2. Describe Hertz's experience in detecting electromagnetic waves
In Hertz's experiment, the source of electromagnetic disturbance was electromagnetic oscillations that arose in a vibrator (a conductor with an air gap in the middle). A high voltage was applied to this gap, it caused a spark discharge. After a moment, a spark discharge arose in the resonator (an analogous vibrator). The most intense spark arose in the resonator, which was located parallel to the vibrator.3. Explain the results of Hertz's experiment using Maxwell's theory. Why is an electromagnetic wave transverse?
The current through the discharge gap creates induction around itself, the magnetic flux increases, and an inductive displacement current occurs. The tension at point 1 (Fig. 155, b of the textbook) is directed counterclockwise in the plane of the drawing, at point 2 the current is directed upwards and causes induction at point 3, the tension is directed upwards. If the magnitude of the tension is sufficient for an electrical breakdown of the air in the gap, then a spark occurs and a current flows in the resonator.Because the directions of the magnetic field induction vectors and the electric field strength are perpendicular to each other and to the direction of the wave.
4. Why does the radiation of electromagnetic waves occur during the accelerated movement of electric charges? How does the electric field strength in a radiated electromagnetic wave depend on the acceleration of the radiating charged particle?
The strength of the current is proportional to the speed of movement of charged particles, so an electromagnetic wave occurs only if the speed of movement of these particles depends on time. The intensity in the emitted electromagnetic wave is directly proportional to the acceleration of the emitting charged particle.5. How does the energy density of an electromagnetic field depend on the strength of the electric field?
The energy density of an electromagnetic field is directly proportional to the square of the electric field strength.In 1864, James Clerk Maxwell predicted the possibility of the existence of electromagnetic waves in space. He put forward this statement based on the conclusions arising from the analysis of all the experimental data known at that time regarding electricity and magnetism.
Maxwell mathematically unified the laws of electrodynamics, connecting electrical and magnetic phenomena, and thus came to the conclusion that electric and magnetic fields that change over time give rise to each other.
Initially, he emphasized the fact that the relationship between magnetic and electrical phenomena is not symmetrical, and introduced the term "vortex electric field", offering his own, truly new explanation for the phenomenon of electromagnetic induction discovered by Faraday: "every change in the magnetic field leads to the appearance of a the surrounding space of a vortex electric field having closed lines of force.
Fair, according to Maxwell, was the converse statement that "a changing electric field gives rise to a magnetic field in the surrounding space", but this statement remained at first only a hypothesis.
Maxwell wrote down a system of mathematical equations that consistently described the laws of mutual transformations of magnetic and electric fields, these equations later became the basic equations of electrodynamics, and became known as "Maxwell's equations" in honor of the great scientist who wrote them down. Maxwell's hypothesis, based on the written equations, had several extremely important conclusions for science and technology, which are given below.
Electromagnetic waves really exist
In space, transverse electromagnetic waves can exist, which are propagating over time. The fact that the waves are transverse is indicated by the fact that the vectors of magnetic induction B and electric field strength E are mutually perpendicular and both lie in a plane perpendicular to the direction of propagation of an electromagnetic wave.
The speed of propagation of electromagnetic waves in a substance is finite, and it is determined by the electrical and magnetic properties of the substance through which the wave propagates. In this case, the length of the sinusoidal wave λ is related to the speed υ by a certain exact relation λ = υ / f, and depends on the frequency f of the field oscillations. The speed c of an electromagnetic wave in a vacuum is one of the fundamental physical constants - the speed of light in a vacuum.
Since Maxwell declared the finiteness of the speed of propagation of an electromagnetic wave, this created a contradiction between his hypothesis and the long-range theory accepted at that time, according to which the speed of propagation of waves should have been infinite. Maxwell's theory was therefore called the theory of short-range action.
In an electromagnetic wave, the transformation of electric and magnetic fields into each other occurs simultaneously, therefore the volumetric densities of magnetic energy and electric energy are equal to each other. Therefore, the statement is true that the modules of the electric field strength and magnetic field induction are interconnected at each point in space by the following relationship:
An electromagnetic wave in the process of its propagation creates a flow of electromagnetic energy, and if we consider the area in a plane perpendicular to the direction of wave propagation, then in a short time a certain amount of electromagnetic energy will move through it. The electromagnetic energy flux density is the amount of energy carried by an electromagnetic wave through the surface of a unit area per unit of time. By substituting the values of velocity, as well as magnetic and electrical energy, we can obtain an expression for the flux density in terms of the quantities E and B.
Since the direction of wave energy propagation coincides with the direction of the wave propagation velocity, the energy flux propagating in an electromagnetic wave can be specified using a vector directed in the same way as the wave propagation velocity. This vector is called the "Poynting vector" - in honor of the British physicist Henry Poynting, who developed in 1884 the theory of propagation of the energy flow of the electromagnetic field. Wave energy flux density is measured in W/sq.m.
When an electric field acts on a substance, small currents appear in it, which are an ordered movement of electrically charged particles. These currents in the magnetic field of an electromagnetic wave are subjected to the action of the Ampère force, which is directed deep into the substance. Ampere's force and generates as a result pressure.
This phenomenon was later, in 1900, investigated and confirmed experimentally by the Russian physicist Pyotr Nikolaevich Lebedev, whose experimental work was very important for confirming Maxwell's theory of electromagnetism and its acceptance and approval in the future.
