ε \u003d 1 + χ (s)

12) Permanent electric current. Current conditions. Current power. Current density. Resistance. Conductivity. Ohm and Jowle Lenza laws in integral and differential form

Permanent electric current.

Electricity - an ordered uncompensated movement of free electrically charged particles, for example, under the influence of an electric field. Such particles may be: in conductors - electrons, in electrolytes - ions (cations and anions), in gases - ions and electrons, in vacuum under certain conditions - electrons, in semiconductors - electrons and holes (electron-hole conductivity). It is historically accepted that the direction of current coincides with the direction of movement of positive charges in the conductor. D.C - Current, direction and the magnitude of which is weakly changing over time.

Current conditions.

To occur and maintain current in any environment, you must perform two conditions:
- the presence in the medium of free electrical charges
- Creating an electric field in the environment. ( the presence of the current source. in which there is a transformation of any type of energy into the energy of the electric field.)
In different environments, electrical current carriers are different charged particles.

To maintain current in an electrical circuit on charges, in addition to the Coulomb forces, the forces of non-electric nature (third-party strength) must act.
A device that creates third-party strength supporting the potential difference in the chain and transforming various types of energy into electrical energy is called the current source.
For the existence of an electric current in a closed circuit, it is necessary to turn on the current source into it.

Current power. Current density. Resistance. Conductivity.

1. Current strength - I, unit of measurement - 1 A (amp).
The current is called the value equal to the charge flowing through the cross-section of the conductor per unit of time.
I \u003d Δq / Δt.
Formula (1) is valid for direct current, in which the current and its direction does not change over time. If the current and its direction varies with time, then such a current is called variables.
For alternating current:
I \u003d lim Δq / Δt, (*)
ΔT -\u003e 0
those. I \u003d Q ', where q' is a derivative of charge in time.

2. Current density - j, unit unit - 1 A / m2.
The current density is called the value equal to the strength of the current flowing through a single cross-section of the conductor:
j \u003d i / s.

3. Electrical power source of current - EDs (ε), Unit of measurement - 1 V (volt). E.D.S.- The physical value equal to the work performed by third-party forces when moving along the electrical circuit of a single positive charge:
ε \u003d AST. / Q.

4. Explorer resistance - R, Unit of measurement - 1 Ohm.
Under the influence of the electric field in vacuo, free charges would move accelerated. In the substance, they move on average evenly, because Part of the energy is given to particles of substance in collisions.

The theory argues that the energy of the ordered movement of charges is dissipated on distortions of the crystal lattice. Based on the nature of electrical resistance, it follows that
R \u003d ρ * L / S,
Where
L - Explorer length,
S - cross-sectional area
ρ is the proportionality coefficient called the specific resistance of the material.
This formula is well confirmed by experience.
The interaction of the conductor particles with the charges moving in the current depends on the chaotic movement of particles, i.e. From the temperature of the conductor. It is known that
ρ \u003d ρ0 (1 + Δ t),
R \u003d R0 (1 + Δ T)

The coefficient K is called the temperature coefficient of resistance:
k \u003d (r - r0) / r0 * t.

For chemically pure metals K\u003e 0 and equal to 1/273 K-1. For alloys, temperature coefficients have a smaller value. R (T) Dependency for Metals Linear:

In 1911, the phenomenon of superconductivity was discovered in the fact that at a temperature close to absolute zero, the resistance of some metals drops with a jump to zero.

In some substances (for example, electrolytes and semiconductors), the resistivity with increasing temperature decreases, which is explained by the growth of the concentration of free charges.
The value inverse resistivity is called the specific electrical conductivity G
G \u003d 1 / ρ.

Ohm and Jowle Lenza laws in integral and differential form

Uniform section of the chain (E \u003d 0):

Observations show that the power of the current on the plot of the chain is straight-proportional to the voltage (I ~ U) and inversely resistance (I ~ 1 / R). Hence,

Formula (10) is the law of Oma for a homogeneous section of the chain.

The voltampear characteristic is viewed on the schedule:

From formula (10) it follows that u \u003d i * r. The product I * R is called the voltage drop.

When writing equations for direct current in metals, all time derivatives in Maxwell equations should be equal to zero. Thus, the following equations are accepted as the main equations for direct current in metals:

Joule Law - Lenza - physical law, which gives a quantitative assessment of the thermal action of electric current. Installed in 1841 by James Joule and regardless of him in 1842 by Emily Lenz.

Mathematically, it can be expressed in the following form:

where w. - the power of heat release in unit volume is the density of the electric current - the electric field strength, σ - The conductivity of the medium.

The law can also be formulated in an integral form for the occasion of the flow of currents in thin wires:

The amount of heat released per unit of time in the area under consideration of the circuit is proportional to the product of the current of the current strength on this site and the resistance of the site

In mathematical form, this law has the form

where dQ. - the amount of heat allocated during the period of time dt., I. - current strength R. - resistance, Q. - the total amount of heat allocated during the period of time from t 1. before t 2.. In case of constant strength of current and resistance.

Around 1860, thanks to the works of Neuman, Weber, Helmholtz and Felici (see § 11), electrodynamics was already considered to be completely systematic, with clearly defined boundaries. The main research now seemed to have to follow the path of finding and withdrawing all the consequences of the established principles and their practical application to which inventive techniques have already begun.

However, the prospect of such a quiet work violated the young Scottish physicist James Clark Maxwell (1831-1879), indicating a much wider range of electrodynamics. With a full base, Duem wrote:

"No logical necessity was pushing Maxwell to invent new electrodynamics; He was guided only by some analogies and desire to complete the work of Faraday in the same spirit, as the works of Coulomb and Poisson were completed with an amper electrodynamics, as well as, possibly, the intuitive sensation of the electromagnetic nature of the world " (P. Duhem, Les Theories Electriques de J. Cerrk Maxwell, Paris, 1902, p. 8).

Perhaps the main motivation that Maxwell began to work, at all, not demanded by the science of those years, was admirable for the new ideas of Faraday, so original that scientists were not able to perceive them and assimilate them. The generation of physicists-theorists, brought up on the concepts and mathematical grace of the works of Laplace, Poisson and Ampere, the thoughts of Faraday seemed too vague, and experimenter physicists are too wise and abstract. There was a strange thing: Faraday, who was not a mathematician in his education (he began his career a peddler in the book shop, and then entered the Davy's laboratory to the position of semi-system-heater), felt the urgent need to develop a certain theoretical method, just as effective as and mathematical equations. Maxwell guess it.

"Starting the Labor of Faraday," Maxwell wrote in the preface to his famous "treatise", "I found that his method of understanding the phenomena was also mathematical, although not presented in the form of ordinary mathematical symbols. I also found that this method1 can be expressed in conventional mathematical form and, thus, compare with the methods of professional mathematicians. So, for example, Faraday saw power lines that permeate all the space, where mathematicians saw the centers of forces attracting at a distance; Faraday saw Wednesday where they did not see anything other than the distance; Faradays suggested a source and cause of phenomena in real actions occurring in the environment, they were satisfied with the fact that they were in force at a distance attributed to electrical fluids.

When I translated that I considered the ideas of Faraday, in a mathematical form, I found that in most cases the results of both methods coincided, so they explained the same phenomena and the same laws of action were explained, but that the Faraday methods were like For those under which we begin with a whole and come to a particular analysis, while conventional mathematical methods are based on the principle of movement from particulars and constructing a whole synthesis.

I also found that many of the fruitful research methods opened by mathematicians could be significantly expressed with the help of ideas arising from the works of Faraday than in their original form. " J. Cerrk Maxwell, A Treatise On Electricity and Magnetism, London, 1873; 2nd ED., Oxford, 1881. (Journal of Preface and Part IV, see the book J. K. Maxwell, Selected Works on the theory of the Electromagnetic Field, 1954, p. 345-361. - Note).

