Lecture 1

The subject of classical electrodynamics. Electric field. tension electric field.

subject of electrodynamics. Electrodynamics - branch of physics that studies the interaction electrically charged particles and a special kind of matter generated by these particles - electromagnetic field .

1. ELECTROSTATICS

Electrostatics- a section of electrodynamics that studies the interaction motionless charged bodies . The electric field that carries out this interaction is called electrostatic .

1.1. Electric charges.

Ways to get charges. The law of conservation of electric charge.

In nature, there are two kinds of electric charges, conventionally called positive and negative. Historically, it is customary to call positive charges, similar topics that occur when glass is rubbed against silk; negative - charges similar to those that arise when amber is rubbed against fur. Charges of the same sign repel each other, charges of different signs attract (Fig. 1.1).

Essentially, electric charges atomistic (discrete). This means that in nature there is the smallest, further indivisible charge, called the elementary charge. Value elementary charge by absolute value in SI:

Electric charges are inherent in many elementary particles, in particular, electrons and protons, which are part of various atoms, from which all bodies in nature are built. It should be noted, however, that according to modern ideas strongly interacting particles - hadrons (mesons and baryons) - are built from the so-called quarks – special particles, bearing fractional charge. Currently, six types of quarks are known - u, d, s, t, b and c - according to the first letters of the words: up-upper, down-lower, side-way- lateral (or strange-strange), top- top, bottom- extreme and charm-charmed. These quarks split into pairs: (u,d), (c,s), (t,b). Quarks u, c, t have a charge of +2/3, and the charge of quarks d, s, b is -1/3. Each quark has its own antiquark. In addition, each of the quarks can be in one of three color states (red, yellow, and blue). Mesons are made up of two quarks, baryons are made up of three. In the free state quarks not observed. This allows us to consider that the elementary charge in nature is still integer charge e, but not fractional quark charge. The charge of macroscopic bodies is formed by a combination elementary charges and is thus integer multiple of e.

For experiments with electric charges, use various ways receiving them. The simplest and oldest way rubbing one body by another. In this case, friction itself does not play a fundamental role here. Electric charges always arise when the surfaces of contacting bodies are in close contact. Friction (grinding) only helps to eliminate irregularities on the surface of the bodies in contact, which prevent them from tightly adhering to each other, which creates favorable conditions for the transfer of charges from one body to another. This method of obtaining electric charges underlies the operation of some electrical machines, for example, the Van de Graaff electrostatic generator (Van de Graaff R., 1901-1967), used in high energy physics.

Another way to obtain electric charges is based on the use of the phenomenon electrostatic induction . Its essence is illustrated in Fig.1.2. Let's bring it to the divided into two halves uncharged to a metallic body (without touching it) another body, charged, say, positively. Due to the displacement of a certain fraction of the free negatively charged electrons present in the metal, the left half of the original body will acquire an excess negative charge, and the right half will acquire a positive charge of the same magnitude, but opposite in sign. If now, in the presence of an external charged body, we separate both halves in different directions and remove the charged body, then each of them will turn out to be charged. As a result, we will get two new bodies charged with charges equal in magnitude and opposite in sign.

In our particular case, the total charge of the original body before and after the experiment did not change - it remained equal to zero:

q = q - + q + = 0

1.2. Interaction of electric charges.

Coulomb's law. Application of Coulomb's law to calculate the interaction forces of extended charged bodies.

The law of interaction of electric charges was established in 1785 by Charles Coulomb (CoulombSh., 1736-1806). Coulomb measured the force of interaction between two small charged balls, depending on the magnitude of the charges and the distance between them, using a torsion balance specially designed by him (Fig. 1.3). As a result of his experiments, Coulomb found that the force of interaction of two point charges is directly proportional to the magnitude of each of the charges and inversely proportional to the square of the distance between them, while the direction of the force coincides with the straight line passing through both charges:

In other words, we can write:

The coefficient of proportionality k depends on the choice of units of measurement of the quantities included in this formula:

In common now international system units of measurement (SI) Coulomb's law is written, therefore, in the form:

It must be emphasized once again that in this form the Coulomb law is formulated only for point charges, that is, such charged bodies, the dimensions of which can be neglected in comparison with the distance between them. If this condition is not met, then Coulomb's law must be written in differential form for each pair of elementary charges dq1 and dq2 into which the charged bodies "break":

Then the total force of interaction of two macroscopic charged bodies will be represented as:

Integration in this formula is performed over all charges of each body.
Example. Find the force F acting on the point charge Q from the side of an infinitely extended rectilinear charged thread (Fig. 1.4). The distance from the charge to the filament a, the linear charge density of the filament τ.

The required force is F = Fx= Qτ/(2πε0a).

1.3. Electric field. Electric field strength. The principle of superposition of electric fields.
The interaction of electric charges is carried out through a special kind of matter generated by charged particles - an electric field. Electric charges change the properties of the surrounding space. This is manifested in the fact that another charge placed near a charged body (let's call it a test charge) is affected by a force (Fig. 1.5). By the magnitude of this force, one can judge the "intensity" of the field created by the charge q. In order for the force acting on the test charge to characterize the electric field precisely at a given point in space, the test charge must obviously be a point charge.

