Electromagnetic field, its influence on humans, measurement and protection. Electromagnetic fields

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 a certain point in space the magnetic field changes in time, then an electric field is also formed there. If there is a closed conductor in the field, then the electric field causes an induced current in it. From Maxwell's theory it follows that the reverse process is also possible. If in a certain region of space the electric field changes with time, then a magnetic field is also formed there.

Thus, any change in the magnetic field over time gives rise to a changing electric field, and any change in the electric field over time gives rise to a changing magnetic field. These alternating electric and magnetic fields generating each other 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 a vacuum propagate at 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 a vacuum. The relationship between wavelength, its speed, period and frequency of oscillations obtained for mechanical waves is also true for electromagnetic waves:

Voltage 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 transfers 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 10000 m to 0.005 m), used 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. lying between the radio wave range and the visible light range are called infrared radiation. Infrared radiation is emitted by any heated body. The sources of infrared radiation are stoves, batteries, and incandescent electric lamps. Using 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 extremely great, since a person receives almost all information about the world around him through vision.

Electromagnetic radiation with a wavelength shorter than violet, invisible to the eye, 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.

Principle of radio communication

An 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 oscillating circuit - antenna.

Radio communication is 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. Radiation is carried out in short pulses. The pulses are reflected from objects, allowing, after receiving and processing the signal, to establish the distance to the object.

Speed radar works on a similar principle. Think about how radar detects the speed of a moving car.

1. Introduction. Subject of study in valeology.

3. Main sources of electromagnetic field.

5. Methods of protecting human health from electromagnetic influence.

6. List of materials and literature used.

1. Introduction. Subject of study in valeology.

1.1 Introduction.

Valeology - from lat. “valeo” - “hello” is a scientific discipline that studies the individual health of a healthy person. The fundamental difference between valeology and other disciplines (in particular, from practical medicine) lies precisely in the individual approach to assessing the health of each specific subject (without taking into account general and averaged data for any group).

For the first time, valeology as a scientific discipline was officially registered in 1980. Its founder was the Russian scientist I. I. Brekhman, who worked at Vladivostok State University.

Currently, the new discipline is actively developing, scientific works are being accumulated, and practical research is being actively conducted. There is a gradual transition from the status of a scientific discipline to the status of an independent science.

1.2 Subject of study in valeology.

The subject of study in valeology is the individual health of a healthy person and the factors influencing it. Also, valeology deals with the systematization of a healthy lifestyle, taking into account the individuality of a particular subject.

The most common definition of the concept of “health” at the moment is the definition proposed by experts from the World Health Organization (WHO):

Health is a state of physical, mental and social well-being.

Modern valeology identifies the following main characteristics of individual health:

1. Life is the most complex manifestation of the existence of matter, which surpasses in complexity various physicochemical and bioreactions.

2. Homeostasis is a quasi-static state of life forms, characterized by variability over relatively large time periods and practical staticity over short periods.

3. Adaptation – the ability of life forms to adapt to changing conditions of existence and overloads. In case of adaptation disorders or too sudden and radical changes in conditions, maladjustment occurs - stress.

4. Phenotype is a combination of environmental factors that influence the development of a living organism. Also, the term “phenotype” characterizes a set of features of the development and physiology of an organism.

5. Genotype is a combination of hereditary factors that influence the development of a living organism, being a combination of the genetic material of the parents. When deformed genes are transmitted from parents, hereditary pathologies arise.

6. Lifestyle – a set of behavioral stereotypes and norms that characterize a specific organism.

Health (as defined by WHO).

2. Electromagnetic field, its types, characteristics and classification.

2.1 Basic definitions. Types of electromagnetic field.

An electromagnetic field is a special form of matter through which interaction between electrically charged particles occurs.

Electric field – created by electric charges and charged particles in space. The figure shows a picture of the field lines (imaginary lines used to visually represent fields) of the electric field for two charged particles at rest:

Magnetic field - created by the movement of electric charges along a conductor. The picture of the field lines for a single conductor is shown in the figure:

The physical reason for the existence of an electromagnetic field is that a time-varying electric field excites a magnetic field, and a changing magnetic field excites a vortex electric field. Continuously changing, both components support the existence of the electromagnetic field. The field of a stationary or uniformly moving particle is inextricably linked with the carrier (charged particle).

However, with the accelerated movement of carriers, the electromagnetic field “breaks off” from them and exists in the environment independently, in the form of an electromagnetic wave, without disappearing with the removal of the carrier (for example, radio waves do not disappear when the current (movement of carriers - electrons) in the antenna emitting them disappears).

2.2 Basic characteristics of the electromagnetic field.

The electric field is characterized by the electric field strength (designation “E”, SI dimension – V/m, vector). The magnetic field is characterized by the magnetic field strength (designation “H”, SI dimension – A/m, vector). The module (length) of the vector is usually measured.

Electromagnetic waves are characterized by wavelength (designation "(", SI dimension - m), their emitting source - frequency (designation - "(", SI dimension - Hz). In the figure E is the electric field strength vector, H is the magnetic field strength vector .

At frequencies of 3 – 300 Hz, the concept of magnetic induction (designation “B”, SI dimension - T) can also be used as a characteristic of the magnetic field.

2.3 Classification of electromagnetic fields.

The most commonly used is the so-called “zonal” classification of electromagnetic fields according to the degree of distance from the source/carrier.

According to this classification, the electromagnetic field is divided into “near” and “far” zones. The “near” zone (sometimes called the induction zone) extends to a distance from the source equal to 0-3(,de ( - the length of the electromagnetic wave generated by the field. In this case, the field strength quickly decreases (proportional to the square or cube of the distance to the source). In this zone the generated electromagnetic wave is not yet fully formed.

The “far” zone is the zone of the formed electromagnetic wave. Here the field strength decreases in inverse proportion to the distance to the source. In this zone, the experimentally determined relationship between the electric and magnetic field strengths is valid:

where 377 is a constant, wave impedance of vacuum, Ohm.

