What are the conclusions regarding electromagnetic. Electromagnetic waves concept of electromagnetic waves

From the theory created by Maxwell, we can conclude that a rapidly varying electromagnetic field should propagate in space in the form of transverse waves. Moreover, these waves can exist not only in matter, but also in vacuum. Based solely on theoretical conclusions, Maxwell also determined that electromagnetic waves should propagate in a vacuum at a speed of 300,000 km/s, i.e., at the speed of light (the speed of light, as is known, was measured long before this).

You already know that in mechanical waves, for example in sound waves, energy is transferred from one particle of the medium to another. In this case, the particles enter into oscillatory motion, i.e., their displacement from the equilibrium position changes periodically. To transmit sound, a material medium is required.

Due to the fact that electromagnetic waves propagate in matter and in vacuum, the question arises: what oscillates in an electromagnetic wave, that is, what physical quantities change periodically in it?

• An electromagnetic wave is a system of variable electric and magnetic fields generating each other and propagating in space

Let us recall that a quantitative characteristic of a magnetic field is the magnetic induction vector B.

The main quantitative characteristic of the electric field is a vector quantity called the electric field strength, which is denoted by the symbol E. The electric field strength E at any point is equal to the ratio of the force F with which the field acts on a point positive charge placed at this point to the value of this charge q.

When they say that the magnetic and electric fields change, this means that the magnetic field induction vector B and the electric field strength vector E change respectively.

In an electromagnetic wave, it is the vectors B and E that periodically change in magnitude and direction, that is, they oscillate.

Rice. 135. Model of an electromagnetic wave: E - electric field strength, B - magnetic field induction; c - wave speed

Figure 135 shows the electric field strength vector E and the magnetic field induction vector B of an electromagnetic wave at the same moment in time. This is like a “snapshot” of a wave propagating in the direction of the Z axis. The plane drawn through vectors B and E at any point is perpendicular to the direction of propagation of the wave, which indicates the transverseness of the wave.

In a time equal to the oscillation period, the wave will move along the Z axis to a distance equal to the wavelength. For electromagnetic waves, the same relationships between wavelength λ, its speed c, period T and oscillation frequency v are valid as for mechanical waves:

Maxwell not only scientifically substantiated the possibility of the existence of electromagnetic waves, but also pointed out that in order to create an intense electromagnetic wave that could be registered by instruments at some distance from the source, it is necessary that the oscillations of the vectors E and B occur with a sufficiently high frequency (about 100,000 oscillations per second or more).

Heinrich Hertz (1857-1894)
German physicist, one of the founders of electrodynamics. Experimentally proved the existence of electromagnetic waves

In 1888, the German scientist Heinrich Hertz managed to obtain and register electromagnetic waves. As a result of Hertz's experiments, all the properties of electromagnetic waves theoretically predicted by Maxwell were also discovered.

The entire space around us is literally permeated with electromagnetic waves of various frequencies. Currently, all electromagnetic waves are divided by wavelength (and, accordingly, by frequency) into six main ranges, which are presented in Figure 136.

Rice. 136. Electromagnetic wave scale

The boundaries of the ranges are very arbitrary, therefore, as can be seen from the figure, in most cases, adjacent ranges somewhat overlap each other.

Electromagnetic waves of different frequencies differ from each other in penetrating ability, speed of propagation in matter, visibility, color and some other properties.

They can have both positive and negative effects on living organisms. For example, infrared, i.e. thermal, radiation plays a decisive role in maintaining life on Earth, since people, animals and plants can exist and function normally only at certain temperatures.

Visible light gives us information about the world around us and the ability to navigate in space. It is also necessary for the process of photosynthesis in plants, which results in the release of oxygen necessary for the respiration of living organisms.

The effect on humans of ultraviolet radiation (which causes tanning) is largely determined by the intensity and duration of exposure. In acceptable doses, it increases the human body’s resistance to various diseases, in particular infectious ones. Exceeding the permissible dose can cause skin burns, the development of cancer, weakened immunity, and damage to the retina. Eyes can be protected with glass glasses (both dark and transparent, but not plastic), since glass absorbs a significant portion of ultraviolet rays.

