§ 1. Coulomb's law
§ 2. Electric field strength
§ 3. Gauss's theorem
§ 4. Differential form of Gauss's theorem
§ 5. The second equation of electrostatics and scalar potential
§ 6. Surface distributions of charges and dipoles. Electric field and potential jumps
§ 7. Laplace and Poisson equations
§ 8. Green's theorem
§ 9. Uniqueness of the solution under Dirichlet or Neumann boundary conditions
§ 10. Formal solution of boundary value problems of electrostatics using the Green's function
§ 11. Potential energy and energy density of the electrostatic field
Recommended reading
Tasks
§ 1. Method of images
§ 2. Point charge near a grounded spherical conductor
§ 3. Point charge near a charged insulated spherical conductor
§ 4. Point charge near a spherical conductor with a given potential
§ 5. Spherical conductor in a uniform electric field
§ 6. Inversion method
§ 7. Green's function for a sphere. General expression for potential
§ 8. Two adjacent conducting hemispheres having different potentials
§ 9. Expansion in orthogonal functions
§ 10. Separation of variables. Laplace's equation in Cartesian coordinates
Recommended reading
Tasks
§ 1. Laplace's equation in spherical coordinates
§ 2. Legendre's equation and Legendre's polynomials
§ 3. Boundary value problems with azimuthal symmetry
§ 4. Associated Legendre functions and spherical harmonics
§ 5. Addition theorem for spherical harmonics
§ 6. Laplace's equation in cylindrical coordinates. Bessel functions
§ 7. Boundary value problems in cylindrical coordinates
§ 8. Expansion of Green's functions in spherical coordinates
§ 9. Finding the potential using expansions for spherical Green's functions
§ 10. Expansion of Green's functions in cylindrical coordinates
§ 11. Expansion of Green's functions in terms of eigenfunctions
§ 12. Mixed boundary conditions. Charged conductive disk
Recommended reading
Tasks
§ 1. Multipole expansion
§ 2. Expansion into energy multipoles of charge distribution in an external field
§ 3. Macroscopic electrostatics. Effects of the combined action of atoms
§ 4. Isotropic dielectrics and boundary conditions
§ 5. Boundary value problems in the presence of dielectrics
§ 6. Polarizability of molecules and dielectric susceptibility
§ 7. Models of molecular polarizability
§ 8. Electric field energy in a dielectric
Recommended reading
Tasks
§ 1. Introduction and basic definitions
§ 2. Law of Biot and Savart
§ 3. Differential equations of magnetostatics and Ampere’s law
§ 4. Vector potential
§ 5. Vector potential and magnetic induction of a circular current loop
§ 6. Magnetic field of limited current distribution. Magnetic moment
§ 7. Force and torque acting on a limited current distribution in an external magnetic field
§ 8. Macroscopic equations
§ 9. Boundary conditions for magnetic induction and field
§ 10. Uniformly magnetized ball
§ 11. Magnetized ball in an external field. Permanent magnets
§ 12. Magnetic shielding. Spherical shell of magnetic material in a uniform field
Recommended reading
Tasks
§ 1. Faraday's law of induction
§ 2. Magnetic field energy
§ 3. Maxwellian displacement current. Maxwell's equations
§ 4. Vector and scalar potentials
§ 5. Gauge transformations. Lorentz gauge. Coulomb gauge
§ 6. Green's function for the wave equation
§ 7. Problem with initial conditions. Kirchhoff integral representation
§ 8. Poynting's theorem
§ 9. Conservation laws for a system of charged particles and electromagnetic fields
§ 10. Macroscopic equations
Recommended reading
Tasks
§ 1. Plane waves in a non-conducting medium
§ 2. Linear and circular polarization
§ 3. Superposition of waves in one dimension. Group speed
§ 4. Examples of pulse propagation in a dispersive medium
§ 5. Reflection and refraction of electromagnetic waves at a flat interface between dielectrics
§ 6. Polarization during reflection and total internal reflection
§ 7. Waves in a conducting medium
§ 8. Simple model of conductivity
§ 9. Transverse waves in rarefied plasma
Recommended reading
Tasks
§ 1. Fields on the surface and inside a conductor
§ 2. Cylindrical resonators and waveguides
§ 3. Waveguides
§ 4. Waves in a rectangular waveguide
§ 5. Energy flow and attenuation in waveguides
§ 6. Resonators
§ 7. Power losses in the resonator. Resonator quality factor
§ 8. Dielectric waveguides
Recommended reading
Tasks
§ 1. Fields created by limited oscillating sources
§ 2. Electric dipole field and radiation
§ 3. Magnetic dipole and electric quadrupole fields
§ 4. Linear antenna with central excitation