Electromagnetic waves are usually classified by frequency:

| Extremely low, | Hz | Decamegameter | Mm |

|Ultra-low, SLF | Hz | Megameter | Mm |

|Very low, VLF | KHz | Myriameter | km |

|Low frequencies, LF| KHz|Kilometer | km |

|Average, midrange | MHz | Hectometer | km |

|High, HF | MHz |Decameter | m |

|Very high, VHF| MHz|Meter | m |

|Ultrahigh, UHF| GHz |Decimeter | m |

|Ultra-high, microwave | GHz | Centimeter | cm |

| Extremely high, | GHz|Millimeter | mm |

Usually only the electric field strength E is measured. At frequencies above 300 MHz, the wave energy flux density, or the Pointing vector (designation “S”, SI dimension - W/m2) is sometimes measured.

3. The main sources of the electromagnetic field.

The main sources of the electromagnetic field can be identified:

Power lines.

Electrical wiring (inside buildings and structures).

Household electrical appliances.

Personal computers.

TV and radio broadcasting stations.

Satellite and cellular communications (devices, repeaters).

Electric transport.

Radar installations.

3.1 Power lines (PTL).

The wires of a working power line create an electromagnetic field of industrial frequency (50 Hz) in the adjacent space (at distances of the order of tens of meters from the wire). Moreover, the field strength near the line can vary within wide limits, depending on its electrical load. The standards establish the boundaries of sanitary protection zones near power lines (according to SN 2971-84):

|Operating voltage |330 and below |500 |750 |1150 |

|Size |20 |30 |40 |55 |

(in fact, the boundaries of the sanitary protection zone are established along the boundary line of maximum electric field strength, equal to 1 kV/m, farthest from the wires).

3.2 Electrical wiring.

Electrical wiring includes: power supply cables for building life support systems, current distribution wires, as well as distribution boards, power boxes and transformers. Electrical wiring is the main source of industrial frequency electromagnetic fields in residential premises. In this case, the level of electric field strength emitted by the source is often relatively low (does not exceed 500 V/m).

3.3 Household electrical appliances.

Sources of electromagnetic fields are all household appliances that operate using electric current. In this case, the radiation level varies within wide limits depending on the model, device design and specific operating mode. Also, the level of radiation strongly depends on the power consumption of the device - the higher the power, the higher the level of the electromagnetic field during operation of the device. The electric field strength near electrical household appliances does not exceed tens of V/m.

The table below shows the maximum permissible levels of magnetic induction for the most powerful magnetic field sources among household electrical appliances:

|Device |Interval of maximum permissible |

| |magnetic induction values, µT|

|Coffee maker | |

|Washing machine | |

|Iron | |

|Vacuum cleaner | |

|Electric stove | |

| Daylight lamp (fluorescent lamps LTB, | |

| Electric drill (electric motor | |

| power W) | |

| Electric mixer (electric motor power | |

| W) | |

|TV | |

|Microwave oven (induction, microwave) | |

3.4 Personal computers.

The main source of adverse effects on the health of a computer user is the visual display facility (VDI) of the monitor. In most modern monitors, the CVO is a cathode ray tube. The table lists the main factors affecting the health of SVR:

|Ergonomic |Factors of electromagnetic influence |

| |fields of a cathode ray tube |

| Significant reduction in contrast | Electromagnetic field in frequency |

| reproduced image in the | MHz range. |

| external illumination of the screen with direct rays | |

|light. | |

| Mirror reflection of light rays from | Electrostatic charge on the surface |

|screen surface (glare). |monitor screen. |

|Cartoon character |Ultraviolet radiation (range |

|image reproduction |wavelength nm). |

|(high frequency continuous update | |

| Discrete nature of the image | Infrared and X-ray |

|(subdivision into points). |ionizing radiation. |

In the future, as the main factors of the impact of SVO on health, we will consider only the factors of exposure to the electromagnetic field of a cathode ray tube.

In addition to the monitor and system unit, a personal computer may also include a large number of other devices (such as printers, scanners, surge protectors, etc.). All these devices operate using electric current, which means they are sources of an electromagnetic field. The following table shows the electromagnetic environment near the computer (the contribution of the monitor is not taken into account in this table, as it was discussed earlier):

| Source | Frequency range generated |

| |electromagnetic field |

|System unit assembly. |. |

| I/O devices (printers, | Hz. |

|scanners, disk drives, etc.). | |

|Uninterruptible power supplies, |. |

|line filters and stabilizers. | |

The electromagnetic field of personal computers has a very complex wave and spectral composition and is difficult to measure and quantify. It has magnetic, electrostatic and radiation components (in particular, the electrostatic potential of a person sitting in front of a monitor can range from –3 to +5 V). Considering the fact that personal computers are now actively used in all sectors of human activity, their impact on human health is subject to careful study and control.

3.5 Television and radio transmitting stations.

Russia currently hosts a significant number of radio broadcasting stations and centers of various affiliations.

Transmitting stations and centers are located in specially designated areas and can occupy fairly large areas (up to 1000 hectares). In their structure, they include one or more technical buildings where radio transmitters are located, and antenna fields on which up to several dozen antenna-feeder systems (AFS) are located. Each system includes a transmitting antenna and a feed line supplying the broadcast signal.

The electromagnetic field emitted by the antennas of radio broadcasting centers has a complex spectral composition and individual distribution of strengths depending on the configuration of the antennas, the terrain and the architecture of the adjacent buildings. Some average data for various types of radio broadcasting centers are presented in the table:

| |fields, V/m. |A/m. | |

| LW - radio stations | 630 | 1.2 | Highest tension |

|KHz, | | |distances less than 1 length |

|500 kW). | | | |

|200 kW). | | | |

| HF radio stations | 44 | 0.12 | Transmitters can be |

|MHz, | | |densely built up |

|100 kW). | | | |

| MHz, | | |building level. |

3.6 Satellite and cellular communications.

3.6.1 Satellite communications.

Satellite communication systems consist of a transmitting station on Earth and travelers - repeaters in orbit. Satellite communication transmitting stations emit a narrowly directed wave beam, the energy flux density of which reaches hundreds of W/m. Satellite communication systems create high electromagnetic field strengths at significant distances from the antennas. For example, a 225 kW station operating at a frequency of 2.38 GHz creates an energy flux density of 2.8 W/m2 at a distance of 100 km. Energy dissipation relative to the main beam is very small and occurs most of all in the area where the antenna is directly located.