You are also familiar with X-ray radiation, in particular with its widespread use in medicine - each of you has probably had a fluorographic examination or an X-ray. But too large doses or frequent X-ray examinations can cause serious illness.

The production of electromagnetic waves is of great scientific and practical importance. This can be seen in the example of just one range - radio waves used for television and radio communications, in radar (i.e., for detecting objects and measuring the distance to them), in radio astronomy and other fields of activity.

Questions

1. What conclusions about electromagnetic waves can be drawn from Maxwell's theory?
2. What physical quantities change periodically in an electromagnetic wave?
3. What relationships between the wavelength, its speed, period and oscillation frequency are valid for electromagnetic waves?
4. Under what condition will the wave be intense enough to be detected?
5. When and by whom were electromagnetic waves first received?
6. Give examples of the use of different ranges of electromagnetic waves and their effects on living organisms.

Exercise

1. On what frequency do ships transmit the SOS distress signal if, according to international agreement, the radio wavelength should be 600 m?
2. A radio signal sent from Earth to the Moon can bounce off the Moon's surface and return to Earth. Suggest a way to measure the distance between the Earth and the Moon using a radio signal.

   Note: the problem is solved by the same method as measuring the depth of the sea using echolocation (see § 30).

3. Is it possible to measure the distance between the Earth and the Moon using a sound or ultrasonic wave? Justify your answer.

• Concept of electromagnetic waves

• Generation of electromagnetic waves

• Types of electromagnetic radiation, their properties and application

Nature of electromagnetic wave

• An electromagnetic wave is the propagation of alternating (vortex) electric and magnetic fields in space over time.

Formation of electromagnetic waves

• Electromagnetic waves are studied by oscillating charges, and it is important that the speed of movement of such charges changes with time, i.e. they move with acceleration.

• The electromagnetic field is emitted in a noticeable manner not only when the charge oscillates, but also during any rapid change in its speed. Moreover, the greater the acceleration with which the charge moves, the greater the intensity of the wave radiation.

• Vectors E and B in an electromagnetic wave are perpendicular to each other and perpendicular to the direction of propagation of the wave.

• The electromagnetic wave is transverse

Historical reference

• Maxwell was deeply convinced of the reality of electromagnetic waves, but did not live to see their experimental discovery.

• Only 10 years after his death, electromagnetic waves were experimentally obtained by Hertz.

• In 1895 A.S. Popov demonstrated the practical application of electromagnetic waves for radio communications.

• Now we know that all the space around us is literally permeated with electromagnetic waves of different frequencies.

Electromagnetic waves of different frequencies are different from each other.

• Currently, all electromagnetic waves are divided by wavelength (and, accordingly, by frequency) into six main ranges: radio waves, infrared radiation, visible radiation, ultraviolet radiation, x-rays, γ-radiation

Radio waves

• They are obtained using oscillatory circuits and macroscopic vibrators.

• Properties:

• Radio waves of different frequencies and with different wavelengths are absorbed and reflected differently by media.

• exhibit diffraction and interference properties.

• Application: Radio communications, television, radar.

Infrared radiation (thermal)

• Emitted by atoms or molecules of a substance. Infrared radiation is emitted by all bodies at any temperature.

• Properties :

• passes through some opaque bodies, as well as through rain, haze, snow, fog;

• produces a chemical effect (photoglastinki);

• being absorbed by a substance, it heats it up;

• invisible;

• capable of interference and diffraction phenomena;

• recorded by thermal methods.

• Application : Night vision device, forensics, physiotherapy, in industry for drying products, wood, fruits.

Visible radiation

• The portion of electromagnetic radiation perceived by the eye.

• Properties:

• reflection,

• refraction,

• affects the eye

• capable of dispersion,

• interference,

• diffraction.