As for the mathematical method of Faraday, Maxwell still notices that mathematicians who considered the Faraday method deprived of scientific accuracy, did not come up with anything better as the use of a hypotheses on the interaction of things that do not have physical reality, such as current elements, " which arise from nothing, pass the area of \u200b\u200bthe wire and then turn into nothing again. "

To give the ideas of Faraday mathematical form, Maxwell began with the fact that he created electrodynamics of dielectrics. Maxwell Theory is directly related to Mossotti theory. While Faradays, in their theory of dielectric polarization, intentionally left the question about 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 the molecule is under the action of the power of induction, the ether is concentrated at one end of the molecule and is solved on the other; Because of this, positive strength appears at the first end and the negative equal to it - on the second. Maxwell is entirely accepting this concept. In his "treatise" he writes:

"The electric polarization of the dielectric is a state of deformation into which the body comes under the action of the electromotive force and which disappears simultaneously with the cessation of this force. We can imagine it as something that can be called an electrically displacement produced by the electromotive force. When the electromotive force acts in a conductive medium, it causes current there, but if the environment is non-conductive or dielectric, the current cannot pass through this environment. Electricity, however, is shifted 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, in the same proportion, the electrical displacement increases accordingly or decreases.

The displacement value is measured by the amount of electricity crossing the surface unit with an increase in the displacement from zero to the maximum value. Such is, consequently, the measure of electric polarization. "

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

"Changes in electrical displacement obviously cause electric currents. But these currents can exist only during the change of displacement, and since the displacement cannot exceed some value, without causing a devastating discharge, then these currents cannot continue infinitely in the same direction, like currents in the conductors ".

After Maxwell introduces the concept of the field strength, which is a mathematical interpretation of the Faraday concept of the field of force, it records the mathematical ratio for the concepts of electrical offset and the offset current. It comes to the conclusion that the so-called conductor's charge is the surface charge of the surround dielectric, which the energy accumulates in a dielectric in the form of a voltage state that the movement of electricity is subject to the same conditions as the movement of incompressible fluid. Maxwell himself will compare his theory so much:

"Electrification energy is concentrated in a dielectric medium, whether it is a solid, liquid or gas, a dense medium, or rarefied, or absolutely deprived of weighty matter, if only it was able to transmit an electrical action.

The energy is enclosed at each point of the medium in the form of a deformation state called by electric polarization, the value of which depends on the electromotive force acting at this point ...

In dielectric fluids, electric polarization is accompanied by tension in the direction of induction lines and equal pressure in all directions perpendicular to the induction lines; The magnitude of this tension or pressure per unit surface is numerically equal to energy per unit volume at this point. "

It is difficult to more clearly express the basic idea of \u200b\u200bthis approach, which is the idea of \u200b\u200bFaraday: a place in which electrical phenomena is performed is a medium. As if wishing to emphasize that this is the main thing in his treatise, Maxwell finishes him with the following words:

"If we accept this environment as a hypothesis, I believe that it should occupy an outstanding place in our research and that we should try to construct a rational idea of \u200b\u200ball the details of its action, which was my constant goal in this treatise".

Justificate the theory of dielectrics, Maxwell transfers its concepts with the necessary amendments to magnetism and creates the theory of electromagnetic induction. It will summarize all its theoretical constructions in several equations that are now famous: in six Maxwell equations.

These equations differ greatly from conventional equations of mechanics - they define the structure of the electromagnetic field. While the laws of mechanics are applicable to areas of space in which matter is present, the Maxwell equations are applicable for the entire space, regardless of whether there is no body or electrical charges there. They determine the changes in the field, while the laws of mechanics determine changes in material particles. In addition, the Newtonian mechanics refused how we were already talked to ch. 6, on the continuity of action in space and time, while the Maxwell equations establish the continuity of phenomena. They link events adjacent in space and in time: according to the specified state of the field "here" and "now" we can withdraw the state of the field in close proximity to close points of time. Such an understanding of the field is absolutely consistent with the idea of \u200b\u200bFaraday,. But it is in an insurmountable contradiction with a two-century tradition. Therefore, there is nothing surprising in the fact that it met resistance.

Objections that have been put forward against the theory of electricity Maxwell were numerous and treated both fundamental concepts based on the theory, and may be even more, to that too free manner, which Maxwell uses when deriving consequences of it. Maxwell step by step is building his theory with the help of the "dexterity of fingers", as Poincare was successfully expressed, having in mind those logical stretches that sometimes allow themselves scientists in the formulation of new theories. When Maxwell comes up for an obvious contradiction during the analytical construction, he, without hesitation, overcomes ERA with the help of discouraging liberties. For example, it is worth it to exclude any member, replace an inappropriate sign of expression reverse, replace the value of some letter. For those who admired the infallible logical construction of an amper electrodynamics, Maxwell's theory was supposed to produce an unpleasant impression. Physics failed to bring it into a slim order, i.e., to free from logical errors and inconsistencies. But. On the other hand, they could not refuse the theory, which, as we will see in the future, organically tied optics with electricity. Therefore, at the end of the last century, the biggest physicists adhered to the thesis, nominated in 1890 by Herz: since the reasoning and calculations, with the help of which Maxwell came to his theory of electromagnetism, are full of errors that we cannot correct, we will take six, Maxwell equations as the initial hypothesis, As postulates, which will rely on the whole theory of electromagnetism. "The main thing in the theory of Maxwell is the Maxwell equations," says Hertz.

21. Electromagnetic theory of light

In the weather found formula for the interaction force of two electrical charges, moving relative to each other, a coefficient has a meaning of some speed. The magnitude of this speed itself Weber and Kollarush was determined experimentally in the work of 1856, which became classical; This value was somewhat more than the speed of light. Next year, Kirchhof "from Weber's theory brought the law of propagation of electrodynamic induction on the wire: if the resistance is zero, the speed of the electrical wave does not depend on the cross section of the wire, from its nature and density of electricity and is almost equal to the speed of light propagation in emptiness. Weber in one of his theoretical and experimental work of 1864 confirmed the results of Kirchhoff, showing that the Kirchhoff constant is quantitatively equal to the number of electrostatic units contained in the electromagnetic unit, and noticed that the coincidence of the speed of the propagation of electrical waves and the speed of light can be considered as an indication on The presence of a close connection between two phenomena. However, before talking about this, you should first find out exactly what the true meaning of the concept of the spread of electricity is: "And this meaning is the meaning of the Weber, it seems not to cause high hopes at all."

Maxwell just had no doubt, perhaps because he found support in the ideas of Faraday regarding the nature of light (see § 17).

"In various places of this treatise, Maxwell writes, starting in the XX chapter of the fourth part to the exposition of the electromagnetic theory of light," an attempt was made to explain electromagnetic phenomena with the help of a mechanical action transmitted from one body to another with the medium that occupies the space between these bodies. Wave the theory of light also allows for the existence of some environment. We must now show that the properties of the electromagnetic medium are identical to the properties of the luminous medium ...

We can obtain the numerical value of some properties of the medium, such as the rate at which the perturbation extends through it, which can be calculated from electromagnetic experiments, and is also observed directly in the event of light. If it was found that the speed of propagation of electromagnetic perturbations is as well as the speed of light, not only in the air, but also in other transparent environments, we would get a serious basis in order to consider the light by electromagnetic phenomenon, and then the combination of optical and electrical Evidence will give the same proof of the reality of the environment as we receive in the case of other forms of matter on the basis of a set of testimonies of our senses "( In the same place p. 550-551 Russian publication).