§ 5. Kirchhoff integral
§ 6. Vector equivalents of the Kirchhoff integral
§ 7. Babinet's principle for additional screens
§ 8. Diffraction by a round hole
§ 9. Diffraction by small holes
§ 10. Scattering of short waves by a conducting sphere
Recommended reading
Tasks
§ 1. Introduction and basic concepts
§ 2. Equations of magnetohydrodynamics
§ 3. Magnetic diffusion, viscosity and pressure
§ 4. Magnetohydrodynamic flow between boundaries in crossed electric and magnetic fields
§ 5. Pinch effect
§ 6. Dynamic model of the pinch effect
§ 7. Instabilities of a compressed plasma column
§ 8. Magnetohydrodynamic waves
§ 9. High-frequency plasma oscillations
§ 10. Short-wave plasma oscillations. Debye screening radius
Recommended reading
Tasks
§ 1. Historical background and main experiments
§ 2. Postulates of the special theory of relativity and the Lorentz transformation
§ 3. Fitzgerald-Lorentz contraction and time dilation
§ 4. Addition of velocities. Aberration and Fizeau's experience. Doppler shift
§ 5. Thomas Precession
§ 6. Proper time and the light cone
§ 7. Lorentz transformations as orthogonal transformations in four-dimensional space
§ 8. Four vectors and four tensors. Covariance of physics equations
§ 9. Covariance of electrodynamic equations
§ 10. Transformation of the electromagnetic field
§ 11. Covariance of the expression for the Lorentz force and conservation laws
Recommended reading
Tasks
§ 1. Momentum and energy of a particle
§ 2. Kinematics of fragments during the decay of an unstable particle
§ 3. Conversion to the center of mass system and reaction thresholds
§ 4. Conversion of momentum and energy from the center of mass system to the laboratory system
§ 5. Covariant equations of motion. Lagrangian and Hamiltonian for a relativistic charged particle
§ 6. First-order relativistic corrections for the Lagrangians of interacting charged particles
§ 7. Motion in a uniform static magnetic field
§ 8. Motion in uniform static electric and magnetic fields
§ 9. Particle drift in a non-uniform static magnetic field
§ 10. Adiabatic invariance of magnetic flux through the orbit of a particle
Recommended reading
Tasks
§ 1. Energy transfer during Coulomb collisions
§ 2. Transfer of energy to a harmonic oscillator
§ 3. Classical and quantum mechanical expression for energy losses
§ 4. Influence of density on energy loss during collision
§ 5. Energy losses in electron plasma
§ 6. Elastic scattering of fast particles by atoms
§ 7. Root mean square value of the scattering angle and angular distribution for multiple scattering
§ 8. Electrical conductivity of plasma
Recommended reading
Tasks
§ 1. Lienard-Wiechert potentials and the field of a point charge
§ 2. Total power emitted by an accelerated moving charge. Larmore's formula and its relativistic generalization
§ 3. Angular distribution of radiation from an accelerated charge
§ 4. Charge emission during arbitrary ultrarelativistic motion
§ 5. Spectral and angular distributions of energy emitted by accelerated charges
§ 6. Radiation spectrum of a relativistic charged particle during instantaneous motion in a circle
§ 7. Scattering by free charges. Thomson's formula
§ 8. Coherent and incoherent scattering
§ 9. Vavilov-Cherenkov radiation
Recommended reading
Tasks
§ 1. Radiation during collisions
§ 2. Bremsstrahlung during nonrelativistic Coulomb collisions
§ 3. Bremsstrahlung during relativistic motion
§ 4. Effect of shielding. Radiation losses in the relativistic case
§ 5. Weizsäcker-Williams virtual photon method
§ 6. Bremsstrahlung as scattering of virtual photons
§ 7. Radiation from beta decay
§ 8. Radiation during the capture of orbital electrons. Disappearance of charge and magnetic moment
Recommended reading
Tasks
§ 1. Eigenfunctions of the scalar wave equation
§ 2. Expansion of electromagnetic fields into multipoles
§ 3. Properties of multipole fields. Energy and angular momentum of multipole radiation
§ 4. Angular distribution of multipole radiation
§ 5. Sources of multipole radiation. Multipole moments
§ 6. Multipole radiation of atomic and nuclear systems
§ 7. Radiation of a linear antenna with central excitation
§ 8. Expansion of a vector plane wave in spherical waves
§ 9. Scattering of electromagnetic waves on a conducting sphere
§ 10. Solving boundary value problems using multipole expansions
Recommended reading
Tasks
§ 1. Introductory remarks
§ 2. Determination of the radiation reaction force from the law of conservation of energy