Ultraviolet radiation

• Sources: gas discharge lamps with quartz tubes. It is emitted by all solids with t0> 1 000°C, as well as by luminous mercury vapor.

• Properties: High chemical activity, invisible, high penetrating ability, kills microorganisms, in small doses has a beneficial effect on the human body (tanning), but in large doses it has a negative effect, changes cell development, metabolism.

• Application: in medicine, in industry.

X-rays

• Emitted at high electron accelerations.

• Properties: interference, X-ray diffraction on a crystal lattice, high penetrating power. Irradiation in large doses causes radiation sickness.

• Application: in medicine for the purpose of diagnosing diseases of internal organs; in industry to control the internal structure of various products.

γ radiation

• Sources: atomic nucleus (nuclear reactions).

• Properties: Has enormous penetrating power and has a strong biological effect.

• Application: In medicine, production (γ-flaw detection).

• electromagnetic radiation with a frequency of 50 Hz, which is created by AC wires, with prolonged exposure causes drowsiness, signs of fatigue, and headaches.

In order not to increase the effect of household electromagnetic radiation, experts recommend not placing electrical appliances operating in our apartments close to each other - a microwave oven, an electric stove, a TV, a washing machine, a refrigerator, an iron, an electric kettle. The distance between them should be at least 1.5-2 m. Your beds should be the same distance from the TV or refrigerator.

The influence of electromagnetic radiation on living organisms

• Radio waves

• Infrared

• Ultraviolet

• X-ray

• γ radiation

Questions for consolidation

• What is an electromagnetic wave called?

• What is the source of an electromagnetic wave?

• How are vectors E and B oriented relative to each other in an electromagnetic wave?

• What is the speed of propagation of electromagnetic waves in air?

Questions for consolidation

• 5. What conclusions regarding electromagnetic waves followed from Maxwell’s theory?

• 6. What physical quantities change periodically in an electromagnetic wave?

• 7. What relationships between the wavelength, its speed, period and frequency of oscillations are valid for electromagnetic waves?

• 8. Under what condition will the wave be intense enough to be detected?

Questions for consolidation

• 9. When and by whom were electromagnetic waves first received?

• 10. Give examples of the application of electromagnetic waves.

• 11. Arrange in order of increasing wavelength the electromagnetic waves of various natures: 1) infrared radiation; 2) X-ray radiation; 3) radio waves; 4) γ-waves.

A charged particle, such as an electron, moving at a constant speed does not emit electromagnetic waves. Electromagnetic radiation occurs only during the accelerated () movement of charged particles.

Thus, X-ray radiation arises as a result of sharp deceleration of a beam of electrons colliding with the anticathode.

D Another very important source of electromagnetic waves for understanding many physical processes is an electric dipole that performs harmonic oscillations (Fig. 7.11). The electric moment of the dipole changes in time according to the harmonic law:

,

Where
.

The reciprocating displacement of an electric charge is equivalent to the existence of a current element around which, according to the Biot-Savart-Laplace law, a magnetic field arises. However, the magnetic field in this case will be variable, because the current element causing it is changing. An alternating magnetic field causes an alternating electric field - an electromagnetic wave propagates through the medium. At large distances from the dipole (
, - the length of the electromagnetic wave) the wave becomes spherical, in this wave the vectors And perpendicular to each other and to the velocity vector , which in turn is directed along the radius vector . In this case, the vector - tangent to the parallel (in accordance with the Biot-Savart-Laplace law). In the case of an electric dipole emitting an electromagnetic wave, electric charges have acceleration
.

Similarly, electromagnetic radiation occurs when electron shells are displaced relative to atomic nuclei. Such a displacement can occur either as a result of exposure to an alternating electric field, or as a result of thermal vibrations of the atoms of the substance. The latter mechanism is the cause of the so-called “thermal cure” of heated bodies.

It is interesting to note that during periodic deformations of the magnetic dipole, an electromagnetic wave is also emitted.

N and fig. Figure 7.12 shows a cylindrical magnet magnetized along its axis. Longitudinal deformation of the cylinder (at a constant radius) will lead to a change in magnetization and magnetic moment:

.