As in the first work of 1864, Maxwell proceeds from its equations and after a series of transformations it comes to the conclusion that in the void transverse shifting currents spread at the same speed as the light as "represents the confirmation of the electromagnetic theory of light", - Confidently say Maxwell.

The Maxwell then studies in more detail the properties of electromagnetic perturbations and comes to the conclusions, today is already well known: the oscillating electrical charge creates an alternating electric field that is inextricably linked with a variable magnetic field; This is a generalization of Ersteda's experience. Maxwell equations allow you to trace the change in time in any point of space. The result of such a study shows that electrical and magnetic oscillations arise at each point of space, i.e. the intensity of electrical and magnetic fields changes periodically; These fields are inseparable from each other and polarized mutually perpendicularly. These oscillations are distributed 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 propagation of the wave.

Among the many private consequences arising from Maxwell's theory, we mention the following: especially often criticized the assertion that the dielectric constant is equal to the square of the refractive index of optical rays in this medium; the presence of light pressure in the direction of light propagation; The orthogonality of the two polarized waves - elecrtric and magnetic.

22. Electromagnetic waves

In § 11, we have already said that the oscillatory nature of the discharge of Leiden bank was established. This phenomenon from 1858 to 1862 was again subjected to attentive analysis by Wilhelm Feddersen (1832-1918). He noticed that if two capacitor plates are connected by a low resistance, the discharge is the oscillatory nature and the duration of the oscillation period is proportional to the square root from the capacitor tank. In 1855, Thomson brought out the potential theory that the period of oscillations of the oscillating discharge is proportional to the square root from the product of the capacitor of the capacitor to its self-induction coefficient. Finally, in 1864, Kirchhogof gave the theory of an oscillatory discharge, and in 1869, Helmgoltz showed that similar oscillations can be obtained in an induction coil, the ends of which are connected to the condenser's plates.

In 1884, Henry Herz (1857-1894), a former student and an assistant Helmholtz, began to study the Maxwell theory (see ch. 12). In 1887, he repeated Helmholtz's experiments with two induction coils. After several attempts, he managed to put his classic experiences, well-known now. With the help of the "generator" and "resonator", Hertz was experimentally proved (in a manner that today describe in all textbooks), which the oscillatory discharge causes a wave space consisting of two oscillations - electrical and magnetic, polarized perpendicular to each other. Hertz also had a reflection, refraction and interference of these waves, showing that all his experiments are fully explained by the theory of Maxwell.

Many experimenters rushed along the path, but they did not succeed much to add to the understanding of the similarities of light and electrical waves, for, using the same wavelength that hertz took (about 66 cm), they came out on the phenomena of diffraction, which donate all the others Effects. To avoid this, we needed the installations of such large sizes, which were unrealizable in almost those times. Augusto Riga (1850-1920), which, with the help of a new type of generator created by the new type of generator, managed to excite a wave a length of several centimeters (most often it worked with 10.6 cm long waves). Thus, Riga managed to reproduce all optical phenomena with the help of devices that are mainly analogues of the corresponding optical instruments. In particular, Riga was the first to obtain the double refraction of electromagnetic waves. The works of Riga begun in 1893 and from time to time they described them in notes and articles published in scientific journals were then combined and supplemented in now the classical book "Ottica delle Oscillazioni Elettriche" ("Optics of Electric oscillations"), published in 1897, the name of which expresses the content of the whole era in the history of physics.

The ability of a metal powder placed in the tube becomes carried out under the action of the discharge located near the electrostatic machine, it was studied to demolish (1853-1922) in 1884 and ten years later, this ability was used by Dodge and for the information and many others to indicate electromagnetic waves. Combining the Riga generator and the indicator to demolish with the brilliant ideas of "antenna" and "grounding", at the end of 1895 Gulielmo Marconi (1874-1937) successfully produced the first practical experiments ( As is known, 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 physical branch of the Russian Physical and Chemical Society, a report containing the description) In the field of radiotelegraph, the rapid development and the amazing results of which truly borders with a miracle.

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

know

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

be able to

• Assess the role of Maxwell in the development of the teachings on electricity and magnetism, the fundamental meaning of the Maxwell equations, the place of the book "Treatise on electricity and magnetism" in the history of science, historical experiments of Hertz and P. N. Lebedev;
• discuss biographies of the largest scientists who worked in the field of electromagnetism;

own

Operation skills with the main concepts of the theory of the electromagnetic field.

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

The opening of Faraday revolutionized the science of electricity. With his light hand, electricity began to conquer all new positions in the technique. Earned electromagnetic telegraph. In the early 70s. XIX century, he has already connected Europe with the USA, India and South America, the first electric current generators and electric motors appeared, the electricity began to be widely used in chemistry. Electromagnetic processes were increasing deeper into science. Epoch has come when the electromagnetic picture of the world was ready to change mechanical. We needed a brilliant person who could, as in his time Newton, to unite the facts and knowledge accumulated by this time and on their basis to create a new theory describing the foundations of the new world. J. K. Maxwell became such a person.

James Clerk Maxwell (Fig. 10.1) Born in 1831. His father-John Clerk Maxwell was a man clearly outstanding. A lawyer on a greener, he, however, paid considerable time to others, more interesting things for him: traveled, designed cars, put physical experiences, and even published several scientific articles. When Maxwell turned 10 years old, his father sent him to learn to the Edinburgh Academy, where he stayed six years old - until admission to the university. At the age of 14, Maxwell wrote the first scientific work dedicated to the geometry of oval curves. Her summary was published in the "Warmings of the Royal Society" of the Edinburgh Society for 1846

In 1847, Maxwell entered the University of Edinburgh, where he began to in-depth to study mathematics. At this time, two more scientific works of the gifted student were published in the "Labor of the Edinburgh Royal Society". With the content of one of them (about rolling curves), the company was introduced by Professor Kelland, another (about the elastic properties of solids) was first introduced by the author himself.

In 1850, Maxwell continued her education in St. Petersburg - St. Peter's College of Cambridge University, and from there switched to the college of the Holy Trinity - Trinity College, who gave the world I. Newton, and later V. V. Nabokova, B. Russell, etc. in 1854 Maxwell is withstanding the exam and receives a bachelor's degree. Then he was left in Trinity College as a teacher. However, scientific problems were more worried. In 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 paints. Maxwell is developing the theory of color vision, designed the color top (Fig. 10.2).

Fig. 10.1.

Fig. 10.2.

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

"Dear Thomson! Now, when I entered into the wicked school of bachelors, I began to think about reading. It is very pleasant sometimes to be among the deservedly recognized books that have not yet read, but should read. But we have a strong desire to return to physical subjects, and some of us here want to attack electricity. "

After graduating course, Maxwell became a member of the Trinity College of Cambridge University, and in 1855 he entered the Edinburgh Royal Society. However, he soon left Cambridge and returned to his native Scotland. Professor Forbes informed him that in Aberdeen, a vacancy of professors of physics was opened in Marihan College, and he has every chance to take her. Maxwell accepted the proposal and in April 1856 (in 24 years!) Entered a new position. In Aberdeen Maxwell continues to work on the problems of electrodynamics. In 1857, he sends M. Faraday his work "On Faraday power lines".

Of other works, Maxwell in Aberdeen widely fame received his work on the stability of the rings of Saturn. From the study of the mechanics of Saturn rings, the transition to the consideration of the movements of gas molecules was completely natural. In 1859, Maxwell made a meeting of the British Association for the Development of Sciences with a report on the dynamic theory of gases. This report marked its fruitful research in the field of kinetic theory of gases and statistical physics.

In 1860, Maxwell accepted the invitation of the London Royal College and worked out there in the rank of Professor. He was not a brilliant lecturer and did not particularly love to lecture. Therefore, the next break in teaching was rather desirable than annoying, and allowed to fully immerse themselves in solving the fascinating problems of theoretical physics.