§ 3. Calculation of the radiation reaction force according to Abraham and Lorentz
§ 4. Difficulties of the Abraham-Lorentz model
§ 5. Transformation properties of the Abraham-Lorentz model. Poincaré tensions
§ 6. Covariant determination of the intrinsic electromagnetic energy and momentum of a charged particle
§ 7. Integro-differential equation of motion taking into account radiative attenuation
§ 8. Line width and level shift for the oscillator
§ 9. Scattering and absorption of radiation by an oscillator
Recommended reading
Tasks
§ 1. Units of measurement and dimensions. Basic and derived units
§ 2. Units of measurement and equations of electrodynamics
§ 3. Various systems of electromagnetic units
§ 4. Translation of formulas and numerical values of quantities from the Gaussian system of units to the MKS system
MINISTRY OF EDUCATION AND SCIENCE OF RUSSIA FEDERAL STATE BUDGET
EDUCATIONAL INSTITUTION OF HIGHER
PROFESSIONAL EDUCATION
"Don State Technical University"
(DSTU)
Test
by discipline "Concepts of modern natural science"
Topic No. 1.25 Formation and development of classical electrodynamics
(M. Faraday, D. Maxwell, G. Hertz).
Electrodynamic picture of the world.
Performed: Onuchina A.A.
student 1 course direction of preparation distance learning
group IZES11 Grade book no. 1573242
Checked ________________
Rostov-on-Don
Plan:
1. History of electrodynamics……………………………………………………..3
2. Formation and development of classical electrodynamics.…………….…… 5
3. Electrodynamic picture of the world.…………………..………………………10
List of references……..………………………………….……13
History of electrodynamics.
Classical electrodynamics is a theory of electromagnetic processes in various media and in a vacuum. Covers a huge set of phenomena in which the main role is played by interactions between charged particles carried out through an electromagnetic field.
The history of electrodynamics is the history of the evolution of fundamental physical concepts. Until the middle of the 18th century, important experimental results were established due to electricity: attraction and repulsion, the division of substances into conductors and insulators, the existence of two types of electricity was discovered. Progress has been made in the study of magnetism.
The practical use of electricity began in the second half of the 18th century. The name of Fraclin (1706-1790) is associated with the emergence of the hypothesis about electricity as a special material substance. In 1785, C. Coulomb established the law of interaction of two point charges. A number of inventions of electrical measuring instruments are associated with the name of A. Volta (1745-1827). Ohm's law was established in 1826. In 1820, Oersted discovered the magnetic effect of electric current. In 1820, a law was established that determines the mechanical force with which a magnetic field acts on an element of electric current introduced into it - Ampere's law. Ampere also established the law of force interaction between two currents.
Of particular importance in physics is the hypothesis of molecular currents, proposed by Ampere in 1820.
In 1831, Faraday discovered the law of electromagnetic induction. In 1873, James Clerk Maxwell (1831-1879) outlined short equations that became the theoretical basis of electrodynamics. One of the consequences of Maxwell's equations was the prediction of the EM nature of light, and he also predicted the possibility of the existence of EM waves. Gradually, science developed an idea of the EM field as an independent material entity that is the carrier of EM interactions in space. The various electrical and magnetic phenomena that people have observed since time immemorial have always aroused their curiosity and interest. Most often, the term electrodynamics refers to classical electrodynamics, which describes only the continuous properties of the electromagnetic field. The electromagnetic field is the main subject of study of electrodynamics, a type of matter that manifests itself when interacting with charged bodies. In 1895, Popov A.S. made the greatest invention - radio. It had a tremendous impact on the subsequent development of science and technology. All electromagnetic phenomena can be described using Maxwell's equations, which establish a connection between the quantities characterizing electric and magnetic fields and the distribution of charges and currents in space.
Formation and development of classical electrodynamics
(M. Faraday, D. Maxwell, G. Hertz).