Periodic deformation of the magnetized cylinder is accompanied by a periodic change in the magnetic moment and the emission of an electromagnetic wave. However, in this case the vector is directed tangentially to the meridian, and the vector - tangent to a parallel on a spherical wave surface.

Lecture 8. The principle of relativity in electrodynamics

Relativistic transformation of electromagnetic fields, charges and currents. Electric field in various reference systems. Magnetic field in different reference systems. Electromagnetic field in various reference systems. Proof of the invariance of electric charge. Invariance of Maxwell's equations under Lorentz transformations.

8.1. Relativistic transformation of electromagnetic fields, charges and currents

8.1.1. Electric field in various reference systems

As is known, mechanical phenomena in all inertial reference systems (reference systems moving relative to each other rectilinearly and uniformly) proceed in the same way. In this case, it is impossible to establish which of these systems is at rest and which are moving, and therefore we can only talk about the relative motion of these systems in relation to each other.

With the help of electromagnetic phenomena it is also impossible to obtain evidence of the existence of absolute motion, and therefore, evidence of the existence of absolute reference systems. All reference systems moving relative to each other rectilinearly and uniformly are equal, and in all these reference systems the laws of electromagnetic phenomena are the same. This is the principle of relativity for electromagnetic phenomena: electromagnetic phenomena occur in the same way in all inertial frames of reference. Therefore, we can formulate the relativity principle of dividing the electromagnetic field into an electric field and a magnetic field: separate consideration of the electric and magnetic fields has only a relative meaning.

Previously, mutual transformations of electric and magnetic fields caused by changes in fields over time were considered. Similar phenomena occur when the electromagnetic field moves relative to the observer.

Suppose that a positive charge moves in a magnetic field in a vacuum. From the point of view of the first observer (stationary relative to the magnetic field), the Lorentz force acts on the charge:

,

where q is the charge value;

- magnetic field induction;

v – charge speed;

α is the angle between the direction of the magnetic field induction vector and the particle velocity vector.

The direction of this force is perpendicular to And , coincides with the direction of the vector product
.

ABOUT relative to the second observer, moving along with the charge, the charge is motionless, although the same force acts on it F. But if a force proportional to the magnitude of the charge acts on a stationary charge, then this means that there is an electric field. The strength of such a field can be determined by the formula

. (8.1)

The vector of the intensity of such an electric field coincides in direction with the direction of the force F, i.e. the electric field strength vector is perpendicular to the vectors And (Fig. 8.1).

Thus, the electromagnetic field depends on the reference frame. If in any reference frame there is one magnetic field, then in other reference frames moving relative to the first, both magnetic and electric fields exist.

R Let's consider the behavior of the electric field in different reference systems. We will consider the reference system in which electric charges or conductors with charges are at rest as a stationary reference system - a system
. A frame of reference moving at a certain speed v relative to the reference system K, moving reference system, system –
(Fig. 8.2).

Let us assume that in the reference system
there are two stationary, uniformly charged parallel plates carrying charges with a density
And
. The plates are squares with side “b”, parallel to the plane
. The distance between the plates 0 is small compared to the size of the plates “b”. In this regard, the electric field between the plates can be considered uniform. The plates are in a vacuum, i.e.
. The magnitude of the electric field measured by an observer located in
- system, equal to
. In this case, the component of the electric field strength vector parallel to the axis is determined
. In the reference system
, moving at speed in the direction
, according to Lorentz transformations, the distance decreases in once. Since the distance between planes does not affect the magnitude of the vector , then the electric field in a given direction does not change. The picture of the electric field lines for this case is shown in Fig. 8.3.

