An electromagnetic wave is a process of successive, interrelated changes in the electric and magnetic field strength vectors directed perpendicular to the wave propagation beam, in which a change in the electric field causes changes in the magnetic field, which, in turn, cause changes in the electric field.

Wave (wave process) - the process of propagation of oscillations in continuum. When a wave propagates, the particles of the medium do not move along with the wave, but oscillate around their equilibrium positions. Together with the wave, only the states of oscillatory motion and its energy are transferred from particle to particle of the medium. Therefore, the main property of all waves, regardless of their nature, is the transfer of energy without the transfer of matter

Electromagnetic waves occur whenever there is a changing electric field in space. Such a changing electric field is caused, most often, by the movement of charged particles, and as a special case of such movement, by an alternating electric current.

The electromagnetic field is an interconnected oscillation of the electric (E) and magnetic (B) fields. The distribution of a single electromagnetic field in space is carried out by means of electromagnetic waves.

Electromagnetic wave - electromagnetic oscillations that propagate in space and carry energy

Features of electromagnetic waves, the laws of their excitation and propagation are described by Maxwell's equations (which are not considered in this course). If in some region of space there are electric charges and currents, then their change over time leads to the emission of electromagnetic waves. The description of their propagation is similar to the description of mechanical waves.

If the medium is homogeneous and the wave propagates along the X axis with a speed v, then electrical (E) and magnetic (B) the field components at each point of the medium change according to the harmonic law with the same circular frequency (ω) and in the same phase (plane wave equation):

where x is the coordinate of the point and t is the time.

Vectors B and E are mutually perpendicular, and each of them is perpendicular to the direction of wave propagation (X axis). Therefore, electromagnetic waves are transverse

Sinusoidal (harmonic) electromagnetic wave. Vectors , and are mutually perpendicular

1) Electromagnetic waves propagate in matter with final speed

Speed c propagation of electromagnetic waves in vacuum is one of the fundamental physical constants.

Maxwell's conclusion about the finite propagation velocity of electromagnetic waves was in conflict with the accepted at that time long-range theory , in which the propagation velocity of the electric and magnetic fields was assumed to be infinitely large. Therefore, Maxwell's theory is called the theory short range.

Mutual transformations of electric and magnetic fields occur in an electromagnetic wave. These processes go on simultaneously, and the electric and magnetic fields act as equal "partners". Therefore, the volume densities of electric and magnetic energy are equal to each other: w e = w m.

4. Electromagnetic waves carry energy. When waves propagate, a flow of electromagnetic energy arises. If you select a site S(Fig. 2.6.3), oriented perpendicular to the direction of wave propagation, then in a short time Δ t energy Δ will flow through the platform W uh, equal

Substituting here the expressions for w uh, w m and υ, you can get:

where E 0 is the amplitude of the electric field strength oscillations.

The energy flux density in SI is measured in watts per square meter(W / m 2).

5. It follows from Maxwell's theory that electromagnetic waves must exert pressure on an absorbing or reflecting body. The pressure of electromagnetic radiation is explained by the fact that under the influence of the electric field of the wave, weak currents arise in the substance, that is, the ordered movement of charged particles. These currents are affected by the Ampère force from the side of the magnetic field of the wave, directed into the thickness of the substance. This force creates the resulting pressure. Usually the pressure of electromagnetic radiation is negligible. So, for example, the pressure of solar radiation coming to the Earth on an absolutely absorbing surface is approximately 5 μPa. The first experiments to determine the radiation pressure on reflecting and absorbing bodies, which confirmed the conclusion of Maxwell's theory, were carried out by P. N. Lebedev in 1900. Lebedev's experiments were of great importance for the approval of Maxwell's electromagnetic theory.

The existence of pressure of electromagnetic waves allows us to conclude that the electromagnetic field is inherent in mechanical impulse. The momentum of the electromagnetic field in a unit volume is expressed by the relation

This implies:

This relationship between the mass and energy of an electromagnetic field in a unit volume is a universal law of nature. According to the special theory of relativity, it is true for any bodies, regardless of their nature and internal structure.

Thus, the electromagnetic field has all the features of material bodies - energy, finite propagation velocity, momentum, mass. This suggests that the electromagnetic field is one of the forms of existence of matter.

6. The first experimental confirmation of Maxwell's electromagnetic theory was given approximately 15 years after the creation of the theory in the experiments of G. Hertz (1888). Hertz not only experimentally proved the existence of electromagnetic waves, but for the first time began to study their properties - absorption and refraction in different media, reflection from metal surfaces, etc. He managed to measure the wavelength and propagation velocity of electromagnetic waves, which turned out to be equal to the speed of light .

Hertz's experiments played a decisive role in the proof and recognition of Maxwell's electromagnetic theory. Seven years after these experiments, electromagnetic waves found application in wireless communications (A. S. Popov, 1895).

7. Electromagnetic waves can only be excited fast moving charges. DC circuits, in which charge carriers move at a constant speed, are not a source of electromagnetic waves. In modern radio engineering, the radiation of electromagnetic waves is produced using antennas of various designs, in which fast alternating currents are excited.