Fig.1.5. To the determination of the electric field strength.
By placing a test charge qpr at a certain distance r from the charge q (Fig. 1.5), we find that it is affected by a force whose magnitude

depends on the value of the test charge taken qpr. It is easy, however, to see that for all test charges the ratio F/ qpr will be the same and depends only on the quantities q and r that determine the charge field q at a given point r. It is natural, therefore, to take this ratio as a value that characterizes the "intensity" or, as they say, the strength of the electric field (in this case, the field of a point charge):
.
Thus, the strength of the electric field is its power characteristic. Numerically, it is equal to the force acting on the test charge qpr = +1 placed in this field.
The field strength is a vector. Its direction coincides with the direction of the force vector acting on a point charge placed in this field. Therefore, if a point charge q is placed in an electric field with strength, then a force will act on it:

The dimension of the electric field strength in SI: .
The electric field is conveniently depicted using lines of force. A line of force is a line whose tangent vector at each point coincides with the direction of the electric field strength vector at that point. It is generally accepted that lines of force begin on positive charges and end on negative charges (or go to infinity) and are not interrupted anywhere. Examples of lines of force of some electric fields are shown in Fig. 1.6.
Fig.1.6. Examples of the image of electric fields using lines of force: a point charge (positive and negative), a dipole, a uniform electric field.
The electric field obeys the principle of superposition (addition), which can be formulated as follows: the strength of the electric field created at a certain point in space by a system of charges is equal to the vector sum of the strengths of the electric fields created at the same point in space by each of the charges separately:

Example. Find the electric field strength E of a dipole (a system of two rigidly connected point charges opposite sign) at a point located at a distance r1 from the charge - q and at a distance r2 from the charge + q (Fig. 1.7). The distance between charges (dipole arm) is equal to l.

Fig.1.7. On the calculation of the electric field strength of a system of two point charges.

From the history of electrodynamics

Course of General Physics (lectures)

Section II Electrodynamics

Moscow, 2003

Lecture 1 "Fundamentals of electrostatics"

Lecture plan

1. Introduction. The subject of classical electrodynamics.

a. From the history of electrodynamics.

b. Electrodynamics and scientific and technical progress.

2. Electric charges.

a. Properties of electric charges.

b. Coulomb's law.

3. Electric field.

a. Ideas close - and long-range.

b. Electric field strength. The field of a point charge. Graphical representation electric fields.

4. The principle of superposition of electric fields.

a. dipole field.

b. The field of an infinite charged thread.

Introduction. The subject of classical electrodynamics

From the history of electrodynamics

Various electrical and magnetic phenomena, which people have been observing since time immemorial, have always aroused their curiosity and interest. However, "observe" does not mean "explore".

The first scientific steps in the study of electricity and magnetism were made only at the end of the 16th century by the physician of the English Queen Elizabeth William Gilbert (1540 - 1603). In his monograph "On a magnet, magnetic bodies and a large magnet - the Earth", Gilbert first introduced the concept of "the Earth's magnetic field" ... Experimenting with various materials, he discovered that not only amber rubbed on silk has the property to attract light objects, but also many other bodies: diamond, crystal, resin, sulfur, etc. He called these substances "electric", that is, "like amber". This is how the term "electricity" was born.

The first theory electrical phenomena tried to create the French explorer Charles Dufay (1698 - 1739). He established that there are two kinds of electricity: “One kind,” he wrote, “I called “glass” electricity, the other “resin”. The peculiarity of these two kinds of electricity is to repel what is homogeneous with it and attract the opposite ... ”(1733).

The theory of electricity was further developed in the works of the American scientist Benjamin Franklin (1706-1790). He introduced the concept of "positive" and "negative" electricity, established the law of conservation of electric charge, investigated "atmospheric electricity", proposed the idea of ​​a lightning rod. Whole line created by him experimental facilities have become classics and have been decorating physics laboratories for more than 200 years educational institutions(e.g. "Franklin's wheel").

In 1785, the French researcher Charles Coulomb (1736 - 1806) experimentally established the law of interaction of fixed electric charges and later - magnetic poles. Coulomb's law is the foundation of electrostatics. He allowed, finally, to establish a unit of measurement for electric charge and magnetic masses. The discovery of this law stimulated the development mathematical theory electrical and magnetic phenomena.

However, for a long time (since the time of Gilbert) it was believed that electricity and magnetism have nothing in common. Only in 1820, the Dane Hans Oersted (1777 - 1851) discovered the effect of electric current on a magnetic needle, which he explained by the fact that "a magnetic vortex forms around a current-carrying wire." In other words, Oersted established that the electric current is the source of the magnetic field. This provision became the first of the two fundamental laws of electrodynamics. The second was established experimentally by the English physicist Michael Faraday (1791 - 1867). In 1831, he first observed the phenomenon of "magnetoelectric induction", when an inductive electric current appeared in a conducting circuit when magnetic flux penetrating this contour.