In another case (Fig. 8.4), when the plates are parallel to glossiness
in system
, the length of the longitudinal sides is reduced and the squares become rectangles, flattened in the direction of movement. Since the electric charge is an invariant quantity (does not change) with respect to the choice of the reference system, i.e.
, then with the charge remaining constant, the surface area decreases, therefore, in times the surface charge density increases
. Therefore, the electric field strength in a given direction will be equal to

, (8.2)

T .e. the transverse component of the electric field strength increases in times compared to a stationary reference system. As a result of this, the pattern of the electric field lines of the positive point charge will change (Fig. 8.5). They condense in a direction perpendicular to the direction of charge movement.

It can be shown that a similar change in the electric field strength will occur in the ZOX plane.

The results obtained can be presented in another form. Let there be two frames of reference
And . System moving relation specifically the system
at constant speed v parallel to the X axis (Fig. 8.6). In system
there is a magnetic field, which is characterized by the intensity vector H. At the considered point in space “A” the components of the magnetic field strength vector are respectively equal
. Then at the same point, but in the system , as a result of the movement, an electric field will appear with a intensity E, whose components are respectively equal
. Applying formula (8.1) to the individual components of the electric field strength, we obtain

(8.3)

If in the system there is also an electric field, then the resulting electric field in the system
will be characterized by the resulting tension vector E, whose components are respectively equal

(8.4)

Let us emphasize that v is the speed of the system relative to the system
.

8.1.2. Magnetic field in different reference systems

It is known that when electric charges move (when an electric field moves, in the presence of current) a magnetic field arises in space.

To determine this field, consider the charge +q moving relative to the first observer with speed v. Such a charge creates a magnetic field with a intensity

, (8.5)

Where r– radius vector drawn from the charge to the considered point in space.

Since in expression (8.5)
- induction of the electric field created by the charge at the point A under consideration, which is related to the electric field strength by the relation
, then taking into account the direction of the vector D(the direction of which coincides with the direction of the radius vector r at a given point) can be written

. (8.6)

Expression (8.6) is the modulus of the vector product, i.e.

. (8.7)

Relationship (8.7) allows us to state that the vector H perpendicular to the vectors v And D.

For the second observer, moving along with the charge, there is only an electric field, the induction vector of which is equal to D. Thus, in a stationary reference frame there is only an electric field, and in a moving reference frame there are electric and magnetic fields (Fig. 8.7).

U We establish a connection between the characteristics of electric and magnetic fields. To do this, we introduce two reference systems, one of which (K) moves relative to the other (K ​​") in the direction X 1 (Fig. 8.8). We assume that the charge is at rest in the reference frame K ". In this case, the electric field of the selected charge will move relative to the system K at a speed of “-v”. Using formula (8.6) for the components of the magnetic field strength vector (taking into account the sign of the velocity v), we will have

(8.8)

If in the K system there is also a magnetic field with strength components
, then the resulting magnetic field at the point in space under consideration will be characterized by the components of the intensity vector of this magnetic field:

(8.9)

In relations (8.9), speed v is the speed of movement of the system K (in which there is a magnetic field with components of the intensity vector
) relative to the system K ".

It should be noted that relations (8.9) for the transformation of magnetic fields are valid only in the case when the movement occurs at speeds much lower than the speed of light propagation in vacuum.

8.1.3. Electromagnetic field in various reference systems

The expression for the Lorentz force acting on a point charge in an electromagnetic field was obtained taking into account the invariance requirements of the relativistic equation of motion:

.

Consequently, the expression for the Lorentz force must also be relativistically invariant, i.e. have the same appearance in all inertial frames of reference. Thus, if there are two reference systems K and K ", one of which, for example K ", moves uniformly and rectilinearly with speed v relative to frame K, then the expressions for the Lorentz force in these reference systems will have the form

(8.10)

. (8.11)

Using the relativistic invariance of the expression for the Lorentz force (8.10) and (8.11) and taking into account the transformation formulas for forces during the transition from one inertial frame to another, it is possible to obtain relations between the vectors of the electric and magnetic fields of the electromagnetic field in different reference systems. A special case of such transformations was considered earlier.

Force transformation formulas have the form

(8.12)

(8.13)

, (8.14)

where v is the relative speed of movement of the reference systems;

u x , u y , u z – projections of the speed of motion of a charged particle onto the corresponding coordinate axes;

.