3.6.2 Cellular communications.

Cellular radiotelephony is one of the most rapidly developing telecommunication systems today. The main elements of a cellular communication system are base stations and mobile radiotelephones. Base stations maintain radio communication with mobile devices, as a result of which they are sources of electromagnetic fields. The system uses the principle of dividing the coverage area into zones, or so-called “cells,” with a radius of km. The table below presents the main characteristics of the cellular communication systems operating in Russia:

| | | | |Tue |km. |

|NMT450. | |

|Analog. |5] |5] | | | |

|AMPS. |||100 |0.6 | |

|DAMPS (IS – |||50 |0.2 | |

|136). | | | | | |

|CDMA. |||100 |0.6 | |

|GSM – 900. |||40 |0.25 | |

|GSM – 1800. | |

|Digital. |0] |5] | | | |

The radiation intensity of a base station is determined by the load, that is, the presence of cell phone owners in the service area of a particular base station and their desire to use the phone for a conversation, which, in turn, fundamentally depends on the time of day, location of the station, day of the week and other factors. At night, the station load is almost zero. The intensity of radiation from mobile devices depends to a large extent on the state of the communication channel “mobile radiotelephone - base station” (the greater the distance from the base station, the higher the radiation intensity of the device).

3.7 Electric transport.

Electric transport (trolleybuses, trams, subway trains, etc.) is a powerful source of electromagnetic field in the Hz frequency range. In this case, in the vast majority of cases, the role of the main emitter is played by the traction electric motor (for trolleybuses and trams, aerial pantographs compete with the electric motor in terms of the intensity of the emitted electric field). The table shows data on the measured value of magnetic induction for some types of electric transport:

|Mode of transport and type |Average value |Maximum value |

| current consumption. |magnetic induction, µT. | Magnetic magnitude |

| | |induction, µT. |

|Commuter electric trains.|20 |75 |

|Electric transport with |29 |110 |

|DC drive | | |

|(electric cars, etc.). | | |

3.8 Radar installations.

Radar and radar installations usually have reflector-type antennas (“dishes”) and emit a narrowly directed radio beam.

Periodic movement of the antenna in space leads to spatial intermittency of the radiation. Temporary intermittency of radiation is also observed, due to the cyclic operation of the radar on radiation. They operate at frequencies from 500 MHz to 15 GHz, but some special installations can operate at frequencies up to 100 GHz or more. Due to the special nature of the radiation, they can create areas with a high energy flux density (100 W/m2 or more).

4. The influence of the electromagnetic field on individual human health.

The human body always reacts to an external electromagnetic field. Due to different wave composition and other factors, the electromagnetic field of different sources affects human health in different ways. As a result, in this section we will consider the impact of various sources on health separately. However, the field of artificial sources, which is sharply dissonant with the natural electromagnetic background, in almost all cases has a negative impact on the health of people in the zone of its influence.

Extensive research into the effects of electromagnetic fields on health began in our country in the 60s. It was found that the human nervous system is sensitive to electromagnetic influence, and also that the field has a so-called informational effect when exposed to a person at intensities below the threshold value of the thermal effect (the magnitude of the field strength at which its thermal effect begins to manifest itself).

The table below shows the most common complaints about the deterioration of the health of people in the area of exposure to fields from various sources. The sequence and numbering of sources in the table corresponds to their sequence and numbering adopted in Section 3:

|Source |The most common complaints. |

|electromagnetic | |

|1. Lines |Short-term irradiation (on the order of several minutes) can|

| power transmission lines (power lines). |lead to a negative reaction only in those who are particularly sensitive |

| | people or patients with certain types of allergies |

| | diseases. Prolonged exposure usually leads to |

| |various pathologies of the cardiovascular and nervous systems |

| |(due to imbalance of the nervous regulation subsystem). When |

| |ultra-long (about 10-20 years) continuous irradiation |

| |possible (according to unverified data) the development of some |

| |oncological diseases. |

|2. Internal |Current data on complaints of deterioration |

|electrical wiring of buildings|health related directly to the work of internal |

| and buildings. |there are no electrical networks. |

|3. Household | There are unverified data on skin complaints, |

| electrical appliances. |cardiovascular and nervous pathologies in long-term |

| | systematic use of old microwave ovens |

| |models (up to 1995). There are also similar |

| |data regarding the use of all microwave ovens |

| |models in production conditions (for example, for heating |

| | food in a cafe). In addition to microwave ovens, there is data on |

| | negative impact on the health of people with televisions |

| | as a visualization device, a cathode ray tube. |

An electromagnetic field is alternating electric and magnetic fields that generate each other.
The theory of the electromagnetic field was created by James Maxwell in 1865.

He theoretically proved that:
any change in the magnetic field over time gives rise to a changing electric field, and any change in the electric field over time gives rise to a changing magnetic field.
If electric charges move with acceleration, then the electric field they create periodically changes and itself creates an alternating magnetic field in space, etc.

Sources of electromagnetic field can be:
- moving magnet;
- an electric charge moving with acceleration or oscillating (in contrast to a charge moving at a constant speed, for example, in the case of direct current in a conductor, a constant magnetic field is created here).

An electric field always exists around an electric charge, in any reference system, a magnetic field exists in the one relative to which the electric charges move.
An electromagnetic field exists in a reference frame relative to which electric charges move with acceleration.

TRY SOLVING

A piece of amber was rubbed against a cloth, and it became charged with static electricity. What kind of field can be found around motionless amber? Around a moving one?

A charged body is at rest relative to the surface of the earth. The car moves uniformly and rectilinearly relative to the surface of the earth. Is it possible to detect a constant magnetic field in the reference frame associated with a car?

What field appears around an electron if it: is at rest; moves at a constant speed; moving with acceleration?

A kinescope creates a stream of uniformly moving electrons. Is it possible to detect a magnetic field in a reference frame associated with one of the moving electrons?