The simplest system that emits electromagnetic waves is a small electric dipole, the dipole moment p (t) which changes rapidly with time.

Such an elementary dipole is called Hertzian dipole . In radio engineering, the Hertzian dipole is equivalent to a small antenna, the size of which is much smaller than the wavelength λ (Fig. 2.6.4).

Rice. 2.6.5 gives an idea of ​​the structure of the electromagnetic wave emitted by such a dipole.

It should be noted that the maximum electromagnetic energy flux is emitted in a plane perpendicular to the dipole axis. A dipole does not radiate energy along its axis. Hertz used an elementary dipole as a transmitting and receiving antenna in experimental proof of the existence of electromagnetic waves.

M. Faraday introduced the concept of a field:

an electrostatic field around a charge at rest

around moving charges (current) there is a magnetic field.

In 1830, M. Faraday discovered the phenomenon of electromagnetic induction: when the magnetic field changes, a vortex electric field arises.

Figure 2.7 - Vortex electric field

where,
- electric field strength vector,
- vector of magnetic induction.

An alternating magnetic field creates a vortex electric field.

In 1862 D.K. Maxwell put forward a hypothesis: when the electric field changes, a vortex magnetic field arises.

The idea of ​​a single electromagnetic field arose.

Figure 2.8 - Unified electromagnetic field.

The alternating electric field creates a vortex magnetic field.

Electromagnetic field- this is a special form of matter - a combination of electric and magnetic fields. Variable electric and magnetic fields exist simultaneously and form a single electromagnetic field. It is material:

It manifests itself in action on both resting and moving charges;

It spreads at a high but finite speed;

It exists independently of our will and desires.

At a charge rate of zero, there is only an electric field. At a constant charge rate, an electromagnetic field is generated.

With the accelerated movement of the charge, an electromagnetic wave is emitted, which propagates in space with a finite speed .

The development of the idea of ​​electromagnetic waves belongs to Maxwell, but Faraday already knew about their existence, although he was afraid to publish the work (it was read more than 100 years after his death).

The main condition for the emergence of an electromagnetic wave is the accelerated movement of electric charges.

What is an electromagnetic wave, it is easy to imagine the following example. If you throw a pebble on the surface of the water, then waves diverging in circles are formed on the surface. They move from the source of their occurrence (perturbation) with a certain speed of propagation. For electromagnetic waves, disturbances are electric and magnetic fields moving in space. A time-varying electromagnetic field necessarily causes an alternating magnetic field, and vice versa. These fields are interconnected.

The main source of the spectrum of electromagnetic waves is the Sun star. Part of the spectrum of electromagnetic waves sees the human eye. This spectrum lies within 380...780 nm (Fig. 2.1). In the visible spectrum, the eye perceives light differently. Electromagnetic oscillations with different wavelengths cause the sensation of light with different colors.

Figure 2.9 - Spectrum of electromagnetic waves

Part of the spectrum of electromagnetic waves is used for the purposes of radio and television broadcasting and communications. The source of electromagnetic waves is a wire (antenna) in which electric charges fluctuate. The process of formation of fields, which began near the wire, gradually, point by point, captures the entire space. The higher the frequency of the alternating current passing through the wire and generating an electric or magnetic field, the more intense the radio waves of a given length created by the wire.

Radio(lat. radio - emit, emit rays ← radius - beam) - a type of wireless communication in which radio waves freely propagating in space are used as a signal carrier.

radio waves(from radio...), electromagnetic waves with a wavelength > 500 µm (frequency< 6×10 12 Гц).

Radio waves are electric and magnetic fields that change over time. The speed of propagation of radio waves in free space is 300,000 km/s. Based on this, you can determine the length of the radio wave (m).

λ=300/f, where f - frequency (MHz)

The sound vibrations of the air created during a telephone conversation are converted by the microphone into electrical vibrations of sound frequency, which are transmitted by wires to the subscriber's equipment. There, at the other end of the line, with the help of the phone's emitter, they are converted into air vibrations perceived by the subscriber as sounds. In telephony, the means of communication are wires; in radio broadcasting, radio waves.

The "heart" of the transmitter of any radio station is a generator - a device that generates oscillations of a high, but strictly constant frequency for a given radio station. These radio frequency oscillations, amplified to the required power, enter the antenna and excite in the surrounding space electromagnetic oscillations of exactly the same frequency - radio waves. The speed of removal of radio waves from the antenna of the radio station is equal to the speed of light: 300,000 km / s, which is almost a million times faster than the propagation of sound in air. This means that if a transmitter was turned on at a certain moment in time at the Moscow Broadcasting Station, then its radio waves would reach Vladivostok in less than 1/30 s, and the sound during this time would have time to propagate only 10-11 m.

Radio waves propagate not only in the air, but also where there is none, for example, in outer space. In this they differ from sound waves, for which air or some other dense medium, such as water, is absolutely necessary.

electromagnetic wave is an electromagnetic field propagating in space (oscillations of vectors
). Near the charge, the electric and magnetic fields change with a phase shift p/2.

Figure 2.10 - Unified electromagnetic field.