At the end of the 19th century, the scattered results of studies of electromagnetic phenomena were summarized by the young Scottish physicist James Clark Maxwell (1831 - 1879). He created classical theory electrodynamics, in which, in particular, he predicted the existence electromagnetic waves, put forward the idea of ​​the electromagnetic nature of light, calculated the volumetric energy density of an electromagnetic wave, calculated the pressure that an electromagnetic wave should produce when it falls on an absorbing surface.

The subject of classical electrodynamics

Classical electrodynamics is a theory that explains the behavior of an electromagnetic field that carries out electromagnetic interaction between electric charges.

The laws of classical macroscopic electrodynamics are formulated in Maxwell's equations, which allow you to determine the values ​​of the characteristics of the electromagnetic field: the electric field strength E and magnetic induction AT in vacuum and in macroscopic bodies, depending on the distribution of electric charges and currents in space.

The interaction of stationary electric charges is described by the equations of electrostatics, which can be obtained as a consequence of Maxwell's equations.

The microscopic electromagnetic field created by individual charged particles in classical electrodynamics is determined by the Lorentz-Maxwell equations, which underlie the classical statistical theory of electromagnetic processes in macroscopic bodies. Averaging these equations leads to Maxwell's equations.

Among all known types of interaction, electromagnetic interaction ranks first in terms of breadth and variety of manifestations. This is due to the fact that all bodies are built of electrically charged (positive and negative) particles, the electromagnetic interaction between which, on the one hand, is many orders of magnitude more intense than the gravitational and weak one, and on the other hand, is long-range, in contrast to the strong interaction.

Electromagnetic interaction determines the structure of atomic shells, the adhesion of atoms into molecules (forces chemical bond) and the formation of condensed matter (interatomic interaction, intermolecular interaction).

The laws of classical electrodynamics are inapplicable at high frequencies and, accordingly, small lengths of electromagnetic waves, i.e. for processes occurring on small space-time intervals. In this case, the laws of quantum electrodynamics are valid.

1.2. Electric charge and its discreteness.
Short range theory

The development of physics has shown that physical and Chemical properties substances are largely determined by the interaction forces due to the presence and interaction of electric charges of molecules and atoms of various substances.

It is known that in nature there are two types of electric charges: positive and negative. They may exist in the form elementary particles: electrons, protons, positrons, positive and negative ions, etc., as well as "free electricity", but only in the form of electrons. Therefore, a positively charged body is a collection of electric charges with a lack of electrons, and a negatively charged body - with their excess. Charges of different signs compensate each other, therefore, in uncharged bodies there are always charges of both signs in such quantities that their total effect is compensated.

redistribution process positive and negative charges uncharged bodies, or among separate parts of the same body, under the influence various factors called electrization.

Since electrification is a redistribution free electrons, then, for example, both interacting bodies are electrified, and one of them is positive, and the other is negative. The number of charges (positive and negative) remains unchanged.

This implies the conclusion that charges are not created and do not disappear, but are only redistributed between interacting bodies and parts of the same body, in quantitatively remaining unchanged.

This is the meaning of the law of conservation of electric charges, which can be written mathematically as follows:

those. in an isolated system algebraic sum electric charges remains constant.

An isolated system is understood as a system through which no other substance penetrates, with the exception of photons of light, neutrons, since they do not carry a charge.

It must be borne in mind that the total electric charge of an isolated system is relativistically invariant, since observers located in any given inertial system coordinates, measuring the charge, get the same value.

A number of experiments, in particular the laws of electrolysis, Millikan's experiment with a drop of oil, have shown that in nature electric charges are discrete to the charge of an electron. Any charge is a multiple of an integer number of the electron charge.

In the process of electrification, the charge changes discretely (quantized) by the value of the electron charge. Charge quantization is a universal law of nature.

In electrostatics, the properties and interactions of charges that are immobile in the frame of reference in which they are located are studied.

The presence of an electric charge in bodies causes them to interact with other charged bodies. At the same time, bodies charged with the same name repel each other, and charged oppositely, they attract.

The theory of short-range interaction is one of the theories of interaction in physics. In physics, interaction is understood as any influence of bodies or particles on each other, leading to a change in the state of their motion.

In Newtonian mechanics, the mutual action of bodies on each other is quantitatively characterized by force. More common characteristic interaction is potential energy.

Initially, in physics, the idea was established that the interaction between bodies can be carried out directly through empty space, which does not take part in the transfer of interaction. The transfer of interaction occurs instantly. Thus, it was believed that the movement of the Earth should immediately lead to a change in the gravitational force acting on the Moon. This was the meaning of the so-called theory of interaction, called the theory of long-range action. However, these ideas were abandoned as untrue after the discovery and study of the electromagnetic field.

It was proved that the interaction of electrically charged bodies is not instantaneous and the movement of one charged particle leads to a change in the forces acting on other particles, not at the same moment, but only after a finite time.

Each electrically charged particle creates an electromagnetic field that acts on other particles, i.e. interaction is transmitted through an "intermediary" - an electromagnetic field. The speed of propagation of an electromagnetic field is equal to the speed of propagation of light in a vacuum. arose new theory interaction theory of short-range interaction.