ELECTROMAGNETIC WAVES

Electromagnetic waves are an electromagnetic field propagating in space with a finite speed depending on the properties of the medium

Properties of electromagnetic waves:
- propagate not only in matter, but also in vacuum;
- propagate in vacuum at the speed of light (C = 300,000 km/s);
- these are transverse waves;
- these are traveling waves (transfer energy).

The source of electromagnetic waves are accelerated moving electrical charges.
Oscillations of electric charges are accompanied by electromagnetic radiation having a frequency equal to the frequency of charge oscillations.

ELECTROMAGNETIC WAVE SCALE

All the space around us is permeated with electromagnetic radiation. The sun, the bodies around us, and transmitter antennas emit electromagnetic waves, which, depending on their oscillation frequency, have different names.

Radio waves are electromagnetic waves (with a wavelength from more than 10000m to 0.005m), used to transmit signals (information) over a distance without wires.
In radio communications, radio waves are created by high-frequency currents flowing in an antenna.
Radio waves of different wavelengths travel differently.

Electromagnetic radiation with a wavelength less than 0.005 m but greater than 770 nm, i.e., lying between the radio wave range and the visible light range, is called infrared radiation (IR).
Infrared radiation is emitted by any heated body. Sources of infrared radiation are stoves, water heating radiators, and incandescent electric lamps. Using special devices, infrared radiation can be converted into visible light and images of heated objects can be obtained in complete darkness. Infrared radiation is used for drying painted products, building walls, and wood.

Visible light includes radiation with wavelengths from approximately 770 nm to 380 nm, from red to violet light. The significance of this part of the spectrum of electromagnetic radiation in human life is extremely large, since a person receives almost all information about the world around him through vision. Light is a prerequisite for the development of green plants and, therefore, a necessary condition for the existence of life on Earth.

Invisible to the eye, electromagnetic radiation with a wavelength shorter than that of violet light is called ultraviolet radiation (UV). Ultraviolet radiation can kill benign bacteria, so it is widely used in medicine. Ultraviolet radiation in the composition of sunlight causes biological processes that lead to darkening of human skin - tanning. Discharge lamps are used as sources of ultraviolet radiation in medicine. The tubes of such lamps are made of quartz, transparent to ultraviolet rays; That's why these lamps are called quartz lamps.

X-rays (Ri) are invisible. They pass without significant absorption through significant layers of matter that are opaque to visible light. X-rays are detected by their ability to cause a certain glow in certain crystals and act on photographic film. The ability of X-rays to penetrate thick layers of substances is used to diagnose diseases of human internal organs.

An electromagnetic field is a type of matter that arises around moving charges. For example, around a conductor carrying current. The electromagnetic field consists of two components: electric and magnetic field. They cannot exist independently of each other. One thing begets another. When the electric field changes, a magnetic field immediately appears. Electromagnetic wave propagation speed V=C/EM Where e And m respectively, the magnetic and dielectric constants of the medium in which the wave propagates. An electromagnetic wave in a vacuum travels at the speed of light, that is, 300,000 km/s. Since the dielectric and magnetic permeability of a vacuum are considered to be equal to 1. When the electric field changes, a magnetic field appears. Since the electric field that caused it is not constant (that is, it changes over time), the magnetic field will also be variable. A changing magnetic field in turn generates an electric field, and so on. Thus, for the subsequent field (it does not matter whether it is electric or magnetic), the source will be the previous field, and not the original source, that is, a conductor with current. Thus, even after turning off the current in the conductor, the electromagnetic field will continue to exist and spread in space. An electromagnetic wave propagates in space in all directions from its source. You can imagine turning on a light bulb, the rays of light from it spread in all directions. An electromagnetic wave, when propagating, transfers energy in space. The stronger the current in the conductor that causes the field, the greater the energy transferred by the wave. Also, the energy depends on the frequency of the emitted waves; if it increases by 2,3,4 times, the wave energy will increase by 4,9,16 times, respectively. That is, the energy of wave propagation is proportional to the square of the frequency. The best conditions for wave propagation are created when the length of the conductor is equal to the wavelength. The magnetic and electric lines of force will fly mutually perpendicular. Magnetic lines of force surround a current-carrying conductor and are always closed. Electrical lines of force go from one charge to another. An electromagnetic wave is always a transverse wave. That is, the lines of force, both magnetic and electric, lie in a plane perpendicular to the direction of propagation. Electromagnetic field strength is a strength characteristic of the field. Also, tension is a vector quantity, that is, it has a beginning and a direction. The field strength is directed tangentially to the lines of force. Since the electric and magnetic field strengths are perpendicular to each other, there is a rule by which the direction of wave propagation can be determined. When the screw rotates along the shortest path from the electric field strength vector to the magnetic field strength vector, the forward movement of the screw will indicate the direction of wave propagation.

Magnetic field and its characteristics. When an electric current passes through a conductor, a a magnetic field. A magnetic field represents one of the types of matter. It has energy, which manifests itself in the form of electromagnetic forces acting on individual moving electric charges (electrons and ions) and on their flows, i.e. electric current. Under the influence of electromagnetic forces, moving charged particles deviate from their original path in a direction perpendicular to the field (Fig. 34). The magnetic field is formed only around moving electric charges, and its action also extends only to moving charges. Magnetic and electric fields inseparable and form together a single electromagnetic field. Any change electric field leads to the appearance of a magnetic field and, conversely, any change in the magnetic field is accompanied by the appearance of an electric field. Electromagnetic field propagates at the speed of light, i.e. 300,000 km/s.

Graphic representation of the magnetic field. Graphically, the magnetic field is represented by magnetic lines of force, which are drawn so that the direction of the field line at each point of the field coincides with the direction of the field forces; magnetic field lines are always continuous and closed. The direction of the magnetic field at each point can be determined using a magnetic needle. The north pole of the arrow is always set in the direction of the field forces. The end of a permanent magnet from which the field lines emerge (Fig. 35, a) is considered to be the north pole, and the opposite end, into which the field lines enter, is the south pole (the field lines passing inside the magnet are not shown). The distribution of field lines between the poles of a flat magnet can be detected using steel filings sprinkled on a sheet of paper placed on the poles (Fig. 35, b). The magnetic field in the air gap between two parallel opposite poles of a permanent magnet is characterized by a uniform distribution of magnetic force lines (Fig. 36)

Shmelev V.E., Sbitnev S.A.