At a large distance from the charge, the electric and magnetic fields change in phase.

Figure 2.11 - In-phase change in electric and magnetic fields.

The electromagnetic wave is transverse. The direction of the speed of the electromagnetic wave coincides with the direction of movement of the right screw when turning the handle of the vector gimlet to the vector .

Figure 2.12 - Electromagnetic wave.

Moreover, in an electromagnetic wave, the relation
, where c is the speed of light in vacuum.

Maxwell theoretically calculated the energy and speed of electromagnetic waves.

Thus, wave energy is directly proportional to the fourth power of frequency. This means that in order to more easily fix the wave, it is necessary that it be of high frequency.

Electromagnetic waves were discovered by G. Hertz (1887).

A closed oscillatory circuit does not radiate electromagnetic waves: all the energy of the electric field of the capacitor is converted into the energy of the magnetic field of the coil. The oscillation frequency is determined by the parameters of the oscillatory circuit:
.

Figure 2.13 - Oscillatory circuit.

To increase the frequency, it is necessary to decrease L and C, i.e. turn the coil to a straight wire and, as
, reduce the area of ​​​​the plates and spread them to the maximum distance. This shows that we get, in essence, a straight conductor.

Such a device is called a Hertz vibrator. The middle is cut and connected to a high frequency transformer. Between the ends of the wires, on which small spherical conductors are fixed, an electric spark jumps, which is the source of the electromagnetic wave. The wave propagates in such a way that the electric field strength vector oscillates in the plane in which the conductor is located.

Figure 2.14 - Hertz vibrator.

If the same conductor (antenna) is placed parallel to the emitter, then the charges in it will oscillate and weak sparks will jump between the conductors.

Hertz discovered electromagnetic waves in an experiment and measured their speed, which coincided with the one calculated by Maxwell and equal to c=3. 10 8 m/s.

An alternating electric field generates an alternating magnetic field, which, in turn, generates an alternating electric field, that is, an antenna that excites one of the fields causes the appearance of a single electromagnetic field. The most important property of this field is that it propagates in the form of electromagnetic waves.

The propagation velocity of electromagnetic waves in a lossless medium depends on the relatively dielectric and magnetic permeability of the medium. For air, the magnetic permeability of the medium is equal to one, therefore, the speed of propagation of electromagnetic waves in this case is equal to the speed of light.

The antenna can be a vertical wire powered by a high frequency generator. The generator expends energy to accelerate the movement of free electrons in the conductor, and this energy is converted into an alternating electromagnetic field, that is, electromagnetic waves. The higher the generator current frequency, the faster the electromagnetic field changes and the more intense the wave healing.

Connected to the antenna wire are both an electric field, the lines of force of which begin at positive and end at negative charges, and a magnetic field, the lines of which close around the current of the wire. The shorter the oscillation period, the less time remains for the energy of the bound fields to return to the wire (that is, to the generator) and the more it passes into free fields, which propagate further in the form of electromagnetic waves. Effective radiation of electromagnetic waves occurs under the condition of commensurability of the wavelength and the length of the radiating wire.

Thus, it can be determined that radio wave- this is an electromagnetic field not associated with the emitter and channel-forming devices, freely propagating in space in the form of a wave with an oscillation frequency of 10 -3 to 10 12 Hz.

Oscillations of electrons in the antenna are created by a source of periodically changing EMF with a period T. If at some moment the field at the antenna had a maximum value, then it will have the same value after a while T. During this time, the electromagnetic field that existed at the initial moment at the antenna will move to a distance

λ = υТ (1)

The minimum distance between two points in space where the field has the same value is called wavelength. As follows from (1), the wavelength λ depends on the speed of its propagation and the period of oscillation of the electrons in the antenna. As frequency current f = 1 / T, then the wavelength λ = υ / f .

The radio link includes the following main parts:

Transmitter

Receiver

The medium in which radio waves propagate.

The transmitter and receiver are controllable elements of the radio link, since it is possible to increase the transmitter power, connect a more efficient antenna, and increase the sensitivity of the receiver. The medium is an uncontrolled element of the radio link.

The difference between a radio communication line and wired lines is that wired lines use wires or cables as a connecting link, which are controlled elements (you can change their electrical parameters).

it is the process of propagation of electromagnetic interaction in space.
Electromagnetic waves are described by Maxwell's equations common to electromagnetic phenomena. Even in the absence of electric charges and currents in space, Maxwell's equations have nonzero solutions. These solutions describe electromagnetic waves.
In the absence of charges and currents, Maxwell's equations take the following form:

,

By applying the operation rot to the first two equations, you can obtain separate equations for determining the strength of the electric and magnetic fields

These equations have the typical form of wave equations. Their decouplings are the superposition of expressions of the following type