According to this theory, the interaction between bodies is carried out through certain fields (for example, gravitation through a gravitational field), continuously distributed in space.

After the advent of quantum field theory, the concept of interactions has changed significantly.

According to quantum theory, any field is not continuous, but has a discrete structure.

Owing to corpuscular-wave dualism, certain particles correspond to each field. Charged particles continuously emit and absorb photons, which form the electromagnetic field surrounding them. The electromagnetic interaction in quantum field theory is the result of the exchange of particles by photons (quanta) of the electromagnetic field, i.e. photons are carriers of such interaction. Similarly, other types of interactions arise as a result of the exchange of particles by quanta of the corresponding fields.

Despite the variety of influences of bodies on each other (depending on the interaction of their constituent elementary particles), in nature, according to modern data, there are only four types of fundamental interactions: gravitational, weak, electromagnetic and strong (in order of increasing interaction intensity). The intensities of interactions are determined by the coupling constants (in particular, the electric charge for the electromagnetic interaction is the coupling constant).

Modern quantum theory electromagnetic interaction perfectly describes all known electromagnetic phenomena.

In the 60s - 70s of the century, it was mainly built unified theory weak and electromagnetic interactions (the so-called electroweak interaction) of leptons and quarks.

Modern theory strong interaction is quantum chromodynamics.

Attempts are being made to combine the electroweak and strong interactions into the so-called "Great Unification", as well as to include them in single scheme gravitational interaction.

Lecture notes

Approved by the Editorial and Publishing Council of the University as lecture notes

Reviewers:

Doctor of Physical and Mathematical Sciences, Head. Department of T and EF KSTU, professor A.A. Rodionov

Candidate of Physical and Mathematical Sciences, Head. department
General Physics KSU Yu.A. Neruchev

Candidate technical sciences, head Department of Physics, KSHA
DI. Yakirevich

Polunin V.M., Sychev G.T.

Physics. Electrostatics. Constant electric current: Lecture notes / Kursk. state tech. un-t. Kursk, 2003. 196 p.

The lecture notes are compiled in accordance with the requirements of the State Educational Standard-2000, Sample program disciplines "Physics" (2000) and work program in physics for students of engineering and technical specialties of KSTU (2000).

The presentation of the material in this paper provides for students' knowledge of physics and mathematics in the scope of the school curriculum, great attention It is given to difficult-to-understand questions, which makes it easier for students to prepare for the exam.

The abstract of lectures on electrostatics and direct electric current is intended for students of engineering and technical specialties of all forms of education.

Il. 96. Bibliography: 11 titles.

Ó Kursk State
Technical University, 2003

Ó Polunin V.M., Sychev G.T., 2003

Introduction.. 7

Lecture 1. Electrostatics in vacuum and matter. Electric field 12

1.1. The subject of classical electrodynamics.. 12

1.2. Electric charge and its discreteness. The theory of close action. thirteen

1.3. Coulomb's law. Electric field strength. The principle of superposition of electric fields.. 16

1.4. Electrostatic field strength vector flux. 22

1.5. The Ostrogradsky-Gauss theorem for an electric field in vacuum. 24

1.6. The work of an electric field on the movement of an electric charge. Circulation of the electric field strength vector. 25

1.7. The energy of an electric charge in an electric field. 26

1.8. Potential and potential difference of the electric field. Connection of electric field strength with its potential.. 28

1.9. Equipotential surfaces.. 30

1.10. Basic equations of electrostatics in vacuum. 32

1.11. Some examples of electric fields generated by the simplest systems of electric charges. 33

Lecture 2. Conductors in an electric field .. 42

2.1. Conductors and their classification. 42

2.2. Electrostatic field in the cavity of an ideal conductor and near its surface. Electrostatic protection. Distribution of charges in the volume of the conductor and over its surface.. 43

2.3. The capacitance of a solitary conductor and its physical meaning. 46

2.4. Capacitors and their capacitance. 47

2.5. Capacitor connections. 51

2.6. Classification of capacitors. 54

Lecture 3. Static electric field in matter.. 55

3.1. Dielectrics. Polar and non-polar molecules. Dipole in homogeneous and inhomogeneous electric fields. 55

3.2. Free and bound (polarization) charges in dielectrics. Polarization of dielectrics. Polarization vector (polarization) 58

3.3. Field in dielectrics. electrical displacement. Dielectric susceptibility of matter. Relative the dielectric constant environment. The Ostrogradsky-Gauss theorem for the flow of the electric field induction vector. 61

3.4. Conditions at the interface between two dielectrics. 63

3.5. Electrostriction. Piezoelectric effect. Ferroelectrics, their properties and applications. electrocaloric effect. 65

3.6. Basic equations of electrostatics of dielectrics. 72

Lecture 4. Electric field energy.. 75

4.1. Energy of interaction of electric charges. 75

4.2. The energy of charged conductors, a dipole in an external electric field, dielectric body in an external electric field, a charged capacitor. 77