"THEORETICAL FUNDAMENTALS OF ELECTRICAL ENGINEERING"

"ELECTROMAGNETIC FIELD THEORY"

Chapter 1. Basic concepts of electromagnetic field theory

§ 1.1. Definition of the electromagnetic field and its physical quantities.
Mathematical apparatus of the theory of electromagnetic field

Electromagnetic field(EMF) is a type of matter that exerts a force on charged particles and is determined at all points by two pairs of vector quantities that characterize its two sides - electric and magnetic fields.

Electric field- this is a component of EMF, which is characterized by the effect on an electrically charged particle with a force proportional to the charge of the particle and independent of its speed.

A magnetic field is a component of EMF, which is characterized by the effect on a moving particle with a force proportional to the charge of the particle and its speed.

The basic properties and methods of calculating EMFs studied in the course of theoretical foundations of electrical engineering involve a qualitative and quantitative study of EMFs found in electrical, electronic and biomedical devices. For this purpose, the equations of electrodynamics in integral and differential forms are most suitable.

The mathematical apparatus of electromagnetic field theory (TEMF) is based on scalar field theory, vector and tensor analysis, as well as differential and integral calculus.

Control questions

1. What is an electromagnetic field?

2. What are called electric and magnetic fields?

3. What is the mathematical apparatus of the electromagnetic field theory based on?

§ 1.2. Physical quantities characterizing EMF

Electric field strength vector at the point Q is the vector of force acting on an electrically charged stationary particle placed at a point Q, if this particle has a unit positive charge.

According to this definition, the electric force acting on a point charge q is equal to:

Where E measured in V/m.

The magnetic field is characterized vector of magnetic induction. Magnetic induction at some observation point Q is a vector quantity whose modulus is equal to the magnetic force acting on a charged particle located at a point Q, having a unit charge and moving with a unit speed, and the vectors of force, speed, magnetic induction, as well as the charge of the particle satisfy the condition

The magnetic force acting on a curved conductor carrying current can be determined by the formula

A straight conductor, if it is in a uniform field, is acted upon by the following magnetic force

In all the latest formulas B - magnetic induction, which is measured in teslas (T).

1 T is a magnetic induction in which a magnetic force equal to 1 N acts on a straight conductor with a current of 1A, if the lines of magnetic induction are directed perpendicular to the conductor with the current, and if the length of the conductor is 1 m.

In addition to the electric field strength and magnetic induction, the following vector quantities are considered in the theory of the electromagnetic field:

1) electrical induction D (electrical displacement), which is measured in C/m 2,

EMF vectors are functions of space and time:

Where Q- observation point, t- moment of time.

If the observation point Q is in a vacuum, then the following relations hold between the corresponding pairs of vector quantities

where is the absolute dielectric constant of vacuum (basic electrical constant), =8.85419*10 -12;

Absolute magnetic permeability of vacuum (basic magnetic constant); = 4π*10 -7 .

Control questions

1. What is electric field strength?

2. What is magnetic induction called?

3. What is the magnetic force acting on a moving charged particle?

4. What is the magnetic force acting on a current-carrying conductor?

5. What vector quantities are characterized by the electric field?

6. What vector quantities are characterized by a magnetic field?

§ 1.3. Electromagnetic field sources

Sources of EMF are electric charges, electric dipoles, moving electric charges, electric currents, magnetic dipoles.

The concepts of electric charge and electric current are given in the physics course. Electric currents are of three types:

1. Conduction currents.

2. Displacement currents.

3. Transfer currents.

Conduction current- the speed of passage of moving charges of an electrically conductive body through a certain surface.

Bias current- the rate of change of the electric displacement vector flow through a certain surface.

Transfer current characterized by the following expression

Where v - speed of transfer of bodies through the surface S; n - vector of the unit normal to the surface; - linear charge density of bodies flying through the surface in the direction of the normal; ρ - volume density of electric charge; ρ v - transfer current density.

Electric dipole called a pair of point charges + q And - q, located at a distance l from each other (Fig. 1).

A point electric dipole is characterized by the vector of the electric dipole moment:

Magnetic dipole called a flat circuit with electric current I. A magnetic dipole is characterized by the vector of the magnetic dipole moment

Where S - vector of the area of a flat surface stretched over a current-carrying circuit. Vector S directed perpendicular to this flat surface, and, when viewed from the end of the vector S , then movement along the contour in the direction coinciding with the direction of the current will occur counterclockwise. This means that the direction of the dipole magnetic moment vector is related to the direction of the current according to the right-hand screw rule.

Atoms and molecules of matter are electric and magnetic dipoles, therefore each point of a material type in the EMF can be characterized by the volumetric density of the electric and magnetic dipole moment:

P - electrical polarization of the substance:

M - magnetization of the substance:

Electrical polarization of matter is a vector quantity equal to the volumetric density of the electric dipole moment at some point of a real body.

Magnetization of a substance is a vector quantity equal to the volumetric density of the magnetic dipole moment at some point of a material body.

Electrical bias is a vector quantity, which for any observation point, regardless of whether it is in a vacuum or in matter, is determined from the relation:

(for vacuum or substance),

(for vacuum only).

Magnetic field strength- a vector quantity, which for any observation point, regardless of whether it is in a vacuum or in a substance, is determined from the relation:

where the magnetic field strength is measured in A/m.

In addition to polarization and magnetization, there are other volumetrically distributed sources of EMF:

- volumetric charge density ; ,

where the volumetric charge density is measured in C/m3;

- electric current density vector, whose normal component is equal to

More generally, the current flowing through an open surface S, is equal to the current density vector flux through this surface:

where the electric current density vector is measured in A/m 2.

Control questions

1. What are the sources of the electromagnetic field?

2. What is conduction current?

3. What is bias current?

4. What is transfer current?

5. What is an electric dipole and an electric dipole moment?

6. What is a magnetic dipole and magnetic dipole moment?

7. What is called the electrical polarization and magnetization of a substance?

8. What is called electrical displacement?

9. What is magnetic field strength called?

10. What is the volumetric density of electric charge and current density?

MATLAB Application Example

Task.