The fact that an electromagnetic wave exerts pressure makes it possible to judge the presence of a mechanical impulse in an electromagnetic field, which can be expressed for a unit volume in terms of the volumetric density of electromagnetic energy and the speed of wave propagation in vacuum:
Since the momentum is associated with the movement of mass, one can also introduce such a concept as electromagnetic mass, and then for a unit volume this ratio (in accordance with SRT) will take on the character of a universal law of nature, and will be valid for any material bodies, regardless of the form of matter. And the electromagnetic field is then akin to a material body - it has energy W, mass m, momentum p and a finite propagation velocity v. That is, the electromagnetic field is one of the forms of matter that actually exists in nature.
For the first time in 1888, Heinrich Hertz confirmed experimentally Maxwell's electromagnetic theory. He empirically proved the reality of electromagnetic waves and studied their properties such as refraction and absorption in various media, as well as the reflection of waves from metal surfaces.
Hertz measured the wavelength, and showed that the speed of propagation of an electromagnetic wave is equal to the speed of light. Hertz's experimental work was the last step towards the recognition of Maxwell's electromagnetic theory. Seven years later, in 1895, Russian physicist Alexander Stepanovich Popov used electromagnetic waves to create wireless communications.
In DC circuits, charges move at a constant speed, and electromagnetic waves in this case are not radiated into space. For radiation to take place, it is necessary to use an antenna in which alternating currents, that is, currents that quickly change their direction, are excited.
In its simplest form, an electric dipole of a small size is suitable for the emission of electromagnetic waves, in which the dipole moment would change rapidly in time. It is such a dipole that is called today the "Hertzian dipole", the size of which is several times smaller than the wavelength it emits.
When emitted by a Hertzian dipole, the maximum flux of electromagnetic energy falls on a plane perpendicular to the axis of the dipole. No electromagnetic energy is emitted along the dipole axis. In the most important experiments of Hertz, elementary dipoles were used both for emitting and receiving electromagnetic waves, and the existence of electromagnetic waves was proved.
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 switched 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.
In this way, 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 experimentally and measured their speed, which coincided with that 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. Because 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).
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 radiating 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 speed of the charge 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 the 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, oscillations 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 the 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: in the direction in which charge oscillations occur, no energy is emitted at all. 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 co 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 a certain 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 polarized in a circle. 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 the rotation of the resulting vector, a phase shift is necessary.
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 electromagnetic waves do not radiate in a closed circuit during electromagnetic quasi-stationary oscillations. 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.
In 1860-1865. one of the greatest physicists of the 19th century James Clerk Maxwell created a theory electromagnetic field. According to Maxwell, the phenomenon of electromagnetic induction is explained as follows. If at some point in space the magnetic field changes with time, then an electric field is also formed there. If there is a closed conductor in the field, then the electric field causes an induction current in it. It follows from Maxwell's theory that the reverse process is also possible. If in some region of space the electric field changes with time, then a magnetic field is also formed here.
Thus, any change over time in the magnetic field results in a changing electric field, and any change over time in the electric field gives rise to a changing magnetic field. These generating each other alternating electric and magnetic fields form a single electromagnetic field.
Properties of electromagnetic waves
The most important result that follows from the theory of the electromagnetic field formulated by Maxwell was the prediction of the possibility of the existence of electromagnetic waves. electromagnetic wave- propagation of electromagnetic fields in space and time.
Electromagnetic waves, unlike elastic (sound) waves, can propagate in a vacuum or any other substance.
Electromagnetic waves in vacuum propagate at a speed c=299 792 km/s, that is, at the speed of light.
In matter, the speed of an electromagnetic wave is less than in vacuum. The relationship between the wavelength , its speed, period and frequency of oscillations obtained for mechanical waves is also valid for electromagnetic waves:
Tension vector fluctuations E and magnetic induction vector B occur in mutually perpendicular planes and perpendicular to the direction of wave propagation (velocity vector).
An electromagnetic wave carries energy.
Electromagnetic Wave Range
Around us is a complex world of electromagnetic waves of various frequencies: radiation from computer monitors, cell phones, microwave ovens, televisions, etc. Currently, all electromagnetic waves are divided by wavelength into six main ranges.
radio waves- these are electromagnetic waves (with a wavelength from 10,000 m to 0.005 m), which serve to transmit signals (information) over a distance without wires. In radio communications, radio waves are created by high frequency currents flowing in an antenna.
Electromagnetic radiation with a wavelength from 0.005 m to 1 micron, i.e. between radio waves and visible light are called infrared radiation. Infrared radiation is emitted by any heated body. The source of infrared radiation are furnaces, batteries, electric incandescent lamps. With the help of special devices, infrared radiation can be converted into visible light and images of heated objects can be obtained in complete darkness.
To visible light include radiation with a wavelength of approximately 770 nm to 380 nm, from red to violet. The significance of this part of the spectrum of electromagnetic radiation in human life is exceptionally great, since a person receives almost all information about the world around him with the help of vision.
Electromagnetic radiation invisible to the eye with a wavelength shorter than violet is called ultraviolet radiation. It can kill pathogenic bacteria.
x-ray radiation invisible to the eye. It passes without significant absorption through significant layers of a substance that is opaque to visible light, which is used to diagnose diseases of internal organs.
Gamma radiation called electromagnetic radiation emitted by excited nuclei and arising from the interaction of elementary particles.
The principle of radio communication
The oscillatory circuit is used as a source of electromagnetic waves. For effective radiation, the circuit is "opened", i.e. create conditions for the field to "go" into space. This device is called an open oscillatory circuit - antenna.
radio communication called the transmission of information using electromagnetic waves, the frequencies of which are in the range from to Hz.
Radar (radar)
A device that transmits ultrashort waves and immediately receives them. The radiation is carried out by short pulses. Pulses are reflected from objects, allowing, after receiving and processing the signal, to set the distance to the object.
The speed radar works on a similar principle. Think about how radar determines the speed of a moving car.