According to A. Einstein, Faraday and Maxwell played in the science of electricity the same roles that Galilee and Newton in mechanics. As Newton gave an open Galilee mechanical effects to a mathematical form and physical justification, and Maxwell made it in relation to Faraday discoveries. Maxwell gave the ideas of the Faraday of a strict mathematical form, introduced the term "electromagnetic field", formulated mathematical laws describing this field. Galilee and Newton laid the foundations of the mechanical picture of the world, Faraday and Maxwell - electromagnetic.

Maxwell began his ideas about the electromagnetism since 1857, when the already mentioned article "On Faraday power lines" was written. Here it is widely used by hydrodynamic and mechanical analogies. This allowed Maxwell to apply the mathematical apparatus of Irish mathematics U. Hamilton and thus express electrodynamic ratios in mathematical language. In the future, methods of the theory of elasticity are replaced by hydrodynamic analogies: the concepts of deformation, pressure, vortex, and the like. Based on this, Maxwell comes to the field equations, which at this stage have not yet been reduced to a single system. Exploring dielectrics, Maxwell expresses the idea of \u200b\u200b"shift current", as well as still foggy, the idea of \u200b\u200bthe connection of light and the electromagnetic field ("electrotonic state") in the Faraday formulation, which Maxwell then used.

These ideas are set forth in the articles "On Physical Lines of Forces" (1861-1862). They are written in the most fruitful London period (1860-1865). At the same time, the famous articles of Maxwell "Dynamic theory of the electromagnetic field" (1864-1865) were released, where the thoughts were made about the unified nature of electromagnetic waves.

From 1866 to 1871, Maxwell lived in his childbirth of Middleby, leaving occasionally to Cambridge for exams. Cashing economic affairs, Maxwell did not leave scientific classes. He hardly worked on the main labor of his life "Treatise on electricity and magnetism," wrote the book "Theory of Heat", a number of articles on the kinetic gases theory.

In 1871, an important event occurred. At the agents of the descendants of Cavendish in Cambridge, the Department of Experimental Physics was established and the construction of an experimental laboratory was launched, which in the history of physics is known as the Cavendish laboratory (Fig. 10.3). Maxwell was invited to become the first professor at the Department and to work the laboratory. In October 1871, he read the inaugural lecture on the directions and the importance of experimental research in university education. This lecture has become a training program to experimental physics for many years ahead. June 16, 1874, the Cavendish laboratory was open.

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

Fig. 10.3.

After the exit "Treatise on electricity and magnetism", in which the theory of the electromagnetic field was formulated, Maxwell decides to write the book "Electricity in elementary presentation" in order to popularize and distribute its ideas. Maxwell worked on the book, but his well-being became worse. He died on November 5, 1879, and without witnessing the triumph of his theory.

Let us dwell on the creative heritage of the scientist. Maxwell left a deep trail in all areas of physical science. No wonder a number of physical theories wear his name. He suggested a thermodynamic paradox, who did not give peace with physicists for many years, "Demon Maxwell." In kinetic theory, they were introduced concepts known as: "Maxwell's distribution" and "Maxwell - Boltzmann" statistics. His Peru also belongs to an elegant study of the stability of the rings of Saturn. In addition, Maxwell has created many small scientific masterpieces in a wide variety of areas - from the first color photography in the world before developing a method for radical removal of fat spots from clothing.

Let us turn to the discussion theories of electromagnetic fields - Quintessence of Scientific Creativity Maxwell.

It is noteworthy that James Clerk Maxwell was born at that very year when Michael Faraday opened the phenomenon of electromagnetic induction. At Maxwell, the Book of Faraday "Experimental Research on Electricity" was made a special impression.

During Maxwell, there were two alternative electricity theories: the theory of "power lines" of Faraday and the theory developed by French scientists pendant, Ampera, Bio, Savar, Arago and Laplas. The initial position of the latter is an idea of \u200b\u200bthe long-range - instantaneous transmission of interaction from one body to another without the help of any intermediate medium. Realistic Thief of Faraday could not reconcile with such a theory. He was absolutely convinced that "Matter cannot act where it is not." Wednesday through which the impact is transmitted, Faradays called the "field". The field, it believed, permeated with magnetic and electric "power lines".

In 1857, the Maxwell article appeared in the "works of the Cambridge Philosophical Society" - "On Faraday power lines". It contained the entire program of research on electricity. Note that in this article, the Maxwell equation was already written, but so far without a shift current. The article "On Faraday Power Lines" required continued. Electro-hydraulic analogies gave a lot. With their help, useful differential equations were recorded. But not all managed to subjugate the electro-hydraulic analogies. It did not fit the most important law of electromagnetic induction in their framework. It was necessary to come up with a new auxiliary mechanism that facilitates the understanding of the process, reflecting at the same time and translational flow of currents, and the rotational, vortex nature of the magnetic field.

Maxwell offered a special environment, whose vortices in which are so small that fit inside the molecules. Rotating "molecular vortices" produce a magnetic field. The direction of the axes of the vortices of molecules coincides with their strength lines, and they themselves can be represented as thin rotating cylinders. But the external, in contact with the vortices should move in opposite directions, i.e. Prevent mutual movement. How can you ensure the rotation of the two next gear in one direction? Maxwell suggested that between the rows of molecular vortices placed a layer of smallest spherical particles ("idle wheels") capable of rotating. Now the vortices could rotate in one direction and interact with each other.

Maxwell 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 occur in the medium that prevents the passage of the current is in the dielectric. Let the "idle wheels" could not in these environments under the action of the electric field to move progressively, but they are shifted from their positions when applying and removing the electric field. A large scientific courage was required by Maxwell to identify this displacement of related charge charge charges. After all, this current - current offset - No one has not watched. After that, Maxwell inevitably had to take the next step - to recognize the ability to create a self-magnetic field behind this current.

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

The next article Maxwell dedicated to electricity and magnetism is "On physical power lines". Electrical phenomena required for their explanation of solid, as steel, ether. Maxwell unexpectedly found itself in the role of O. Fresnel, forced to "invent" to explain the polarization phenomena its "optical" ether, solid, both steel, and permeable as air. Maxwell notes the similarity of two environments: "LIGHTON" and "electrical". He gradually approaches his great discovery of "single nature" of light and electromagnetic waves.

In the next article, the "dynamic theory of the electromagnetic field" - Maxwell first used the term "electromagnetic field". "The theory I suggests may be called the theory of an electromagnetic field, because it deals with space surrounding electrical or magnetic bodies, and it can also be called a dynamic theory because it allows that there is a matter in this space that is in The movement through which the observed electromagnetic phenomena is produced.

When Maxwell brought its equations in the "dynamic theory of the electromagnetic field", one of them evidenced, it seemed that there were still named after Faradays: magnetic effects were actually distributed in the form of transverse waves. Maxwell did not notice then that it should be more from its equations: along with magnetic effects, an electric perturbation is distributed in all directions. The electromagnetic wave in the full sense of the word, including electrical and magnetic perturbation at the same time, appeared at Maxwell later, already in Middleback, in 1868, in the article "On the method of direct comparison of electrostatic power with an electromagnetic with a remark about the electromagnetic theory of light" .

Middleby Maxwell completed the main work of life - "Treatise on electricity and magnetism", first published in 1873 and subsequently reprinted several times. The content of this book, of course, was primarily an articles for electromagnetism. The "Treatise" systematically gives the basics of vector calculus. Then four parts are followed: electrostatics, electrocinctic, magnetism, electromagnetism.