Where - A certain vector, which is called the wave vector, ? - a number called the cyclic frequency, ? - phase. The quantities are the amplitudes of the electric and magnetic components of the electromagnetic wave. They are mutually perpendicular and equal in absolute value. The physical interpretation of each of the introduced quantities is given below.
In a vacuum, an electromagnetic wave travels at a speed called the speed of light. The speed of light is a fundamental physical constant, which is denoted by the Latin letter c. According to the basic postulate of the theory of relativity, the speed of light is the maximum possible speed of information transfer or body movement. This speed is 299,792,458 m/s.
An electromagnetic wave is characterized by frequency. Distinguish the line frequency? and cyclic frequency? = 2??. Depending on the frequency, electromagnetic waves belong to one of the spectral ranges.
Another characteristic of an electromagnetic wave is the wave vector. The wave vector determines the direction of propagation of an electromagnetic wave, as well as its length. The absolute value of the wind vector is called the wavenumber.
The length of the electromagnetic wave? = 2? / k, where k is the wave number.
The length of an electromagnetic wave is related to frequency through the dispersion law. In the void, this connection is simple:

?? = c.

This ratio is often written as

? = c k.

Electromagnetic waves with the same frequency and wave vector can differ in phase.
In a vacuum, the strength vectors of the electric and magnetic fields of an electromagnetic wave are necessarily perpendicular to the direction of wave propagation. Such waves are called transverse waves. Mathematically, this is described by the equations and . In addition, the strengths of the electric and magnetic fields are perpendicular to each other and are always equal in absolute value at any point in space: E = H. If you choose a coordinate system so that the z axis coincides with the direction of propagation of an electromagnetic wave, there are two different possibilities for directions electric field strength vectors. If the eclectic field is directed along the x-axis, then the magnetic field will be directed along the y-axis, and vice versa. These two different possibilities are not mutually exclusive and correspond to two different polarizations. This issue is discussed in more detail in the article Polarization of waves.
Spectral ranges with selected visible light Depending on the frequency or wavelength (these quantities are related), electromagnetic waves are classified into different ranges. Waves in different ranges interact with physical bodies in different ways.
Electromagnetic waves with the lowest frequency (or longest wavelength) are referred to as radio range. The radio band is used to transmit signals over a distance using radio, television, mobile phones. Radar operates in the radio range. The radio range is divided into meter, ditsemeter, centimeter, millimeter, depending on the length of the electromagnetic wave.
Electromagnetic waves are likely to belong to the infrared range. In the infrared range lies the thermal radiation of the body. The registration of this vibration is the basis for the operation of night vision devices. Infrared waves are used to study thermal vibrations in bodies and help to establish the atomic structure of solids, gases and liquids.
Electromagnetic radiation with a wavelength of 400 nm to 800 nm belongs to the visible light range. Visible light has different colors depending on the frequency and wavelength.
Wavelengths less than 400 nm are called ultraviolet. The human eye does not distinguish them, although their properties do not differ from the properties of the waves in the visible range. The high frequency, and, consequently, the energy of the quanta of such light leads to a more destructive effect of ultraviolet waves on biological objects. The earth's surface is protected from the harmful effects of ultraviolet waves by the ozone layer. For additional protection, nature endowed people with dark skin. However, humans need ultraviolet rays to produce vitamin D. That is why people in northern latitudes, where the intensity of ultraviolet waves is less intense, have lost their dark skin color.
Higher frequency electromagnetic waves are x-ray range. They are called so because they were discovered by Roentgen, studying the radiation that is formed during the deceleration of electrons. In foreign literature, such waves are called X-rays respecting Roentgen's wish that the rays not call him by his name. X-ray waves interact weakly with matter, being absorbed more strongly where the density is greater. This fact is used in medicine for x-ray fluorography. X-ray waves are also used for elemental analysis and the study of the structure of crystalline bodies.
have the highest frequency and the shortest length ?-rays. Such rays are formed as a result of nuclear reactions and reactions between elementary particles. ?-rays have a great destructive effect on biological objects. However, they are used in physics to study various characteristics of the atomic nucleus.
The energy of an electromagnetic wave is determined by the sum of the energies of the electric and magnetic fields. The energy density at a certain point in space is given by:

.

The time-averaged energy density is equal to.

,

Where E 0 = H 0 is the wave amplitude.
The energy flux density of an electromagnetic wave is of great importance. In particular, it determines the luminous flux in optics. The energy flux density of an electromagnetic wave is given by the Umov-Poynting vector.

The propagation of electromagnetic waves in a medium has a number of features compared to propagation in a vacuum. These features are related to the properties of the medium and generally depend on the frequency of the electromagnetic wave. The electric and magnetic components of the wave cause polarization and magnetization of the medium. This response of the medium is not the same in the case of low and high frequencies. At a low frequency of an electromagnetic wave, the electrons and ions of the substance have time to respond to changes in the intensity of the electric and magnetic fields. The response of the medium traces the temporal fluctuations into waves. At a high frequency, the electrons and ions of the substance do not have time to shift during the period of oscillation of the wave fields, and therefore the polarization and magnetization of the medium are much less.
The electromagnetic field of low frequency does not penetrate into metals, where there are many free electrons, which are displaced in this way, completely quench the electromagnetic wave. An electromagnetic wave begins to penetrate the metal at a frequency exceeding a certain frequency, which is called the plasma frequency. At frequencies lower than the plasma frequency, an electromagnetic wave can penetrate into the surface layer of the metal. This phenomenon is called the skin effect.
In dielectrics, the dispersion law of an electromagnetic wave changes. If electromagnetic waves propagate with a constant amplitude in a vacuum, then in a medium they decay due to absorption. In this case, the energy of the wave is transferred to the electrons or ions of the medium. In total, the dispersion law in the absence of magnetic effects takes the form