4.3. Electric field energy. Bulk density electric field energy 81

4.4. Forces acting on macroscopic charged bodies placed in an electric field. 82

Lecture 5. Direct electric current .. 84

5.1. Constant electric current. Basic actions and conditions of existence direct current. 84

5.2. The main characteristics of direct electric current: the value /strength/ current, current density. Third party forces.. 85

5.3. Electromotive force(EMF), voltage and potential difference. their physical meaning. Relationship between EMF, voltage and potential difference. 90

Lecture 6. Classical electronic theory of conductivity of metals. Direct current laws.. 92

6.1. Classical electronic theory of electrical conductivity of metals and its experimental substantiations. Ohm's law in differential
and integrated forms. 92

6.2. Electrical resistance conductors. Change of resistance of conductors from temperature and pressure. Superconductivity. 98

6.3. Resistance connections: series, parallel, mixed. Shunting of electrical measuring instruments. Additional resistances to electrical measuring instruments.. 104

6.4. Rules (laws) of Kirchhoff and their application to the calculation of the simplest electrical circuits 108

6.5. Joule-Lenz law in differential and integral forms. 110

6.6. Energy released in a DC circuit. Coefficient useful action(efficiency) of a direct current source. 112

Lecture 7. Electric current in vacuum, gases and liquids .. 115

7.1. Electric current in vacuum. Thermionic emission. 115

7.2. Secondary and field emission. 122

7.3. Electric current in gas. Ionization and recombination processes.. 124

7.4. The concept of plasma. Plasma frequency. Debye length. Plasma electrical conductivity 142

7.5. electrolytes. Electrolysis. Laws of electrolysis. 149

7.6. Electrochemical potentials.. 151

7.7. Electric current through electrolytes. Ohm's law for electrolytes. 152

Lecture 8. Electrons in crystals.. 161

8.1. Quantum theory of electrical conductivity of metals. Fermi level. Elements of the band theory of crystals. 161

8.2. The phenomenon of superconductivity from the point of view of the Fermi-Dirac theory. 170

8.3. Electrical conductivity of semiconductors. The concept of hole conductivity. Intrinsic and extrinsic semiconductors. The concept of p-n - transition. 171

8.4. Electromagnetic Phenomena at the interface between 178

conclusion.. 193

REFERENCES.. 195

This manual is compiled on the basis of materials developed by the authors in the process of lecturing on general physics students of engineering and technical specialties, with a relatively small volume of classroom studies, over a long period of time.

The presence of this lecture notes for students of engineering and technical specialties will allow them and the lecturer to use lecture time more efficiently, pay more attention to difficult-to-understand questions, and make it easier for students to prepare for the exam.

Particularly in need of such a benefit, in our opinion, students of correspondence, accelerated and remote forms students who, starting to study physics, have insufficient skills of adequate perception physical concepts, definitions and laws.

The presentation of the material in this work provides for students' knowledge of physics and mathematics in the scope of the school curriculum, therefore, many concepts are not disclosed in detail, but are used as well-known ones. In addition, this paper assumes that students have already studied or are studying in parallel course the corresponding mathematical apparatus (differential and integral calculus, function analysis, differential equations, vector algebra, rows).

A feature of the manual is that the material is presented in it in a certain, non-traditional sequence, contains the necessary drawings and explanations.

Despite the small volume, the proposed manual contains a statement of issues, the knowledge of which is necessary for the study of disciplines, the foundation of which are the laws and basic provisions of physics.

The reduction in volume was achieved mainly by refusing to consider certain non-principled issues, as well as by submitting some questions for their study in the process of practical and laboratory classes.

Such issues as the band theory of metals and semiconductors, current in vacuum, gases and electrolytes are presented in sufficient detail.

The presentation of the material, with rare exceptions due to methodological considerations, is based on an experiment. Fundamental experiments that served as the basis modern teaching about electromagnetism, are described in sufficient detail.

In addition, some attention is paid to explaining the principles of measuring the main electrical quantities, which, if possible, immediately follows the introduction of the relevant physical concepts. However, the description of various experiments does not claim to be complete and, moreover, only concerns the principles of these experiments, since students listen to a lecture course with demonstrations and work in physical laboratories. For the same reason, most of the drawings are made in the form simple circuits and reflects only qualitative this case dependencies without indicating the units of measurement and numerical values ​​of the quantities under consideration, which contributes to a better perception of the material being studied by students.

Since at present there are problem books corresponding to the university course of physics, the inclusion of specific tasks and exercises for the section under study is not provided. Therefore, only a relatively few examples are given in the lecture notes to illustrate the application of the most important laws.

The presentation is carried out in the International System of Units (SI). Unit designations physical quantities are given in terms of the basic and derived units of the system, in accordance with their definitions in the SI system.

The manual can be used by graduate students and teachers who have insufficient experience in the university.

The authors will be grateful to all who carefully review this manual and make certain comments on the merits. In addition, they will try to take into account all rational comments from fellow physicists, graduate students, and students and make appropriate corrections and additions.

Introduction

This lecture notes are dedicated to one of the sections general course physics, the section "Electricity", which is read to students of those specialties and forms of education, in curricula for which this course is provided.