Note that the Maxwell research method is sharply different from the methods of other researchers. Not only every mathematical value, but each mathematical operation is endowed with a deep physical meaning. At the same time, each physical value corresponds to a clear mathematical characteristic. One of the heads of "Treatise" is called "The main equations of the electromagnetic field". Here are the main equations of the electromagnetic field from this treatise. Thus, with the help of the vector calculation, Maxwell simply did what previously done with the help of mechanical models, it turned out the electromagnetic field equation.

Consider the physical meaning of the Maxwell equations. The first equation suggests that the sources of the magnetic field are current and changing the electric field. The brilliant guessed of Maxwell was the introduction of a fundamentally new concept - the current of the displacement - as a separate term in the generalized AMPER Act - Maxwell:

where N. - vector magnetic field strength; j. - the electric current density vector in which the displacement current is added to Maxwell; D. - vector of electrical induction; C is some permanent.

This equation expresses magnetoelectric induction, open Maxwell and based on shift current views.

Another immediate recognition of Maxwell idea was the idea of \u200b\u200bthe Faraday of the nature of electromagnetic induction - the occurrence of induction current in the circuit, the number of magnetic power lines in which changes or due to the relative movement of the circuit and magnet, or due to the change of the magnetic field. Maxwell recorded the following equation:

where E. - vector electric field strength; AT -

magnetic field tension torque and, accordingly: - -

changing the magnetic field in time, C is some permanent.

This equation reflects the law of electromagnetic induction of Faraday.

It is necessary to take into account another important property of electrical and magnetic induction vectors. E. Both V. While the electric power lines begin and end on charges that are sources of fields, the power lines of the magnetic field are closed on themselves.

In mathematics, the "Divergence" operator (Field Differentiation) - DIV is used to designate the characteristics of the vector field. Using this, Maxwell adds two more to two available equations:

where p is the density of electrical charges.

The third equation Maxwell expresses the law of preserving the amount of electricity, the fourth - the vortex character of the magnetic field (or the absence of magnetic charges).

The electrical and magnetic induction vectors included in the considered equations and the tensions of electrical and magnetic fields are associated with simple ratios and can be recorded in the form of the following equations:

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

In addition, you can write another ratio that binds the vector of tension E. and specific conductivity:

To represent the full system of Maxwell equations, it is necessary to record more boundary conditions. These conditions should satisfy the electromagnetic field on the border of the section of two environments.

where about - surface density of electrical charges; i is the surface density of the conductivity current on the interface under consideration. In the particular case, when there are no surface currents, the last condition goes into:

Thus, J. Maxwell comes to the definition of an 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 the vector designations and recorded its equations in a sufficiently cumbersome component. The modern form of Maxwell equations appeared around 1884 after the works of O. Heviside and Gersi.

Maxwell's equations are one of the greatest achievements of not only physics, but also civilization at all. They combine the strict logicality characteristic of natural sciences, beauty and proportionality, which is distinguished by art and humanitarian science. Equations with the highest possible accuracy reflect the essence of natural phenomena. The potential of the Maxwell equations is far from exhausted, on their basis all new works appear, explanations of the latest discoveries in various fields of physics - from superconductivity to astrophysics. The Maxwell Equations system is the basis of modern physics, and there is still no experienced fact that would contradict these equations. Knowledge of the Maxwell equations, at least their physical entity, is necessarily for any educated person, not only physics.

Maxwell equations were the forerunner of new non-classical physics. Although Maxwell himself, in his scientific convictions, was a "classic" man to the brain of bones, written by the equations themselves belonged to another science other than the one that was known and close to the scientist. This is evidenced by at least the fact that Maxwell's equations are non-invariant relative to the transformations of Galilee, however, they are invariant with regard to Lorentz transformations, which, in turn, underlie relativistic physics.

On the basis of the obtained equations, Maxwell solved specific tasks: determined the coefficients of the electrical permeability of a number of dielectrics, calculated the coefficients of self-induction, mutually induction of coils, etc.

Maxwell equations make it possible to make a number of essential conclusions. May be the main one - the existence of transverse electromagnetic waves propagating at speeds with.

Maxwell found that an unknown number C turned out to be approximately equal to the attitude of the electromagnetic and electrostatic charge units, which is approximately 300,000 kilometers per second. Convinced of the universality of his equations, it shows that "the light is electromagnetic indignation." Recognition of the ultimate, although very large, the speed of the propagation of the electromagnetic field of stone on the stone did not leave the theories of the supporters of the "instant long-range".

The most important consequence of the electromagnetic theory of light was predicted by Maxwell light pressure. He managed to calculate that in the case when in clear weather, the sunlight absorbed by the plane in one square meter gives 123.1 kilogram meter energy per second. This means that it presses on this surface towards its fall with a force of 0.41 milligrams. Thus, Maxwell's theory was strengthened or crumbling depending on the results of not yet implemented experiments. Are there any electromagnetic waves with properties similar to the light? Is there a light pressure? After the death of Maxwell, Heinrich Hertz answered the first question, on the second - Peter Nikolaevich Lebedev.

J. K. Maxwell is a gigantic figure in physical science and as a person. In the memory of Maxwell people will live as much as humanity will exist. Maxwell's name is immortalized in the name of the crater on the moon. The highest mountains on Venus are named after the Great Scientist (Maxwell Mountain). They rise 11.5 km above the middle surface level. Also, his name carries the world's largest telescope, which can work in a submillimeter range (0.3-2 mm) -tolescale. J. K. Maxwell (JCMT). It is located in the Hawaiian Islands (USA), on the highland terrain of Maun Kea (4200 m). The main 15-meter JCMT telescope mirror is made of 276 separate aluminum fragments tightly joined together. The Maxwell telescope is used to explore the 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 a certain interpretation. In this regard, it is necessary to note the merits of the Russian scientist Nikolai Alekseevich Umova, who headed the Department of Physics of Moscow University from 1896 to 1911

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

Work is devoted to various problems of physics. The main one was the creation of the teachings on the movement of energy (vector Umov), which he outlined in 1874 in his doctoral dissertation. The minds of Bay are endowed with high civil liability. Together with other professors (V. I. Vernadsky, K. A. Timiryazev,

N. D. Zelinsky, P. N. Lebedev) He in 1911 left Moscow University in protest against the actions of the reaction-minded Minister of Education L. A. Casso.

The mind was active propaganda of science, popularizer of scientific knowledge. Almost the first of physicists scientists, he understood the need for serious and purposeful studies of the teaching techniques of physics. Most of the eldest generation scientists are his students and followers.

The main merit of Umova - development of exercise on energy movement. In 1874, he received a general expression for the energy flux density vector in relation to elastic media and viscous fluids (vector Umika). After 11 years English scientist John Henry Pointing (1852-1914) did the same for the stream of electromagnetic energy. So in the theory of electromagnetism appeared known vector Umova. - Pointing.

Pointing was one of those scientists who immediately accepted the theory of Maxwell. It is impossible to say that such scientists had a lot of enough, Maxwell himself understood. Maxwell Theory was not immediately understood even in the Cavendish laboratory created by him. Nevertheless, with the advent of the theory of electromagnetism, the knowledge of nature rose to a qualitatively different level, which, as it always happens, is more and more removing us from direct sensual ideas. This is a normal venterity process accompanying all the development of physics. The history of physics gives many similar examples. It suffices to recall the provisions of quantum mechanics, the special theory of relativity, other modern theories. So the electromagnetic field during Maxwell was hardly available to understanding people, including the scientific medium, and the more not available for their sensory perception. Nevertheless, after experimental works, the hertz arose ideas about the creation of wireless communications with the help of electromagnetic waves ended with the invention of radio. Thus, the emergence and development of radio communications technology turned the electromagnetic field into a well-known and habitual concept.