Where the wave number k is a total complex quantity, the imaginary part of which describes the decrease in the amplitude of the electromagnetic wave, is the frequency-dependent complex permittivity of the medium.
In anisotropic media, the direction of the vectors of electric and magnetic fields is not necessarily perpendicular to the direction of wave propagation. However, the direction of the vectors of electric and magnetic induction retains this property.
In a medium, under certain conditions, another type of electromagnetic wave can propagate - a longitudinal electromagnetic wave, for which the direction of the electric field strength vector coincides with the direction of wave propagation.
At the beginning of the twentieth century, in order to explain the radiation spectrum of a black body, Max Planck suggested that electromagnetic waves are emitted by quanta with energy proportional to frequency. A few years later, Albert Einstein, explaining the phenomenon of the photoelectric effect, expanded this idea by assuming that electromagnetic waves are absorbed by the same quanta. Thus, it became clear that electromagnetic waves are characterized by some properties that were previously attributed to material particles, corpuscles.
This idea is called corpuscular-wave dualism.

Many patterns of wave processes are universal in nature and are equally valid for waves of various nature: mechanical waves in an elastic medium, waves on the surface of water, in a stretched string, etc. Electromagnetic waves, which are the process of propagation of electromagnetic field oscillations, are no exception. . But unlike other types of waves, which propagate in some material medium, electromagnetic waves can propagate in a vacuum: no material medium is required for the propagation of electric and magnetic fields. However, electromagnetic waves can exist not only in vacuum, but also in matter.

Prediction of electromagnetic waves. The existence of electromagnetic waves was theoretically predicted by Maxwell as a result of the analysis of his proposed system of equations describing the electromagnetic field. Maxwell showed that an electromagnetic field in a vacuum can exist even in the absence of sources - charges and currents. A field without sources has the form of waves propagating at a finite speed cm/s, in which the vectors of the electric and magnetic fields at each moment of time at each point in space are perpendicular to each other and perpendicular to the direction of wave propagation.

Experimentally, electromagnetic waves were discovered and studied by Hertz only 10 years after Maxwell's death.

open vibrator. To understand how electromagnetic waves can be obtained experimentally, let us consider an “open” oscillatory circuit, in which the capacitor plates are moved apart (Fig. 176) and therefore the electric field occupies a large area of ​​space. With an increase in the distance between the plates, the capacitance C of the capacitor decreases and, in accordance with the Thomson formula, the frequency of natural oscillations increases. If we also replace the inductor with a piece of wire, then the inductance will decrease and the natural frequency will increase even more. In this case, not only the electric, but also the magnetic field, which was previously enclosed inside the coil, will now occupy a large region of space covering this wire.

An increase in the frequency of oscillations in the circuit, as well as an increase in its linear dimensions, leads to the fact that the period of natural

oscillations becomes comparable with the propagation time of the electromagnetic field along the entire circuit. This means that the processes of natural electromagnetic oscillations in such an open circuit can no longer be considered quasi-stationary.

Rice. 176. Transition from an oscillatory circuit to an open vibrator

The current strength in its different places at the same time is different: at the ends of the circuit it is always zero, and in the middle (where the coil used to be) it oscillates with maximum amplitude.

In the limiting case, when the oscillatory circuit has simply turned into a straight wire segment, the current distribution along the circuit at some point in time is shown in Fig. 177a. At the moment when the current strength in such a vibrator is maximum, the magnetic field covering it also reaches a maximum, and there is no electric field near the vibrator. After a quarter of the period, the current strength vanishes, and with it the magnetic field near the vibrator; electric charges are concentrated near the ends of the vibrator, and their distribution has the form shown in Fig. 1776. The electric field near the vibrator at this moment is maximum.

Rice. 177. Distribution along an open vibrator of the current strength at the moment when it is maximum (a), and the distribution of charges after a quarter of the period (b)

These oscillations of charge and current, i.e., electromagnetic oscillations in an open vibrator, are quite analogous to mechanical oscillations that can occur in an oscillator spring if the massive body attached to it is removed. In this case, it is necessary to take into account the mass of individual parts of the spring and consider it as a distributed system, in which each element has both elastic and inert properties. In the case of an open electromagnetic vibrator, each of its elements also simultaneously has both inductance and capacitance.

Electric and magnetic fields of the vibrator. The non-quasi-stationary nature of oscillations in an open vibrator leads to the fact that the fields created by its individual sections at a certain distance from the vibrator no longer compensate each other, as is the case for a “closed” oscillatory circuit with lumped parameters, where the oscillations are quasi-stationary, the electric field is entirely concentrated inside capacitor, and magnetic - inside the coil. Due to such a spatial separation of electric and magnetic fields, they are not directly related to each other: their mutual transformation is due only to current - charge transfer along the circuit.