Let us substitute into formula (8.13) instead of F y and F y " their expression (8.10), (8.11), we will have

. (8.15)

Excluding the quantities from formula (8.15) And using the formulas for adding velocities in the theory of relativity
And
, grouping all terms on the left side of relation (8.15), we find

(8.16)

Equality (8.16) is valid for arbitrary values And . Consequently, the expressions in brackets (8.16) are individually equal to zero. Equating them to zero, we obtain the transformation formulas for the electromagnetic field vectors:

(8.17)

(8.18)

(8.19)

Similarly, based on relation (8.14), we can obtain transformation formulas for other vector components E And B:

(8.20)

(8.21)

(8.22)

Derivation of the conversion formula for the projection of the electric field strength vector ( E) E x can be calculated using the relation

. (8.23)

Doing the same thing as in previous cases, we reduce relation (8.23) to the form

Where
.

Using formulas (8.19) and (8.22), we find that

. (8.25)

Thus, the transformation formulas for the electromagnetic field vectors have the form

(8.26)

Formulas for transforming electromagnetic field vectors (8.26) allow us to determine the vectors of this field in any inertial reference system, if they are known in any one of them.

8.1.4. Proof of electric charge invariance

Let a positive electric charge move in
-system, as shown in Fig. 8.9, across the electric field with intensity . Then in the system , moving at speed , a charge stationary in this system is acted upon by a force

. (8.27)

From relativistic dynamics it is known that in the system (on a moving material particle provided
) force acts

. (8.28)

Since the left sides of equalities (8.27) and (8.28) are equal, then the right sides are also equal, which is possible when
. This conclusion is consistent with the assumption made above about charge invariance and can be considered as a simple proof of this statement.

It should be noted that the volume charge density  changes in accordance with Lorentz transformations. This is due to the fact that the volume charge density

.

With uniform charge distribution

.

The volume during transition from one inertial system to another changes, according to Lorentz transformations, according to the law

.

Consequently, when moving from one inertial reference system to another, the volumetric charge density changes according to the law:

. (8.29)

When transitioning from one inertial system to another, for the electric charge we obtain

. (8.30)

From relation (8.30) it is clear that indeed, when moving from one frame of reference to another, the charge remains a constant value, i.e. electric charge is invariant with respect to Lorentz transformations.

It is known that the Joule-Lenz law in differential form in a stationary reference frame displays the dependence of the current density on the electric field strength:

.

It can be shown that the current density j in a stationary medium in which charges move at speed v in an electromagnetic field with tensions E And B, changes in accordance with Lorentz transformations according to the law

, (8.31)

where are the magnitudes of the vectors E And B(same as vectors E " And B " ) are defined in the same way as in classical electrodynamics, i.e., essentially, by equalities (8.10 and 8.11).

Electromagnetic waves The concept of electromagnetic waves The formation of electromagnetic waves Types of electromagnetic radiation, their properties and application Completed by a student of group TE-21: Sizikov Andrey

The nature of an electromagnetic wave An electromagnetic wave is the propagation of alternating (vortex) electric and magnetic fields in space over time.

Formation of electromagnetic waves Electromagnetic waves are studied by oscillating charges, and it is important that the speed of movement of such charges changes with time, i.e. they move with acceleration.

Historical background Maxwell was deeply convinced of the reality of electromagnetic waves, but did not live to see their experimental discovery. Only 10 years after his death, electromagnetic waves were experimentally obtained by Hertz. In 1895, A. S. Popov demonstrated the practical use of electromagnetic waves for radio communications. Now we know that all the space around us is literally permeated with electromagnetic waves of different frequencies.

Electromagnetic waves of different frequencies are different from each other. Currently, all electromagnetic waves are divided by wavelength (and, accordingly, by frequency) into six main ranges: radio waves, infrared radiation, visible radiation, ultraviolet radiation, x-rays, γ radiation

Radio waves are produced using oscillatory circuits and macroscopic vibrators. Properties: radio waves of different frequencies and with different wavelengths are absorbed and reflected differently by media. exhibit diffraction and interference properties. Application: Radio communications, television, radar.