A crucial role in the victory of the theory of the electromagnetic field Maxwell played a German physicist Heinrich Rudolf Hertz. The Hertz's interest in electrodynamics was stimulated by G. L. Helmholtz, who, considering it necessary to "order" this area of \u200b\u200bphysics, suggested that Herters work in the processes in the unlocked electrical circuits. At first, Hertz abandoned the topic, but then, working in Carlsruhe, discovered the devices there, which could be used for such studies. This predetermined his choice, especially since the hertz itself, good knowing the theory of Maxwell, was fully prepared for such research.

Henry 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 in Helmholts. Since 1885, Hertz works in the Higher Technical School in Karlsruhe, where his research begins, leaving for the discovery of electromagnetic waves. They were continued in 1890 in Bonn, where Hertz moved, replacing as Professor of Experimental Physics R. Clausius. Here he continues to engage in electrodynamics, but gradually his interests are shifted to the mechanics. Hertz died on January 1, 1894 in the heyday of talent aged 36 years.

By the beginning of the works, hertz electrical oscillations were already studied quite detailed. William Thomson (Lord Kelvin) was obtained an expression, which is now known to each schoolchild:

where T. - period of electrical oscillations; BUT - inductance that Thomson called the "electrodynamic capacity" of the conductor; C - capacitance of the capacitor. Formula received confirmation in experiments Berenda Wilhelm Feddersen(1832-1918), who studied the oscillations of the spark discharge of Leiden bank.

The article "On very fast electrical fluctuations" (1887), Hertz leads a description of their experiments. Their essence explains Figure 10.4. In the final form used by Herz, the oscillating circuit was two Conditioners of the SIS ", located at a distance of about 3 m from each other and the connected copper wire, in the middle of which there was a discharge AT induction coil. The receiver was the contour aCDB. with dimensions of 80 x 120 cm, with spark gap M. In one of the short sides. Detection was determined by the presence of a weak spark in the arrester M. The conductors with whom experimented by Hertz is, in modern language, antenna with a detector. They now wear names vibrator and resonator Hertz.

Fig. 10.4.

The essence of the results obtained was that the electrical spark in the arrester AT caused a spark in the arrester M.At first, the hertz, explaining the experiments, does not talk about Maxwell waves. He speaks only about the "interaction of conductors" and is trying to seek an explanation in the theory of long-range. Conducting experiments, Hertz found that at low distances the nature of the distribution of "electric power" is similar to the field of the dipole, and then it decreases slower and has an angular dependence. We would now say that the arrester possesses an anisotropic pattern of orientation. This, of course, is radically contrary to the theory of long-range.

After analyzing the results of experiments and conducting their own theoretical studies, Hertz adopts the Maxwell theory. It comes to the conclusion about the existence of electromagnetic waves propagating the final speed. Now the Maxwell equations are no longer an abstract mathematical system and they should be brought to this species so that they are convenient to use.

Hertz received an experimentally predicted theory of Maxwell electromagnetic waves and, not less important, proved their identity with light. To do this, it was necessary to prove that with the help of electromagnetic waves, it is possible to observe the well-known effects of optics: refraction and reflection, polarization, etc. Hertz fulfilled these studies that demanded virtuoso experimental skills: he conducted experiments on the spread, reflection, refraction, polarization of electromagnetic waves open to them. He built mirrors for experiments with these waves (Hertz mirrors), asphalt prism, etc. The hertz mirrors are shown in Fig. 10.5. Experiments have shown the complete identity of the observed effects with those that were well known for light waves.

Fig. 10.5.

In 1887, in the work "On the influence of ultraviolet light on an electric discharge", Hertz describes the phenomenon that began to call external photoeffect. It discovered that when irradiated with ultraviolet rays, high-voltage electrodes, the discharge occurs at a greater distance between the electrodes than without irradiation.

This effect then comprehensively researched Russian scientist Alexander Grigorievich Tsoletov (1839-1896).

In 1889, at the congress of German naturalists and doctors, Hertz read a report on the relationship between light and electricity, which expressed his opinion on the enormous importance of Maxwell's theory, now confirmed by experiments.

Experiments of Hertz produced a furor in the scientific world. They were repeated many times and varied. One of those who did it was Peter Nikolaevich Lebedev. He received the shortest electromagnetic waves at that time and in 1895 he had done experiments with them on double bempraine. In his work, Lebedev put the task of a gradual decrease in the wavelength of electromagnetic radiation so that in the end, to sick them with long infrared waves. The Lebedev himself could not be done, but this was carried out in the 20s of the 20th century Russian scientists Alexandra Andreevna Glagolev-Arkadyev (1884-1945) and Maria Afanasyevna Levitskaya (1883-1963).

Peter Nikolaevich Lebedev (1866-1912) - Russian physicist, born in 1866 in Moscow, graduated from the University of Strasbourg and began working at Moscow University in 1891. Lebedev remained in the history of physics as an experimenter-virtuoso, the author of the research performed by modest means on the verge of technical capabilities of that time, as well as the founder of the generally accepted scientific school in Moscow, from where the famous Russian scientists P. P. Lazarev, S. I. Vavilov came from. A. R. Collie, etc.

Lebedev died in 1912, soon after he, together with other professors, left the Moscow University in protest against the actions of the reaction-minded Minister of Education L. A. Casso.

However, the main merit of Lebedev in front of the physics is that he experimentally measured the predicted the theory of Maxwell light pressure. The study of this effect of Lebedev dedicated all his life: in 1899 an experiment was raised, which proved the presence of pressure of light on solids (Fig. 10.6), and in 1907 - on Gaza. Lebedev's work on light pressure became classic, they are one of the vertices of the experiment of the end of the XIX - early XX century.

Lebedev's experiments on light pressure brought him world glory. On this occasion, W. Thomson said "I fought all my life with Maxwell, without recognizing his light movement, but ... Lebedev made me surrender before his experiments."

Fig. 10.6.

Experiments of Hertz and Lebedev finally approved the priority of Maxwell's theory. As for practice, i.e. practical application of electromagnetism laws, then by the beginning of the XX century. Humanity has already lived in a world in which electricity has become a huge role. This was facilitated by stormy inventive activities in the application of electrical and magnetic phenomena open physicists. Note some of these inventions.

One of the first applications of electromagnetism found in the communication technique. Telegraph existed since 1831 in 1876. American physicist, inventor and entrepreneur Alexander Bell (1847-1922) invented the phone, which was then improved by the famous American inventor Thomas Alva Edison (1847-1931).

In 1892 English physicist William Cruks (1832-1912) Formulated the principles of radio communications. Russian physicist Alexander Stepanovich Popov (1859-1906) and Italian scientist Gullymo Marconi (1874-1937) In fact, simultaneously applied them in practice. Usually the question of the priority of this invention arises. Popov a little earlier demonstrated the possibilities of the device created by him, but did not patented him as Marconi did. The latter and determined the traditional tradition to consider Marconi "Father" the radio in the West. This was facilitated by the awarded by the Nobel Prize in 1909. Popov, apparently, would also be among the laureates, but he was already alive by that time, and the Nobel Prize was awarded only by Healthy scientists. Read more about the history of the invention, the radio will be told in part VI of the book.