It focuses on the fact that electrical energy plays a big role in technology for the following reasons:

1. The extreme ease with which electricity is converted into other types of energy: mechanical, thermal, light and chemical.

2. Ability to transmit electricity over long distances.

3. High efficiency of electric machines and electric devices.

4. Extremely high sensitivity electrical measuring and recording instruments and development electrical methods measurements of various non-electric quantities.

5. Exceptional opportunities provided by electrical appliances and devices for automation, telemechanics and production control.

6. Development of electrical, electrothermal, electrochemical, electromechanical and electromagnetic methods of material processing.

The doctrine of electricity has its own history, organically linked with the history of the development of the productive forces of society and other areas of natural science. In the history of the doctrine of electricity, three stages can be distinguished:

1. The period of accumulation of experimental facts and the establishment of basic concepts and laws.

2. The period of formation of the doctrine of the electromagnetic field.

3. The period of formation of the atomistic theory of electricity.

The origins of ideas about electricity go to Ancient Greece. The attraction of light bodies by rubbed amber and other objects has been known to people for a long time. However, the electrical forces were completely unclear, the possibility of their practical application was not felt, so there was no incentive for systematic research in this area.

Only the discoveries of the first half of the XYIII century. force a sharp change in attitude towards electrical phenomena. Undoubtedly, this was facilitated by the invention of the electric machine (second half of the 17th century), on the basis of which the possibilities of experimentation were significantly expanded.

By the middle of the XIII century. interest in electricity is growing, natural scientists from many countries are included in the research. Observation of strong electric discharges could not but lead to an analogy between an electric spark and lightning. The electrical nature of lightning was proved by the direct experiments of W. Franklin, M.V. Lomonosov, G.V. Richman (1752 - 1753). The invention of the lightning rod was the first practical application of the doctrine of electricity. This contributed to the development general interest to electricity, attracting new researchers to this area.

The English naturalist R. Simmer (1759) put forward a fruitful hypothesis about the nature of electricity. Developing the ideas of Du Fay, Simmer concluded that the bodies in normal states contain two kinds of electricity in equal amounts, neutralizing each other's action. Electrification causes an excess in the body of one electricity over another. An excellent confirmation of this hypothesis was the discovery of electrostatic induction by the Russian academician F. Epinus (1759).

The law of conservation of energy and matter established by Lomonosov was greatest achievement in physics of the 18th century. The content of the conservation law discovered by Lomonosov was gradually revealed and played a great role in the development of the theory of electricity. Thus, the later discovered law of conservation of electric charges is a particular manifestation of the universal law of conservation of matter and motion.

Until the middle of the XIII century. electrical experiments continued to be purely qualitative. The first step towards a quantitative experiment was taken by Richmann, who proposed the first instrument for measurements, called the electrometer (1745). The most important stage in development experimental technique was the invention in 1784 by Sh. Coulomb of very sensitive torsion balances, which played important role in the study of forces different nature. This device allowed Coulomb to establish the law of interaction between magnets and electric charges (1785). Coulomb's laws served as the basis for the development of the mathematical theory of electrostatics and magnetostatics.

Further, thanks to the experiments of L. Galvani (1789) and A. Volta (1792), contact electrical phenomena were discovered, which, in turn, led to the invention galvanic cells and to the detection of electric current (1800).

English researchers A. Carlyle and W. Nicholson discovered that the galvanic current, passing through water, decomposes it into hydrogen and oxygen. A mutually enriching relationship has been established between physics and chemistry. Electricity is on the rise practical value which stimulates further development this branch of science.

Improving the design of the voltaic column leads to the discovery of new actions of electric current. In 1802 V.V. Petrov, with the help of a powerful voltaic column, receives an electric arc. The Petrov arc gave rise to a number of new applications of the thermal effects of current.

With the discovery of the action of current on a magnetic needle, H. Oersted (1820) laid the foundation for a new chapter in the theory of electricity - the doctrine of magnetic properties current, which made it possible to include magnetism in a unified theory of electromagnetic phenomena.

The study of electric current continued to progress at an increasing pace. It was found that magnetic action current is amplified if the conductor is coiled into a spiral. This opened up the possibility of designing electromagnetic current meters.

In 1820, A. Ampère established a law by which the force of interaction of two elementary currents was determined. Based on this experimental fact, A. Ampère makes an assumption about the electrical nature of magnetism. He suggests that " electric currents… exist around particles in iron, nickel and cobalt already before magnetization. Being, however, directed in all possible directions, they cannot cause any resulting external action, since some of them tend to attract what others repel ... ". This is how the hypothesis of molecular currents appeared in physics, the depth of which was revealed only in the 20th century.

AT further research on electricity, the law established in 1827 by the German physicist G. Ohm and called Ohm's law became an effective tool.

During this period began scientific activity M. Faraday. Especially great importance in the history of physics have two discoveries of Faraday: the phenomenon electromagnetic induction(1831) and the laws of electrolysis (1834). Faraday gave these discoveries theoretical basis many technical applications of electricity. E.Kh. Lenz on electromagnetic induction (Lenz's rule) and the establishment of a law for the thermal action of current (the Joule-Lenz law) contributed to further practical application electricity.