Given: Circuit with electric current I in space represents the perimeter of a triangle, the Cartesian coordinates of the vertices of which are given: x 1 , x 2 , x 3 , y 1 , y 2 , y 3 , z 1 , z 2 , z 3. Here the subscripts are the numbers of the vertices. The vertices are numbered in the direction of flow of electric current.

Required compose a MATLAB function that calculates the dipole magnetic moment vector of the loop. When compiling an m-file, it can be assumed that spatial coordinates are measured in meters, and current in amperes. Arbitrary organization of input and output parameters is allowed.

Solution

% m_dip_moment - calculation of the magnetic dipole moment of a triangular circuit with a current in space

% pm = m_dip_moment(tok,nodes)

% INPUT PARAMETERS

% tok - current in the circuit;

% nodes is a square matrix of the form ".", each row of which contains the coordinates of the corresponding vertex.

% OUTPUT PARAMETER

% pm is a row matrix of the Cartesian components of the magnetic dipole moment vector.

function pm = m_dip_moment(tok,nodes);

pm=tok*)]) det()]) det()])]/2;

% In the last statement, the triangle area vector is multiplied by the current

>> nodes=10*rand(3)

9.5013 4.8598 4.5647

2.3114 8.913 0.18504

6.0684 7.621 8.2141

>> pm=m_dip_moment(1,nodes)

13.442 20.637 -2.9692

In this case it worked P M = (13.442* 1 x + 20.637*1 y - 2.9692*1 z) A*m 2 if the current in the circuit is 1 A.

§ 1.4. Spatial differential operators in electromagnetic field theory

Gradient scalar field Φ( Q) = Φ( x, y, z) is a vector field defined by the formula:

Where V 1 - area containing the point Q; S 1 - closed surface bounding the area V 1 , Q 1 - point belonging to the surface S 1 ; δ - greatest distance from the point Q to points on the surface S 1 (max| Q Q 1 |).

Divergence vector field F (Q)=F (x, y, z) is called a scalar field, defined by the formula:

Rotor(vortex) vector field F (Q)=F (x, y, z) is a vector field defined by the formula:

rot F =

Nabla operator is a vector differential operator, which in Cartesian coordinates is defined by the formula:

Let's represent grad, div and rot through the nabla operator:

Let's write these operators in Cartesian coordinates:

; ;

The Laplace operator in Cartesian coordinates is defined by the formula:

Second order differential operators:

Integral theorems

Gradient theorem ;

Divergence theorem

Rotor theorem

In the theory of EMF, one more of the integral theorems is also used:

Control questions

1. What is called the scalar field gradient?

2. What is called the divergence of a vector field?

3. What is called the curl of a vector field?

4. What is the nabla operator and how are first-order differential operators expressed through it?

5. What integral theorems are true for scalar and vector fields?

MATLAB Application Example

Task.

Given: In the volume of a tetrahedron, the scalar and vector fields change according to a linear law. The coordinates of the tetrahedron vertices are specified by a matrix of the form [ x 1 , y 1 , z 1 ; x 2 , y 2 , z 2 ; x 3 , y 3 , z 3 ; x 4 , y 4 , z 4 ]. The values of the scalar field at the vertices are specified by the matrix [Ф 1 ; F 2; F 3; F 4]. The Cartesian components of the vector field at the vertices are specified by the matrix [ F 1 x, F 1y, F 1z; F 2x, F 2y, F 2z; F 3x, F 3y, F 3z; F 4x, F 4y, F 4z].

Define in the volume of the tetrahedron, the gradient of the scalar field, as well as the divergence and curl of the vector field. Write a MATLAB function for this.

Solution. Below is the text of the m-function.

% grad_div_rot - Calculate gradient, divergence and rotor... in the volume of a tetrahedron

% =grad_div_rot(nodes,scalar,vector)

% INPUT PARAMETERS

% nodes - matrix of coordinates of tetrahedron vertices:

% rows correspond to vertices, columns - coordinates;

% scalar - columnar matrix of scalar field values at the vertices;

% vector - matrix of vector field components at vertices:

% OUTPUT PARAMETERS

% grad - row matrix of Cartesian components of the gradient of the scalar field;

% div - the divergence value of the vector field in the volume of the tetrahedron;

% rot is a row matrix of the Cartesian components of the vector field rotor.

% In the calculations it is assumed that in the volume of the tetrahedron

% vector and scalar fields vary in space according to a linear law.

function =grad_div_rot(nodes,scalar,vector);

a=inv(); % Linear interpolation coefficient matrix

grad=(a(2:end,:)*scalar)."; % Gradient components of the scalar field

div=*vector(:); % Vector field divergence

rot=sum(cross(a(2:end,:),vector."),2).";

An example of running the developed m-function:

>> nodes=10*rand(4,3)

3.5287 2.0277 1.9881

8.1317 1.9872 0.15274

0.098613 6.0379 7.4679

1.3889 2.7219 4.451

>> scalar=rand(4,1)

>> vector=rand(4,3)

0.52515 0.01964 0.50281

0.20265 0.68128 0.70947

0.67214 0.37948 0.42889

0.83812 0.8318 0.30462

>> =grad_div_rot(nodes,scalar,vector)

0.16983 -0.03922 -0.17125

0.91808 0.20057 0.78844

If we assume that spatial coordinates are measured in meters, and vector and scalar fields are dimensionless, then in this example we get:

grad Ф = (-0.16983* 1 x - 0.03922*1 y - 0.17125*1 z) m -1 ;

div F = -1.0112 m -1 ;

rot F = (-0.91808*1 x + 0.20057*1 y + 0.78844*1 z) m -1 .

§ 1.5. Basic laws of electromagnetic field theory

EMF equations in integral form

Total current law:

Circulation of the magnetic field strength vector along the contour l equal to the total electric current flowing through the surface S, stretched on the contour l, if the direction of the current forms a right-handed system with the direction of bypassing the circuit.