Electrical phenomena tried to use for lighting in the XVIII century. (Voltova Arc), In the future, this device was improved Pavlom Nikolayevich Yablochkov(1847-1894), which in 1876 invented the first-suitable electric light source for practical use (Candle of Apple). However, she did not find wide use, first of all, because in 1879. T. Edison was created an incandescent lamp a rather durable design and convenient for industrial manufacture. Note that the incandescent lamp was invented in 1872 by Russian electrical engineering Alexander Nikolayevich Lodygina (1847- 1923).

test questions

• 1. What studies did Maxwell, working in Marisal College? What role did Maxwell play in the development of teachings about electricity and magnetism?
• 2. When was the Cavendish laboratory been organized? Who became her first director?
• 3. What law did not manage to describe with the help of electro-hydraulic analogies?
• 4. With which Maxwell model came to the conclusion about the existence of the shift current and the phenomenon of magnetoelectric induction?
• 5. In what article Maxwell first used the term "electromagnetic field"?
• 6. How is the system of equations drawn up by Maxwell recorded?
• 7. Why are Maxwell equations are considered one of the triumphal achievements of human civilization?
• 8. What conclusions did Maxwell from the theory of the electromagnetic field?
• 9. How did the electrodynamics develop after Maxwell?
• 10. How did hertz concluded about the existence of electromagnetic waves?
• 11. What is the main merit of Lebedev in front of physics?
• 12. How is the theory of the electromagnetic field used in the technique?

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 the theory of the electromagnetic field of Maxwell.
• 3. The history of creating Maxwell equations.
• 4. The physical essence of the Maxwell equations.
• 5. J. K. Maxwell - First Director of the Cavendish Laboratory.
• 6. How the Maxwell equations system is currently recorded: a) in the integral form; b) in differential form?
• 7. G. Herz. Biography and scientific achievements.
• 8. The history of detection of electromagnetic waves and their identification with light.
• 9. Experiments P. N. Lebedev to detect light pressure: scheme, tasks, difficulties and meaning.
• 10. Works A. A. Glagolevoy-Arkadyeva and M. A. Levitskaya to generate short electromagnetic waves.
• 11. The history of the opening and studies of the photo effect.
• 12. Development of Maxwell's electromagnetic theory. Works J. G. Painoving, N. A. Umova, O. Heviside.
• 13. How was the electrical telegraph invented and improved and improved?
• 14. The historical stages of the development of electric and radio engineering.
• 15. History of creating lighting devices.

• 1. Kudryavtsev, P. S. Course of the history of physics. - 2nd ed. - M.: Enlightenment, 1982.
• 2. Kudryavtsev, P. S. History of physics: in 3 tons. - M.: Enlightenment, 1956-1971.
• 3. Spassky, B. I. History of physics: in 2 tons. - M.: Higher School, 1977.
• 4. Dorfman, Ya. G. World History of Physics: 2 tons. - M.: Science, 1974-1979.
• 5. Golin, Mr. Classics of physical science (from ancient times before the beginning of the XX century) / M. Golin, S. R. Filonovich. - M.: Higher School, 1989.
• 6. Khramov, Yu. A. Physics: biographical reference book. - M.: Science, 1983.
• 7. Virginsky, V. S. Essays of the history of science and technology in 1870-1917. / V. S. Virginsky, V. F. Hotenkov. - M.: Education, 1988.
• 8. Viktovski, N. Sentimental history of science. - M.: Hummingbird, 2007.
• 9. Maxwell, J. K. Selected Works on the theory of the electromagnetic field. - M.: Gittle, 1952.
• 10. Kuznetsova, O. V. Maxwell and the development of physics of the XIX-XX centuries: Sat. Articles / d. ed. L. S. Polak. - M.: Science, 1985.
• 11. Maxwell, J. K. Treatise on electricity and magnetism: in 2 tons. - M.: Science, 1989.
• 12. Kartsev, V.P. Maxwell. - M.: Young Guard, 1974.
• 13. Niven, W. Life and scientific activity of J. K. Maxwell: A brief essay (1890) // J. K. Maxwell. Matter and movement. - M.: Izhevsk: RCD, 2001.
• 14. Harman, R. M. The Natural Philosophy of James Clerk Maxwell. - Cambridge: University Press, 2001.
• 15. Bolotovsky, B. M. Oliver Heviside. - M.: Science, 1985.
• 16. Gorokhov, V. G. The formation of radiotechnical theory: from theory to practice on the example of technical consequences from the opening of the city of Hertz // Viet. - 2006. - № 2.
• 17. Book series "ZhZL": "People of science", "Creators of science and technology."

Now almost every person knows that the electric and magnetic fields are directly interconnected with each other. There is even a special section of physics studying electromagnetic phenomena. But in the 19th century, the Maxwell's electromagnetic theory was not formulated, everything was completely different. It was believed, for example, that the electrical fields are inherent in only particles and bodies with magnetic properties - a completely different area of \u200b\u200bscience.

In 1864, the famous British physicist D. K. Maxwell indicates the direct relationship of electrical and magnetic phenomena. The discovery was called the "Theory of the Electromagnetic Field of Maxwell". Due to her, it was possible to solve a number of insoluble, from the point of view of electrodynamics of the time, questions.

Most high-profile discoveries are always based on the results of previous researchers. Maxwell's theory is no exception. A distinctive feature is that Maxwell significantly expanded the results obtained by its predecessors. For example, it indicated that not only a closed contour from a conductive material can be used, but consisting of any material. In this case, the contour is an indicator of a vortex electric field, which affects not only on metals. With such a point of view, when in the field of dielectric material, it is more correct to talk about the currents of polarization. They also make a job that consists in heating the material to a certain temperature.

The first suspicion of the connection is electrical and appeared in 1819. H. Earsted noted that if near the conductor with a current to position the compass, the direction of the arrow deviates from

In 1824, A. Ampere formulated the law of interaction of conductors, subsequently called the "Ampire Law".

And finally, in 1831, Faradays recorded the appearance of the current in the circuit in a changing magnetic field.

Maxwell's theory is designed to solve the main task of electrodynamics: with the well-known spatial distribution of electrical charges (currents), some characteristics of the generated magnetic and electric fields can be determined. This theory does not consider the mechanisms themselves underlying the occurrence of phenomena.

Maxwell's theory is designed for near-locked charges, since the system of equations is considered to be occurring, regardless of the medium. An important feature of the theory is the fact that its fields are considered on its basis, which:

Are generated by relatively large currents and charges distributed in a large volume (many times higher than the size of the atom or molecule);

Magnetic and electrical field variables change faster than the period of processes inside the molecules;

The distance between the calculated point of space and the source of the field exceeds the size of the atoms (molecules).

All this suggests that Maxwell's theory applies primarily to the macromir's phenomena. Modern physics more and more processes explains from the point of view of quantum theory. In Maxwell formulas, quantum manifestations are not taken into account. Nevertheless, the use of Maxwellian systems of equations allows you to successfully solve a certain range of tasks. Interestingly, since the density of electrical currents and charges are taken into account, then theoretically, the existence of them, but magnetic nature. In 1831, he pointed out Dirak, denoting them with magnetic monopulas. In general, the main postulates of theory are as follows:

The magnetic field is created by an alternating electric field;

A variable magnetic field generates an electric field of vortex nature.

Basics of Maxwell theory for electromagnetic field

§ 137. Vortex electric field

From the Faraday Law (see (123.2))

ξ = d.F /dt. follows that anyonechange

the magnetic induction lifted with the circuit of the magnetic induction leads to the occurrence of the electromotive force of the induction and the induction current appears as a result. Consequently, the emergence of er D.S. Electromagnetic induction is possible in a fixed circuit, located in a variable magnetic field. However, er D.S. In any chain arises only when there are third-party forces in it on the current carriers - the forces of non-electrostatic origin (see § 97). Therefore, the question of the nature of third-party forces in this case arises.

Experience shows that these third-party forces are not associated with either thermal or chemical processes in the circuit; Their appearance can also be explained by Lorentz by the forces, since they do not act on fixed charges. Maxwell expressed the hypothesis that any variable magnetic field excites the electric field in the surrounding space, which

and is the cause of induction current in the circuit. According to Maxwell's ideas, the contour in which Eh appears. D.S., plays a minor role, being a kind of only "device" that detects this field.