At an open vibrator, where the electric and magnetic fields overlap in space, their mutual influence occurs: a changing magnetic field generates a vortex electric field, and a changing electric field generates a magnetic field. As a result, the existence of such "self-sustaining" fields propagating in free space at a large distance from the vibrator is possible. This is the electromagnetic waves emitted by the vibrator.

Hertz's experiments. The vibrator, with the help of which G. Hertz in 1888 was the first to experimentally obtain electromagnetic waves, was a straight conductor with a small air gap in the middle (Fig. 178a). Thanks to this gap, significant charges could be imparted to the two halves of the vibrator. When the potential difference reached a certain limit value, a breakdown occurred in the air gap (a spark jumped) and electric charges could flow through the ionized air from one half of the vibrator to the other. In an open circuit, electromagnetic oscillations arose. In order for fast-alternating currents to exist only in the vibrator and not close through the power source, chokes were connected between the vibrator and the source (see Fig. 178a).

Rice. 178. Hertz vibrator

High-frequency vibrations in the vibrator exist as long as the spark closes the gap between its halves. The damping of such oscillations in the vibrator occurs mainly not due to Joule losses on the resistance (as in a closed oscillatory circuit), but due to the radiation of electromagnetic waves.

To detect electromagnetic waves, Hertz used a second (receiving) vibrator (Fig. 1786). Under the action of an alternating electric field of a wave coming from the emitter, the electrons in the receiving vibrator perform forced oscillations, i.e., a rapidly alternating current is excited in the vibrator. If the dimensions of the receiving vibrator are the same as those of the emitting one, then the frequencies of natural electromagnetic oscillations in them coincide and the forced oscillations in the receiving vibrator reach a noticeable value due to resonance. These oscillations were detected by Hertz by the passage of a spark in a microscopic gap in the middle of the receiving vibrator or by the glow of a miniature gas-discharge tube G, connected between the halves of the vibrator.

Hertz not only experimentally proved the existence of electromagnetic waves, but for the first time began to study their properties - absorption and refraction in different media, reflection from metal surfaces, etc. Experimentally, it was also possible to measure the speed of electromagnetic waves, which turned out to be equal to the speed of light.

The coincidence of the speed of electromagnetic waves with the speed of light measured long before their discovery served as the starting point for identifying light with electromagnetic waves and creating an electromagnetic theory of light.

An electromagnetic wave exists without sources of fields in the sense that after its emission, the electromagnetic field of the wave is not associated with the source. In this way, an electromagnetic wave differs from static electric and magnetic fields, which do not exist in isolation from the source.

Mechanism of radiation of electromagnetic waves. The radiation of electromagnetic waves occurs with the accelerated movement of electric charges. It is possible to understand how the transverse electric field of a wave arises from the radial Coulomb field of a point charge using the following simple reasoning proposed by J. Thomson.

Rice. 179. Field of an immobile point charge

Consider the electric field created by a point charge. If the charge is at rest, then its electrostatic field is represented by radial lines of force emerging from the charge (Fig. 179). Let at the moment of time the charge under the action of some external force begins to move with an acceleration a, and after some time the action of this force stops, so that the charge moves further uniformly at a speed. The charge velocity graph is shown in Fig. 180.

Imagine a picture of the lines of the electric field created by this charge, after a long period of time. Since the electric field propagates at the speed of light c,

then the change in the electric field caused by the movement of the charge could not reach the points lying outside the sphere of radius: outside this sphere, the field is the same as it was with a stationary charge (Fig. 181). The strength of this field (in the Gaussian system of units) is equal to

The entire change in the electric field caused by the accelerated movement of the charge over time at the moment of time is inside a thin spherical layer of thickness, the outer radius of which is equal to and the inner one - This is shown in Fig. 181. Inside the sphere of radius, the electric field is the field of a uniformly moving charge.

Rice. 180. Charge rate graph

Rice. 181. Lines of the electric field strength of a charge moving according to the graph in fig. 180

Rice. 182. To the derivation of the formula for the intensity of the radiation field of an accelerated moving charge

If the charge speed is much less than the speed of light c, then this field at the moment of time coincides with the field of a stationary point charge located at a distance from the beginning (Fig. 181): the field of a charge slowly moving at a constant speed moves with it, and the distance traveled by the charge over time , as can be seen from Fig. 180, can be considered equal if r»t.

The picture of the electric field inside the spherical layer is easy to find, given the continuity of the lines of force. To do this, you need to connect the corresponding radial lines of force (Fig. 181). The kink in the lines of force caused by the accelerated motion of the charge "runs away" from the charge at a speed c. A kink in the lines of force between

spheres, this is the radiation field of interest to us, propagating at a speed c.