Infrared radiation (thermal) Emitted by atoms or molecules of a substance. Infrared radiation is emitted by all bodies at any temperature. Properties: passes through some opaque bodies, as well as through rain, haze, snow, fog; produces a chemical effect (photoglastinki); being absorbed by a substance, it heats it up; invisible; capable of interference and diffraction phenomena; recorded by thermal methods. Application: Night vision device, forensics, physiotherapy, in industry for drying products, wood, fruits.

Visible radiation The part of electromagnetic radiation perceived by the eye. Properties: reflection, refraction, affects the eye, capable of dispersion, interference, diffraction.

Ultraviolet radiation Sources: gas-discharge lamps with quartz tubes. It is emitted by all solids for which t 0> 1 000°C, as well as by luminous mercury vapor. Properties: High chemical activity, invisible, high penetrating ability, kills microorganisms, in small doses has a beneficial effect on the human body (tanning), but in large doses it has a negative effect, changes cell development, metabolism. Application: in medicine, in industry.

X-rays are emitted at high electron accelerations. Properties: interference, X-ray diffraction on a crystal lattice, high penetrating power. Irradiation in large doses causes radiation sickness. Application: in medicine for the purpose of diagnosing diseases of internal organs; in industry to control the internal structure of various products.

γ-radiation Sources: atomic nucleus (nuclear reactions). Properties: Has enormous penetrating power and has a strong biological effect. Application: In medicine, production (γ-flaw detection).

The influence of electromagnetic radiation on living organisms electromagnetic radiation with a frequency of 50 Hz, which is created by AC wires, with prolonged exposure causes drowsiness, signs of fatigue, and headaches. In order not to increase the effect of household electromagnetic radiation, experts recommend not placing electrical appliances operating in our apartments close to each other - a microwave oven, an electric stove, a TV, a washing machine, a refrigerator, an iron, an electric kettle. The distance between them should be at least 1.5-2 m. Your beds should be the same distance from the TV or refrigerator.

The influence of electromagnetic radiation on living organisms Radio waves Infrared Ultraviolet X-ray γ-radiation Homework: Write in your notebook about the effect of each radiation on humans, animals, plants.

Questions for consolidation 1. What is called an electromagnetic wave? 2. What is the source of an electromagnetic wave? 3. How are vectors E and B oriented relative to each other in an electromagnetic wave? 4. What is the speed of propagation of electromagnetic waves in air?

Questions for consolidation 5. What conclusions regarding electromagnetic waves followed from Maxwell’s theory? 6. What physical quantities change periodically in an electromagnetic wave? 7. What relationships between the wavelength, its speed, period and frequency of oscillations are valid for electromagnetic waves? 8. Under what condition will the wave be intense enough to be detected?

Questions for consolidation 9. When and by whom were electromagnetic waves first received? 10. Give examples of the application of electromagnetic waves. 11. Arrange in order of increasing wavelength the electromagnetic waves of various natures: 1) infrared radiation; 2) X-ray radiation; 3) radio waves; 4) γ-waves.

The connection between electricity and magnetism is not limited to the similarity of a number of relationships. In essence, both of these fields are different manifestations of a single electromagnetic field. In the mechanics course, we talked about the principle of relativity, that all laws of nature must be invariant when moving from one inertial frame of reference to another. However, electric and magnetic fields by themselves, separately, clearly do not satisfy this principle. Indeed, being in an inertial frame of reference TO, let's take the charge q, moving rectilinearly and uniformly with speed v. It creates a Coulomb electric field and, in addition, a magnetic field, the induction vector of which is given by expression (6.2). Let us associate the reference system with the charge TO", which will also be inertial. In this frame of reference, the charge is at rest, and the field it creates will be purely electrostatic. It turns out that the electric and magnetic fields do not have an absolute nature. When moving to another frame of reference, they must be transformed through each other (Fig. 6.33) .