An important step in the development of electrodynamics was the discovery by M. Faraday of the phenomenon of electromagnetic induction - excitation by an alternating magnetic field of electromotive force in conductors - which became the basis of electrical engineering.
Michael Faraday - English physicist, was born on the outskirts of London in the family of a blacksmith. After graduating from primary school, from the age of twelve he worked as a newspaper delivery boy, and in 1804 he became an apprentice to the bookbinder Ribot, a French emigrant who in every possible way encouraged Faraday’s passionate desire for self-education. By reading and attending lectures, Faraday sought to expand his knowledge, and he was attracted mainly by the natural sciences - chemistry and physics. In 1813, one of the customers presented Faraday with invitation cards to lectures by Humphry Davy, which played a decisive role in the fate of the young man. Having addressed a letter to Davy, Faraday, with his help, received a position as a laboratory assistant at the Royal Institution.
Faraday's scientific activity took place within the walls of the Royal Institution, where he first helped Davy in chemical experiments, and then began independent research. Faraday liquefied chlorine and some other gases and obtained benzene. In 1821, he first observed the rotation of a magnet around a conductor with current and a conductor with current around a magnet, and created the first model of an electric motor. Over the next 10 years, Faraday studied the connection between electrical and magnetic phenomena. His research culminated in the discovery in 1831 of the phenomenon of electromagnetic induction. Faraday studied this phenomenon in detail, deduced its basic law, found out the dependence of the induction current on the magnetic properties of the medium, studied the phenomenon of self-induction and extra-currents of closing and opening.
The discovery of the phenomenon of electromagnetic induction immediately acquired enormous scientific and practical significance; this phenomenon underlies, for example, the operation of all direct and alternating current generators. The desire to identify the nature of electric current led Faraday to experiments on the passage of current through solutions of acids, salts and alkalis. The result of these studies was the discovery of the laws of electrolysis in 1833. In 1845, Faraday discovered the phenomenon of rotation of the plane of polarization of light in a magnetic field. In the same year he discovered diamagnetism, in 1847 - paramagnetism, and in 1833 he invented the voltmeter.
Faraday's ideas about electric and magnetic fields had a great influence on the development of all physics. In 1832, Faraday suggested that the propagation of electromagnetic interactions is a wave process occurring at a finite speed, and in 1845 he first used the term “magnetic field.”
Faraday's discoveries won wide recognition throughout the scientific world. In honor of Michael Faraday, the British Chemical Society established the Faraday Medal, one of the most honorable scientific awards.
Trying to explain the phenomenon of electromagnetic induction based on the concept of long-range action, but encountering difficulties, he suggested that electromagnetic interactions occur through an electromagnetic field, based on the concept of short-range action. This marked the beginning of the formation of the concept of the electromagnetic field, formalized by D. Maxwell. James Clerk Maxwell - English physicist. Born in Edinburgh. Under his leadership, the famous Cavendish Laboratory in Cambridge was created, which he headed until the end of his life.
Maxwell's works are devoted to electrodynamics, molecular physics, general statistics, optics, mechanics, and elasticity theory. Maxwell made his most significant contributions to molecular physics and electrodynamics. In the kinetic theory of gases, of which he is one of the founders, he established the velocity distribution functions of molecules based on the consideration of direct and reverse collisions, developed the theory of transfer in a general form, applying it to the processes of diffusion, thermal conductivity and internal friction, and introduced the concept of relaxation. In 1867, the first showed the statistical nature of the second law of thermodynamics, and in 1878 he introduced the term “statistical mechanics”.
Maxwell's greatest scientific achievement is the theory of the electromagnetic field he created in 1860-1865. In his theory of the electromagnetic field, Maxwell used a new concept - displacement current, defined the electromagnetic field and predicted a new important effect: the existence in free space of electromagnetic radiation, electromagnetic waves and its propagation in space at the speed of light. The scientist also formulated a theorem in the theory of elasticity, established relationships between the main thermophysical parameters, developed the theory of color vision, and studied the stability of Saturn’s rings, showing that the rings are not solid or liquid, but are a swarm of meteorites. Maxwell designed a number of instruments. He was a famous popularizer of physical knowledge.
1) the magnetic field is generated by moving charges and an alternating electric field (displacement current);
2) an electric field with closed lines of force (vortex field) is generated by an alternating magnetic field;
3) the magnetic field lines are always closed (this means that it has no sources - magnetic charges similar to electric ones);
4) an electric field with open lines of force (potential field) is generated by electric charges - the sources of this field.