Law of electromagnetic induction:

Where E c is the intensity of the external electric field.

EMF electromagnetic induction e and in the circuit l equal to the rate of change of magnetic flux through the surface S, stretched on the contour l, and the direction of the rate of change of magnetic flux forms with the direction e and a left-handed screw system.

Gauss's theorem in integral form:

Electric displacement vector flow through a closed surface S equal to the sum of free electric charges in the volume limited by the surface S.

Law of continuity of magnetic induction lines:

The magnetic flux through any closed surface is zero.

Direct application of equations in integral form makes it possible to calculate the simplest electromagnetic fields. To calculate electromagnetic fields of more complex shapes, equations in differential form are used. These equations are called Maxwell's equations.

Maxwell's equations for stationary media

These equations follow directly from the corresponding equations in integral form and from the mathematical definitions of spatial differential operators.

Total current law in differential form:

Total electric current density,

Density of external electric current,

Conduction current density,

Bias current density: ,

Transfer current density: .

This means that the electric current is a vortex source of the vector field of magnetic field strength.

The law of electromagnetic induction in differential form:

This means that the alternating magnetic field is a vortex source for the spatial distribution of the electric field strength vector.

Equation of continuity of magnetic induction lines:

This means that the field of the magnetic induction vector has no sources, i.e. There are no magnetic charges (magnetic monopoles) in nature.

Gauss's theorem in differential form:

This means that the sources of the vector field of electric displacement are electric charges.

To ensure the uniqueness of the solution to the problem of EMF analysis, it is necessary to supplement Maxwell’s equations with equations of material connections between vectors E And D , and B And H .

Relationships between field vectors and electrical properties of the medium

It is known that

(1)

All dielectrics are polarized under the influence of an electric field. All magnets are magnetized under the influence of a magnetic field. The static dielectric properties of a substance can be completely described by the functional dependence of the polarization vector P from the electric field strength vector E (P =P (E )). The static magnetic properties of a substance can be completely described by the functional dependence of the magnetization vector M from the magnetic field strength vector H (M =M (H )). In the general case, such dependences are ambiguous (hysteretic) in nature. This means that the polarization or magnetization vector at a point Q is determined not only by the value of the vector E or H at this point, but also the background of the change in vector E or H at this point. It is extremely difficult to experimentally study and model these dependencies. Therefore, in practice it is often assumed that the vectors P And E , and M And H are collinear, and the electrical properties of a substance are described by scalar hysteresis functions (| P |=|P |(|E |), |M |=|M |(|H |). If the hysteresis characteristics of the above functions can be neglected, then the electrical properties are described by unambiguous functions P=P(E), M=M(H).

In many cases, these functions can be approximately considered linear, i.e.

Then, taking into account relation (1), we can write the following

(4)

Accordingly, the relative dielectric and magnetic permeability of the substance:

Absolute dielectric constant of a substance:

Absolute magnetic permeability of a substance:

Relations (2), (3), (4) characterize the dielectric and magnetic properties of the substance. The electrically conductive properties of a substance can be described by Ohm's law in differential form

where is the specific electrical conductivity of the substance, measured in S/m.

In a more general case, the relationship between the conduction current density and the electric field strength vector has a nonlinear vector-hysteresis character.

Electromagnetic field energy

The volumetric energy density of the electric field is equal to

Where W e is measured in J/m 3.

The volumetric energy density of the magnetic field is equal to

Where W m is measured in J/m 3.

The volumetric energy density of the electromagnetic field is equal to

In the case of linear electrical and magnetic properties of matter, the volumetric energy density of the EMF is equal to

This expression is valid for instantaneous values of specific energy and EMF vectors.

Specific power of heat losses from conduction currents

Power density of third party sources

Control questions

1. How is the law of total current formulated in integral form?

2. How is the law of electromagnetic induction formulated in integral form?

3. How are Gauss’s theorem and the law of magnetic flux continuity formulated in integral form?

4. How is the total current law formulated in differential form?

5. How is the law of electromagnetic induction formulated in differential form?

6. How are Gauss’s theorem and the law of continuity of magnetic induction lines formulated in integral form?

7. What relationships describe the electrical properties of a substance?

8. How is the energy of the electromagnetic field expressed through the vector quantities that determine it?

9. How is the specific power of heat losses and the specific power of third-party sources determined?

MATLAB Application Examples

Problem 1.

Given: Inside the volume of the tetrahedron, the magnetic induction and magnetization of the substance change according to a linear law. The coordinates of the vertices of the tetrahedron are given, the values of the vectors of magnetic induction and magnetization of the substance at the vertices are also given.

Calculate electric current density in the volume of the tetrahedron, using the m-function compiled when solving the problem in the previous paragraph. Perform the calculation in the MATLAB command window, assuming that spatial coordinates are measured in millimeters, magnetic induction in tesla, magnetic field strength and magnetization in kA/m.

Solution.

Let's set the initial data in a format compatible with the m-function grad_div_rot:

>> nodes=5*rand(4,3)

0.94827 2.7084 4.3001

0.96716 0.75436 4.2683

3.4111 3.4895 2.9678

1.5138 1.8919 2.4828

>> B=rand(4.3)*2.6-1.3

1.0394 0.41659 0.088605

0.83624 -0.41088 0.59049

0.37677 -0.54671 -0.49585

0.82673 -0.4129 0.88009

>> mu0=4e-4*pi % absolute magnetic permeability of vacuum, µH/mm

>> M=rand(4,3)*1800-900

122.53 -99.216 822.32

233.26 350.22 40.663

364.93 218.36 684.26

83.828 530.68 -588.68

>> =grad_div_rot(nodes,ones(4,1),B/mu0-M)

0 -3.0358e-017 0

914.2 527.76 -340.67

In this example, the vector of the total current density in the volume under consideration turned out to be equal to (-914.2* 1 x + 527.76*1 y - 340.67*1 z) A/mm 2 . To determine the modulus of the current density, we execute the following operator:

>> cur_d=sqrt(cur_dens*cur_dens.")