So, according to Maxwell, changing in time, the magnetic field generates an electric field E.B.whose circulation, software (123.3),

https://pandia.ru/text/80/088/images/image002_18.jpg "width \u003d" 102 "height \u003d" 48 "\u003e (see (120.2)), we get

Differentiation "href \u003d" / text / category / differentciya / "REL \u003d" BOOKMARK "\u003e differentiation and integration can be changed in places. Consequently,

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function only on time.

According to (83.3), circulation of the vector of the electrostatic field (we denote it e.q) Along any closed circuit is zero:

Whirlwind "Href \u003d" / Text / Category / Vihrmz / "Rel \u003d" Bookmark "\u003e Vortex.

§ 138. Shift current

According to Maxwell, if any variable magnetic field excites the vortex electric field in the surrounding space, then the opposite phenomenon should exist: any change in the electric field should cause the appearance in the surrounding space of the vortex magnetic field. To establish a quantitative relationship between the changing electric field and the Maxwell caused by the magnetic field caused by it, the so-called shift current.

Consider the alternating current circuit containing the capacitor (Fig. 196). There is an alternating electric field between the plates of the charging and discharge capacitor, therefore, according to Maxwell, through the condenser

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(Surface density S on plates is equal to electrical displacement D. in the condenser (see (92.1)). The integrand in (138.1) can be viewed as a special case of a scalar product ( d.D./d.t) D. S.when d.D./d.t and D. S. Mutually parallel. Therefore, for a general case can be recorded

Comparing this expression with I.=I.cM \u003d https: //pandia.ru/text/80 /088/images/image011_2.jpg "width \u003d" 241 "height \u003d" 39 src \u003d "\u003e

Expression (138.2) and was called Maxwell displacement density.

Consider what is the direction of density vectors of conductivity and offset j. and j.see when charging the capacitor (Fig. 197, a) through the conductor connecting the plated, the current flows from the right-layer to the left; The field in the condenser is enhanced, vector D grows with time;

hence, d.D./d.t\u003e 0, i.e. vector d.D./d.t.

Vacuum "href \u003d" / text / category / vakuum / "REL \u003d" Bookmark "\u003e vacuum or substance) Creates a magnetic field in the surrounding space (the induction line of the magnetic fields of displacement currents during charging and discharge of the capacitor is shown in Fig. 197 dash line).

In dielectric shift current consists of two terms. Since, according to (89.2), D.\u003d E0. E.+P.where E. - the tension of the electrostatic field, and R - polarity (see § 88), then the density of the offset current

https://pandia.ru/text/80/088/images/image014_0.jpg "width \u003d" 82 "height \u003d" 48 "\u003e Through the surface S., stretched on a closed outline L.. Then generalized vector circulation theoremwrong in the form

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

2. Generalized vector circulation theorem N. (See (138.4)):

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If the charge is distributed inside the closed surface continuously with the bulk density R, then formula (139.1) is recorded as

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So, complete system of Maxwell equations in an integral form:

The values \u200b\u200bincluded in the Maxwell equations are not independent and between them exists the following connection (isotropic non-ferroelectric and non-ferromagnetic environments):

D.\u003d E0E. E.,

In \u003d.m0m. N,

j.\u003d G. E.,

where E0 and M0 are the electrical and magnetic constant, E and M, respectively, respectively, dielectric and magnetic permeability, G is the specific conductivity of the substance.

Of the Maxwell equations, it follows that either electrical charges or magnetic fields change in time can be sources, and magnetic fields can be excited by either moving electrical charges (electrical currents) or by variable electric fields. Maxwell equations are not symmetric about electric and magnetic fields. This is due to the fact that in nature there are electrical charges, but there are no charges of magnetic.

For stationary fields (e \u003dconst I. AT\u003d const) maxwell equationstake a look

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can be represented complete system of Maxwell equations in differential form(characterizing the field at each point of space):

If charges and currents are distributed in space continuously, both forms of Maxwell equations - integral

and differential - equivalent. However, when there are surface breaks- Surfaces on which the properties of the medium or fields change jump-like, the integral form of equations is more general.

Maxwell's equations in differential form assume that all values \u200b\u200bin space and time change continuously. To achieve mathematical equivalence of both forms of Maxwell equations, the differential form is complemented by boundary conditionswhich should satisfy the electromagnetic field on the border of the two media partition. The integral form of the Maxwell equations contains these conditions. They were reviewed earlier (see § 90, 134):

D.1n.= D.2n., E.1t.= E.2t., B.1n.= B.2 n., H.1t \u003d H2T.

(The first and last equation correspond to cases when there are no free charges on the border of the section, no conductivity currents).

Maxwell equations are the most common equations for electrical and magnetic fields in resting environments.They play in the teaching about electromagnetism the same role as Newton's laws in mechanics. From the Maxwell equations, it follows that the variable magnetic field is always associated with an electric field generated by it, and the alternating electric field is always associated with a magnetic generated by it, i.e., the electric and magnetic fields are inextricably linked with each other - they form a single electromagnetic field.

Maxwell's theory, being a generalization of the basic laws of electrical and magnetic phenomena, was able to explain not only already known experimental facts, which is also an important consequence, but also predicted new phenomena. One of the important findings of this theory was the existence of a magnetic field of displacement currents (see § 138), which allowed Maxwell to predict existence electromagnetic waves- A variable electromagnetic field spreading in space with a finite speed. In the future, it was proved

that the speed of propagation of the free electromagnetic field (not associated with charges and currents) in vacuo is equal to the speed of light C \u003d 3 108 m / s. This conclusion and theoretical study of the properties of electromagnetic waves led Maxwell to the creation of electromagnetic theory of light, according to which the light is also electromagnetic waves. Electromagnetic waves on experience were obtained by German physicist. Herz (1857-1894), which have proven that the laws of their excitation and distribution are fully described by the Maxwell equations. Thus, Maxwell's theory was experimentally confirmed.

Only the principle of Einstein's relativity is applicable to the electromagnetic field, since the fact of the propagation of electromagnetic waves in vacuo in all reference systems at the same speed withnot compatible with the principle of reliability of Galilee.

According to the principle of the relativity of Einstein,mechanical, optical and electromagnetic phenomena in all inertial reference systems are equally described in the same equations. Maxwell's equations are invariant with respect to Lorentz transformations: their appearance does not change during the transition

from one inertial reference system to another, although the values E, in,D., N. They are transformed according to certain rules.

Of the principle of relativity, it implies that a separate consideration of electric and magnetic fields has a relative meaning. So, if the electric field is created by the stationary charge system, then these charges, being fixed relative to one inertial reference system, move relative to the other and, therefore, will generate not only the electric, but also the magnetic field. Similarly, a constant current conductor with a constant current, motionless relative to one inertial reference system, exciting a constant magnetic field at each point of space, moves relative to other inertial systems, and the variable magnetic field created by them excites the vortex electric field.

Thus, Maxwell's theory, its experimental confirmation, as well as the principle of Einstein's relativity lead to a single theory of electric, magnetic and optical phenomena based on the submission of an electromagnetic field.

test questions

What is the cause of the vortex electric field? How does it differ from the electrostatic field?

What is the circulation of the vortex electric field?

Why is the concept of shifting current introduced? What is it essentially present?

Display and explain the expression for the density of the offset current.

In what sense can you compare the shift current and conductivity current?

Write down, explaining the physical meaning, generalized the theorem on the circulation of the magnetic field strength vector.

Record the complete system of Maxwell equations in integral and differential forms and explain their physical meaning.

Why are constant electrical and magnetic fields can be considered apart from each other? Write the Maxwell equation for them in both forms.

Why is Maxwell equations in integrated form are more common?

What are the main conclusions can be made on the basis of Maxwell theory?