Rice. 6.33. A charge is at rest in a moving frame of reference

Let us recall the Lorentz transformations for spatial coordinates and time

Let's not forget that similar transformations relate the momentum and energy of a particle in different reference systems

Will we now be surprised that the electric and magnetic fields in different reference frames are also related? Lorentz transformations

Recall that quantities with a prime refer to the reference system TO", which moves relative to the system TO along the axis X with speed V.

From the Lorentz transformations it follows that the electric field of a moving charge is extended in the direction perpendicular to the speed (Fig. 6.34).

Rice. 6.34. Electric field of a moving charge

Note that the Lorentz transformation formulas for the electromagnetic field differ from transformations for space-time or energy-momentum in that the field components along the line of motion of the reference system are not transformed TO" (that is, along the axis 0x). To illustrate this, consider a laboratory frame of reference TO, in which there is an electric field E , but no magnetic ( IN = 0). In what case does an observer of a moving reference frame TO"will also observe only a purely electric field E "without admixture of magnetic ( IN " = 0)? The answer follows from formulas (6.38) when substituting zero values ​​for IN , IN ": from the second equation it immediately follows E"y = E"z= 0, and from the first - E y = Ez= 0. In other words, this is possible when the electric field (not necessarily uniform) is directed along the motion of the reference frame TO".

The equations of electromagnetism were initially invariant under these transformations, so that the theory of relativity was quite painlessly combined with the electromagnetic theory, while classical mechanics underwent a significant revision. Instead of justifying the validity of transformations (6.38), which is beyond the scope of our course, we will get acquainted with one more of their consequences.

Since we are currently dealing mainly with non-relativistic physics, we will simplify the Lorentz transformations for the case when the speed of the reference system TO"much less than the speed of light: V << With. In this case, as already noted, the square roots

and transformations (6.38) take the form

These equations can be written in vector form

Let's return to our charged particle at rest in the system TO". In this system there is no magnetic field ( IN" = 0), and the electric field is given by Coulomb's law

Since it is assumed V << With, we use Galilean transformations for spatial coordinates and time intervals, so that the radius vector drawn from the particle to the observation point is the same in both reference systems: r =r ". Substituting the indicated expressions for IN ", E " into transformation (6.40), we obtain

Here we used relation (6.3)

The first equation (6.41) is the usual Coulomb charge field q, the second is the magnetic field of a moving charge (6.2). Thus, even classical magnetism is a manifestation of relativistic effects. Electric and magnetic fields turn out to be inextricably linked with each other into a single electromagnetic field, the specific manifestation of which depends on the reference system.

Example. An airplane flies horizontally at a speed of 250 m/s in the Earth's magnetic field with a magnetic induction of 50 μT directed vertically downward. What kind of electromagnetic field will be observed by airplane passengers?

Solution. Let's direct the axis 0x laboratory reference systems TO, connected to the Earth, along the plane's route, so its speed will be written in the form

Axis 0z let's direct it vertically upward, so that the magnetic induction is described by the vector

We need to find the electric and magnetic fields in a moving frame of reference TO" associated with the aircraft. Since the speed of the aircraft is much less than the speed of light, we can apply formulas (6.40). For convenience, however, we use the inverse formulas obtained by replacing the primed values ​​with unprimed ones and changing the sign of the speed: V = –v :

Since there is no electric field in the laboratory system ( E= 0), then from the second equation it immediately follows that IN " = IN : the magnetic field for air passengers will remain the same as for the relatives who accompanied them on the flight. However, an electric field will also appear in the plane. Its tension, as follows from the first equation, is equal to

We used here the fact that the cross product of two unit vectors gives a third unit vector

60 m at their ends a potential difference is created - the value is small, but measurable.

Additional Information

http://www.galileogalilei.ru/ - Galileo Galilei (1564–1642). Biography. Essays. Reflections. Philosophy. Galilean transformations;