To find the radiation field, consider one of the lines of intensity, which makes up a certain angle with the direction of charge movement (Fig. 182). We decompose the vector of the electric field strength in the break E into two components: radial and transverse. The radial component is the strength of the electrostatic field created by the charge at a distance from it:

The transverse component is the strength of the electric field in the wave emitted by the charge during accelerated motion. Since this wave runs along the radius, the vector is perpendicular to the direction of wave propagation. From fig. 182 shows that

Substituting here from (2), we find

Considering that a ratio is the acceleration a, with which the charge moved during the time interval from 0 to, we rewrite this expression in the form

First of all, we pay attention to the fact that the strength of the electric field of the wave decreases inversely with the distance from the center, in contrast to the strength of the electrostatic field, which is proportional to such a dependence on distance, and should be expected if we take into account the law of conservation of energy. Since there is no absorption of energy when a wave propagates in a vacuum, the amount of energy that has passed through a sphere of any radius is the same. Since the surface area of ​​a sphere is proportional to the square of its radius, the energy flux through a unit of its surface must be inversely proportional to the square of the radius. Considering that the energy density of the electric field of the wave is equal, we conclude that

Further, we note that the field strength of the wave in formula (4) at the moment of time depends on the acceleration of the charge and at the moment of time the wave radiated at the moment reaches a point located at a distance after a time equal to

Radiation of an oscillating charge. Let us now assume that the charge moves all the time along a straight line with some variable acceleration near the origin, for example, it performs harmonic oscillations. As long as it is, it will emit electromagnetic waves continuously. The electric field strength of the wave at a point located at a distance from the origin of coordinates is still determined by formula (4), and the field at the moment of time depends on the acceleration of the charge a at an earlier moment

Let the motion of the charge be a harmonic oscillation near the origin with a certain amplitude A and frequency w:

The acceleration of the charge during such a movement is given by the expression

Substituting the charge acceleration into formula (5), we obtain

A change in the electric field at any point during the passage of such a wave is a harmonic oscillation with a frequency , i.e., an oscillating charge radiates a monochromatic wave. Of course, formula (8) is valid at distances greater than the amplitude of charge oscillations A.

The energy of an electromagnetic wave. The energy density of the electric field of a monochromatic wave emitted by a charge can be found using formula (8):

The energy density is proportional to the square of the charge oscillation amplitude and the fourth power of the frequency.

Any fluctuation is associated with periodic transitions of energy from one form to another and vice versa. For example, vibrations of a mechanical oscillator are accompanied by mutual transformations of kinetic energy and potential energy of elastic deformation. When studying electromagnetic oscillations in a circuit, we saw that the analogue of the potential energy of a mechanical oscillator is the energy of the electric field in the capacitor, and the analogue of kinetic energy is the energy of the magnetic field of the coil. This analogy is valid not only for localized oscillations, but also for wave processes.

In a monochromatic wave traveling in an elastic medium, the kinetic and potential energy densities at each point perform harmonic oscillations with a doubled frequency, and in such a way that their values ​​coincide at any time. It is the same in a traveling monochromatic electromagnetic wave: the energy densities of the electric and magnetic fields, making a harmonic oscillation with a frequency, are equal to each other at every point at any time.

The magnetic field energy density is expressed in terms of induction B as follows:

Equating the energy densities of electric and magnetic fields in a traveling electromagnetic wave, we are convinced that the magnetic field induction in such a wave depends on the coordinates and time in the same way as the electric field strength. In other words, in a traveling wave, the magnetic field induction and the electric field strength are equal to each other at any point at any time (in the Gaussian system of units):

Energy flow of an electromagnetic wave. The total energy density of the electromagnetic field in a traveling wave is twice the energy density of the electric field (9). The energy flux density y carried by the wave is equal to the product of the energy density and the wave propagation velocity . Using formula (9), one can see that the energy flux through any surface oscillates with frequency. To find the average value of the energy flux density, it is necessary to average expression (9) over time. Since the mean value is 1/2, we get

Rice. 183. Angular distribution of energy" emitted by an oscillating charge

The energy flux density in a wave depends on the direction: no energy is emitted at all in the direction in which charge oscillations occur. The largest amount of energy is emitted in a plane perpendicular to this direction. 183. A charge oscillates along an axis

energy direction, i.e. The diagram shows a line connecting the ends of these segments.

The distribution of energy in directions in space is characterized by a surface, which is obtained by rotating the diagram around the axis

Polarization of electromagnetic waves. The wave generated by the vibrator during harmonic oscillations is called monochromatic. A monochromatic wave is characterized by a certain frequency ω and wavelength X. The wavelength and frequency are related through the wave propagation speed c:

An electromagnetic wave in vacuum is transverse: the vector of the electromagnetic field strength of the wave, as can be seen from the above reasoning, is perpendicular to the direction of wave propagation. Let's draw through the observation point Р in fig. 184 sphere centered at the origin, around which the radiating charge oscillates along the axis. Draw parallels and meridians on it. Then the vector E of the wave field will be directed tangentially to the meridian, and the vector B is perpendicular to the vector E and directed tangentially to the parallel.