It was experimentally established that electric forces act through a medium that fills the space between interacting bodies. Exploring the interaction of charged bodies, Faraday introduced the concept of electrical forces new lines and gave the idea of ​​magnetic and electric fields - spaces where the action of electric forces is detected. Faraday believed that electric and magnetic fields represent deformed states of some all-penetrating weightless medium - the ether.

According to Faraday, it is not the electric charge that acts on the surrounding bodies, but the lines of force associated with the charge. By this Faraday put forward the idea of ​​the theory of short-range action, according to which the action of some bodies on others is transmitted through environment at a certain speed.

In the 60s years XIX century D. Maxwell generalized Faraday's theory of electrical and magnetic fields and created a unified theory of the electromagnetic field. The main content of this theory lies in Maxwell's equations, which play the same role in electromagnetism as Newton's laws in mechanics.

It should be noted the great importance of the work of a number of Russian physicists late XIX in. on experimental confirmation Maxwell's theories. Among such studies, the experiments of P.N. Lebedev on the detection and measurement of light pressure (1901).

Until the end of the 19th century. electricity was represented as a weightless liquid. The question of whether electricity is discrete or continuous required the analysis of experimental material and the setting up of new experiments. The idea of ​​discreteness of electricity can be seen in the laws of electrolysis discovered by Faraday. Based on these laws, the German physicist G. Helmholtz (1881) suggested the existence of the smallest portions of the electric charge. Since that time, the development of the electronic theory began, which explained such phenomena as thermionic emission, the appearance of cathode rays. The merit of creating the electronic theory belongs mainly to the Dutch physicist G.A. Lorentz, who in his work "Theory of Electrons" (1909) organically connected Maxwell's theory of the electromagnetic field with the electrical properties of matter, considered as a set of elementary electric charges.

Based on electronic representations in the first quarter of the 20th century. developed the theory of dielectrics and magnets. The theory of semiconductors is currently being developed. The study of electrical phenomena led to the modern theory of the structure of matter. The successes of physics in this direction culminated in the discovery of ways to release nuclear energy, which qualitatively raised the science and technology of mankind to a new stage of development.

It should be especially noted that in many technical applications of electricity, in the theory of electricity and magnetism, the primacy belongs to Russian scientists and technicians. So, for example, Russian scientists and engineers invented and used for practice electroplating and electroplating, electric welding, electric lighting, electric motors, and radio. They developed many questions that are not only of great theoretical interest, but also of great practical importance. This includes the physics of dielectrics, semiconductors, magnets, gas discharge physics, thermionic emission, photoelectric effect, electromagnetic oscillations and radio waves, etc. recent times problems of direct transformation are developed solar energy into electrical energy, the creation of magnetohydrodynamic sources of electricity, " fuel cells". Russian scientists play a leading role in research aimed at solving the most important scientific and technical problem of our time - the problem of creating controlled thermonuclear reactions by using magnetic and electromagnetic fields for thermal insulation and heating of a highly ionized gas - plasma.

For a great contribution to the development of world science, Russian scientists - physicists I.E. Tammu, I.M. Frank and P.A. Cherenkov (1958), L.D. Landau (1962), N.G. Basov and A.M. Prokhorov (1964), P.L. Kapitsa (1978), Zh.I. Alferov (2000), V.L. Ginzburg and A.A. Abrikosov (2003) was awarded the Nobili Prizes.

Lecture 1. Electrostatics in vacuum
and substance. Electric field

The subject of classical electrodynamics. Electric charge and its discreteness. The theory of close action. Coulomb's law. Electric field strength. The principle of superposition of electric fields. The electric field of the dipole. Electrostatic field strength vector flux. The Ostrogradsky-Gauss theorem for an electric field in vacuum. The work of an electric field on the movement of an electric charge. Circulation of the electric field strength vector. The energy of an electric charge in an electric field. Potential and potential difference of the electric field. Electric field strength as a gradient of its potential. equipotential surfaces. Basic equations of electrostatics in vacuum. Some examples of electric fields generated by the simplest systems of electric charges.

The subject of classical electrodynamics

Classical electrodynamics is a theory that explains the behavior of an electromagnetic field that carries out electromagnetic interaction between electric charges.

The laws of classical macroscopic electrodynamics are formulated in Maxwell's equations, which make it possible to determine the values ​​of the characteristics of the electromagnetic field - the strength of the electric field E and magnetic induction AT- in vacuum and in macroscopic bodies, depending on the distribution of electric charges and currents in space.

The interaction of stationary electric charges is described by the equations of electrostatics, which can be obtained as a consequence of Maxwell's equations.

The microscopic electromagnetic field created by individual charged particles in classical electrodynamics is determined by the Lorentz-Maxwell equations, which underlie the classical statistical theory of electromagnetic processes in macroscopic bodies. Averaging these equations leads to Maxwell's equations.

Among all known types of interaction, electromagnetic interaction ranks first in terms of breadth and variety of manifestations. This is due to the fact that all bodies are built of electrically charged (positive and negative) particles, the electromagnetic interaction between which, on the one hand, is many orders of magnitude more intense than the gravitational and weak one, and on the other hand, is long-range, in contrast to the strong interaction.