The calculated value of current density cannot be obtained in highly magnetized environments in real technical devices. This example is purely educational. Now let’s check the correctness of specifying the distribution of magnetic induction in the volume of the tetrahedron. To do this, we execute the following statement:

>> =grad_div_rot(nodes,ones(4,1),B)

0 -3.0358e-017 0

0.38115 0.37114 -0.55567

Here we got the div value B = -0.34415 T/mm, which cannot be in accordance with the law of continuity of magnetic induction lines in differential form. It follows from this that the distribution of magnetic induction in the volume of the tetrahedron is specified incorrectly.

Problem 2.

Let a tetrahedron, the coordinates of the vertices of which are given, be in the air (units of measurement are meters). Let the values of the electric field strength vector at its vertices be given (units of measurement - kV/m).

Required calculate the volumetric charge density inside the tetrahedron.

Solution can be done similarly:

>> nodes=3*rand(4,3)

2.9392 2.2119 0.59741

0.81434 0.40956 0.89617

0.75699 0.03527 1.9843

2.6272 2.6817 0.85323

>> eps0=8.854e-3% absolute dielectric constant of vacuum, nF/m

>> E=20*rand(4,3)

9.3845 8.4699 4.519

1.2956 10.31 11.596

19.767 6.679 15.207

11.656 8.6581 10.596

>> =grad_div_rot(nodes,ones(4,1),E*eps0)

0.076467 0.21709 -0.015323

In this example, the volumetric charge density was equal to 0.10685 µC/m 3.

§ 1.6. Boundary conditions for EMF vectors.
Law of conservation of charge. Umov-Poynting theorem

Here it is indicated: H 1 - vector of magnetic field strength at the interface between media in medium No. 1; H 2 - the same in environment No. 2; H 1t- tangential (tangent) component of the magnetic field strength vector at the interface between media in medium No. 1; H 2t- the same in environment No. 2; E 1 vector of the total electric field strength at the interface between media in medium No. 1; E 2 - the same in environment No. 2; E 1 c - third-party component of the electric field strength vector at the interface between media in medium No. 1; E 2c - the same in environment No. 2; E 1t- tangential component of the electric field strength vector at the interface between media in medium No. 1; E 2t- the same in environment No. 2; E 1s t- tangential third-party component of the electric field strength vector at the interface between media in medium No. 1; E 2t- the same in environment No. 2; B 1 - vector of magnetic induction at the interface between media in medium No. 1; B 2 - the same in environment No. 2; B 1n- normal component of the magnetic induction vector at the interface between media in medium No. 1; B 2n- the same in environment No. 2; D 1 - electric displacement vector at the interface between media in medium No. 1; D 2 - the same in environment No. 2; D 1n- normal component of the electric displacement vector at the interface between media in medium No. 1; D 2n- the same in environment No. 2; σ is the surface density of the electric charge at the interface, measured in C/m2.

Law of conservation of charge

If there are no third-party current sources, then

and in the general case, i.e., the total current density vector has no sources, i.e., the total current lines are always closed

Umov-Poynting theorem

The volumetric power density consumed by a material point in an EMF is equal to

In accordance with identity (1)

This is the power balance equation for volume V. In the general case, in accordance with equality (3), the electromagnetic power generated by sources inside the volume V, goes to heat losses, to the accumulation of EMF energy and to radiation into the surrounding space through a closed surface that limits this volume.

The integrand in integral (2) is called the Poynting vector:

Where P measured in W/m2.

This vector is equal to the electromagnetic power flux density at some observation point. Equality (3) is a mathematical expression of the Umov-Poynting theorem.

Electromagnetic power emitted by the area V into the surrounding space is equal to the flux of the Poynting vector through a closed surface S, limiting the area V.

Control questions

1. What expressions describe the boundary conditions for the electromagnetic field vectors at the interfaces between media?

2. How is the law of conservation of charge formulated in differential form?

3. How is the law of conservation of charge formulated in integral form?

4. What expressions describe the boundary conditions for the current density at the interfaces?

5. What is the volumetric power density consumed by a material point in an electromagnetic field?

6. How is the electromagnetic power balance equation written for a certain volume?

7. What is a Poynting vector?

8. How is the Umov-Poynting theorem formulated?

MATLAB Application Example

Task.

Given: There is a triangular surface in space. The coordinates of the vertices are given. The values of the electric and magnetic field strength vectors at the vertices are also specified. The third-party component of the electric field strength is zero.

Required calculate the electromagnetic power passing through this triangular surface. Write a MATLAB function that performs this calculation. When calculating, assume that the positive normal vector is directed in such a way that if viewed from its end, the movement in increasing order of vertex numbers will occur counterclockwise.

Solution. Below is the text of the m-function.

% em_power_tri - calculation of electromagnetic power passing through

% triangular surface in space

% P=em_power_tri(nodes,E,H)

% INPUT PARAMETERS

% nodes is a square matrix of the form ",

% in each line of which the coordinates of the corresponding vertex are written.

% E - matrix of components of the electric field strength vector at the vertices:

% rows correspond to vertices, columns - Cartesian components.

% H - matrix of components of the magnetic field strength vector at the vertices.

% OUTPUT PARAMETER

% P - electromagnetic power passing through the triangle

% During calculations it is assumed that on the triangle

% field strength vectors change in space according to a linear law.

function P=em_power_tri(nodes,E,H);

% Calculate the double area vector of the triangle

S=)]) det()]) det()])];

P=sum(cross(E,(ones(3,3)+eye(3))*H,2))*S."/24;

An example of running the developed m-function:

>> nodes=2*rand(3,3)

0.90151 0.5462 0.4647

1.4318 0.50954 1.6097

1.7857 1.7312 1.8168

>> E=2*rand(3,3)

0.46379 0.15677 1.6877

0.47863 1.2816 0.3478

0.099509 0.38177 0.34159

>>H=2*rand(3,3)

1.9886 0.62843 1.1831

0.87958 0.73016 0.23949

0.6801 0.78648 0.076258

>> P=em_power_tri(nodes,E,H)

If we assume that spatial coordinates are measured in meters, the electric field strength vector is in volts per meter, and the magnetic field strength vector is in amperes per meter, then in this example the electromagnetic power passing through the triangle is equal to 0.18221 W.

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