To verify this, let us consider in more detail the relationship between the electric and magnetic fields in a traveling wave. These fields after the emission of the wave are no longer associated with the source. When the electric field of the wave changes, a magnetic field arises, the lines of force of which, as we saw in the study of the displacement current, are perpendicular to the lines of force of the electric field. This alternating magnetic field, changing, in turn leads to the appearance of a vortex electric field, which is perpendicular to the magnetic field that generated it. Thus, during the propagation of a wave, the electric and magnetic fields support each other, remaining mutually perpendicular all the time. Since in a traveling wave the electric and magnetic fields change in phase with each other, the instantaneous “portrait” of the wave (vectors E and B at different points of the line along the direction of propagation) has the form shown in Fig. 185. Such a wave is called linearly polarized. A harmonic oscillating charge radiates linearly polarized waves in all directions. In a linearly polarized wave traveling in any direction, the vector E is always in the same plane.

Since the charges in a linear electromagnetic vibrator perform just such an oscillating motion, the electromagnetic wave emitted by the vibrator is linearly polarized. It is easy to verify this experimentally by changing the orientation of the receiving vibrator relative to the emitting one.

Rice. 185. Electric and magnetic fields in a traveling linearly polarized wave

The signal is greatest when the receiving vibrator is parallel to the emitting one (see Fig. 178). If the receiving vibrator is turned perpendicular to the emitting vibrator, then the signal disappears. Electrical oscillations in the receiving vibrator can appear only due to the component of the electric field of the wave directed along the vibrator. Therefore, such an experiment indicates that the electric field in the wave is parallel to the radiating vibrator.

Other types of polarization of transverse electromagnetic waves are also possible. If, for example, the vector E at some point during the passage of the wave uniformly rotates around the direction of propagation, remaining unchanged in absolute value, then the wave is called circularly polarized or circularly polarized. An instant "portrait" of the electric field of such an electromagnetic wave is shown in Fig. 186.

Rice. 186. Electric field in a traveling circularly polarized wave

A circularly polarized wave can be obtained by adding two linearly polarized waves of the same frequency and amplitude propagating in the same direction, the electric field vectors in which are mutually perpendicular. In each of the waves, the electric field vector at each point performs a harmonic oscillation. In order for the sum of such mutually perpendicular oscillations to result in a rotation of the resulting vector, a phase shift is necessary. In other words, the linearly polarized waves being added must be shifted by a quarter of the wavelength relative to each other.

Wave momentum and light pressure. Along with energy, an electromagnetic wave also has momentum. If a wave is absorbed, then its momentum is transferred to the object that absorbs it. Hence it follows that during absorption, the electromagnetic wave exerts pressure on the barrier. The origin of the wave pressure and the value of this pressure can be explained as follows.

Directed in a straight line. Then the power absorbed by the charge P is equal to

We assume that all the energy of the incident wave is absorbed by the barrier. Since the wave brings energy per unit area of ​​the barrier surface per unit time, the pressure exerted by the wave at normal incidence is equal to the energy density of the wave The pressure force of the absorbed electromagnetic wave imparts to the barrier per unit time an impulse equal, according to formula (15), to the absorbed energy divided by the speed of light . And this means that the absorbed electromagnetic wave had a momentum, which is equal to the energy divided by the speed of light.

For the first time, the pressure of electromagnetic waves was experimentally discovered by P. N. Lebedev in 1900 in extremely subtle experiments.

How do quasi-stationary electromagnetic oscillations in a closed oscillatory circuit differ from high-frequency oscillations in an open vibrator? Give me a mechanical analogy.

Explain why during electromagnetic quasi-stationary oscillations in a closed circuit there is no radiation of electromagnetic waves. Why does radiation occur during electromagnetic oscillations in an open vibrator?

Describe and explain Hertz's experiments on the excitation and detection of electromagnetic waves. What role does the spark gap play in the transmitting and receiving vibrators?

Explain how, with the accelerated movement of an electric charge, a longitudinal electrostatic field turns into a transverse electric field of an electromagnetic wave emitted by it.

Based on energy considerations, show that the electric field strength of the spherical wave emitted by the vibrator decreases as 1 1r (in contrast to the electrostatic field).

What is a monochromatic electromagnetic wave? What is a wavelength? How is it related to frequency? What is the transverse property of electromagnetic waves?

What is the polarization of an electromagnetic wave? What types of polarization do you know?

What arguments can you give to justify the fact that an electromagnetic wave has momentum?

Explain the role of the Lorentz force in the occurrence of the electromagnetic wave pressure force on the barrier.

), which describes the electromagnetic field, theoretically showed that an electromagnetic field in a vacuum can exist even in the absence of sources - charges and currents. A field without sources has the form of waves propagating at a finite speed, which in vacuum is equal to the speed of light: with= 299792458±1.2 m/s. The coincidence of the speed of propagation of electromagnetic waves in vacuum with the speed of light measured earlier allowed Maxwell to conclude that light is electromagnetic waves. This conclusion later formed the basis of the electromagnetic theory of light.

In 1888, the theory of electromagnetic waves received experimental confirmation in the experiments of G. Hertz. Using a high voltage source and vibrators (see Hertz vibrator), Hertz was able to perform subtle experiments to determine the speed of propagation of an electromagnetic wave and its length. It was experimentally confirmed that the speed of propagation of an electromagnetic wave is equal to the speed of light, which proved the electromagnetic nature of light.