Electromagnetic interaction determines the structure of atomic shells, the adhesion of atoms into molecules (chemical bond forces) and the formation of condensed matter (interatomic interaction, intermolecular interaction).

The laws of classical electrodynamics are inapplicable at high frequencies and, accordingly, small lengths of electromagnetic waves, i.e. for processes occurring on small space-time intervals. In this case, the laws of quantum electrodynamics are valid.

1.2. Electric charge and its discreteness.
Short range theory

The development of physics has shown that the physical and chemical properties of a substance are largely determined by the forces of interaction due to the presence and interaction of electric charges of molecules and atoms of various substances.

It is known that in nature there are two types of electric charges: positive and negative. They can exist in the form of elementary particles: electrons, protons, positrons, positive and negative ions, etc., as well as "free electricity", but only in the form of electrons. Therefore, a positively charged body is a collection of electric charges with a lack of electrons, and a negatively charged body - with their excess. Charges of different signs compensate each other, therefore, in uncharged bodies there are always charges of both signs in such quantities that their total effect is compensated.

redistribution process positive and negative charges of uncharged bodies, or among separate parts of the same body, under the influence of various factors is called electrization.

Since the redistribution of free electrons occurs during electrification, for example, both interacting bodies are electrified, one of them being positive and the other negative. The number of charges (positive and negative) remains unchanged.

This implies the conclusion that charges are not created and do not disappear, but only redistributed between interacting bodies and parts of the same body, quantitatively remaining unchanged.

This is the meaning of the law of conservation of electric charges, which can be written mathematically as follows:

those. in an electrically isolated system, the algebraic sum of electric charges remains constant.

An electrically isolated system is a system through which no other electric charges can penetrate.

It must be borne in mind that the total electric charge of an isolated system is relativistically invariant, since observers located in any given inertial coordinate system, measuring the charge, receive the same value.

A number of experiments, in particular the laws of electrolysis, Millikan's experiment with a drop of oil, have shown that in nature electric charges are discrete to the charge of an electron. Any charge is a multiple of an integer number of the electron charge.

In the process of electrification, the charge changes discretely (quantized) by the value of the electron charge. Charge quantization is a universal law of nature.

In electrostatics, the properties and interactions of charges that are immobile in the frame of reference in which they are located are studied.

The presence of an electric charge in bodies causes them to interact with other charged bodies. At the same time, bodies charged with the same name repel each other, and charged oppositely, they attract.

Interaction in physics is understood as any influence of bodies or particles on each other, leading to a change in the state of their movement or to a change in their position in space. Exist different kinds interactions.

In Newtonian mechanics, the mutual action of bodies on each other is quantitatively characterized by force. A more general characteristic of interaction is potential energy.

Initially, in physics, the idea was established that the interaction between bodies can be carried out directly through empty space, which does not take part in the transfer of interaction. The transfer of interaction occurs instantly. Thus, it was believed that the movement of the Earth should immediately lead to a change in the gravitational force acting on the Moon. This was the meaning of the so-called theory of interaction, called the theory of long-range action. However, these ideas were abandoned as untrue after the discovery and study of the electromagnetic field.

It was proved that the interaction of electrically charged bodies is not instantaneous and the movement of one charged particle leads to a change in the forces acting on other particles, not at the same moment, but only after a finite time.

Each electrically charged particle creates an electromagnetic field that acts on other particles, i.e. interaction is transmitted through an "intermediary" - an electromagnetic field. The speed of propagation of an electromagnetic field is equal to the speed of propagation of light in a vacuum. A new theory of interaction arose - the theory of short-range interaction.

According to this theory, the interaction between bodies is carried out through certain fields (for example, gravitation through a gravitational field), continuously distributed in space.

After the advent of quantum field theory, the concept of interactions has changed significantly.

According to quantum theory, any field is not continuous, but has a discrete structure.

Owing to corpuscular-wave dualism, certain particles correspond to each field. Charged particles continuously emit and absorb photons, which form the electromagnetic field surrounding them. The electromagnetic interaction in quantum field theory is the result of the exchange of particles by photons (quanta) of the electromagnetic field, i.e. photons are carriers of such interaction. Similarly, other types of interactions arise as a result of the exchange of particles by quanta of the corresponding fields.

Despite the variety of influences of bodies on each other (depending on the interaction of their constituent elementary particles), in nature, according to modern data, there are only four types of fundamental interactions: gravitational, weak, electromagnetic and strong (in order of increasing interaction intensity). The intensities of interactions are determined by the coupling constants (in particular, the electric charge for the electromagnetic interaction is the coupling constant).

The modern quantum theory of electromagnetic interaction perfectly describes all known electromagnetic phenomena.

In the 60-70s of the century, a unified theory of weak and electromagnetic interactions (the so-called electroweak interaction) of leptons and quarks was basically built.

The modern theory of the strong interaction is quantum chromodynamics.

Attempts are being made to combine the electroweak and strong interactions into the so-called "Great Unification", as well as to include them in a single scheme of gravitational interaction.