James Maxwell's theory implies the finiteness of the speed of propagation of electromagnetic interaction and the existence of electromagnetic waves. Maxwell's theory of the electromagnetic field is a fundamental generalization of electrodynamics, so it rightfully occupies an honorable place among the greatest scientific achievements of mankind, such as classical mechanics, relativistic physics and quantum mechanics. In 1861-1862, James Maxwell published his article on physical lines of force. Based on the practical coincidence of the speed of propagation of electromagnetic disturbances and the speed of light, Maxwell suggested that light is also an electromagnetic disturbance. And this idea, which seemed absolutely fantastic for that time, suddenly began to acquire experimental confirmation.
And everything seemed fine, but in 1885, a certain teacher at a girls’ school in Basel, Johann Jakob Balmer, after his experiments, wrote a short article, literally a couple of pages long, that said: “Pay attention to the spectral lines of hydrogen.” Which put theoretical physicists into a state of stupor for the next two decades. The clear spectral lines of the Balmer series clearly demonstrated to the global physical scientific community that not everything is so simple in this world.
The development of classical electrodynamics after Maxwell proceeded in several directions, of which we note two main ones. Firstly, the mathematical side of Maxwell's theory was improved and some new results were obtained. Secondly, there was a unification of the theory of the electromagnetic field with the basic ideas of the theory of the structure of matter. The latter direction led to the creation of electronic theory.
I would also like to mention the outstanding German physicist Heinrich Rudolf Hertz. He graduated from the University of Berlin and from 1885 to 1889 was a professor of physics at the University of Karlsruhe. Since 1889 - professor of physics at the University of Bonn.
The main achievement is the experimental confirmation of James Maxwell's electromagnetic theory of light. Hertz proved the existence of electromagnetic waves.
He constructed the electrodynamics of moving bodies based on the hypothesis that the ether is carried away by moving bodies. However, his theory of electrodynamics was not confirmed by experiments and later gave way to the electronic theory of Hendrik Lorentz. The results obtained by Hertz formed the basis for the creation of radio. In 1886, Hertz first observed and described the external photoelectric effect. Hertz developed the theory of a resonant circuit, studied the properties of cathode rays, and investigated the effect of ultraviolet rays on electric discharge. Since 1933, the frequency unit Hertz, which is included in the international metric system of units SI, has been named after Hertz.
Physics is one of the most important sciences studied by man. Its presence is noticeable in all areas of life, sometimes discoveries even change the course of history. That is why great physicists are so interesting and significant for people.
Electrodynamics is a field of physics that studies the properties and patterns of behavior of the electromagnetic field and the movement of electric charges interacting with each other through this field.
Many great physicists have dedicated their lives to trying to find answers to questions that humanity needs. The world does not stand still, everything flows and changes, the planet rotates around its axis, a thunderstorm always comes with lightning and thunder, and leaves fall to the ground. And it was things that were simple at first glance that aroused a person’s interest in the exact and natural sciences.
Related information.
DEFINITION
Electrodynamics is a branch of physics that studies alternating electromagnetic fields and electromagnetic interactions.
The so-called classical electrodynamics describes the properties of the electromagnetic field and the principles of its interaction with bodies carrying an electric charge. This description is carried out using Maxwell's equations, an expression for the Lorentz force. In this case, such basic concepts of electrodynamics are used as: electromagnetic field (electric and magnetic fields); electric charge; electromagnetic potential; Poynting vector.
Special sections of electrodynamics include:
- electrostatics;
- magnetostatics;
- electrodynamics of continuum;
- relativistic electrodynamics.
Electrodynamics forms the basis for optics (as a branch of science) and physics of radio waves. This branch of science is the foundation for radio engineering and electrical engineering.
Basic concepts of electrodynamics
An electromagnetic field is a type of matter that manifests itself in the interaction of charged bodies. The electromagnetic field is often divided into electric and magnetic fields. An electric field is a special type of matter that is created by a body that has an electric charge or a changing magnetic field. The electric field affects any charged body placed in it.
A magnetic field is a special type of matter that is created by moving bodies that have electric charges and alternating electric fields. The magnetic field affects charges (charged bodies) that are in motion.
Electric charge - the source of the electric field, manifests itself through the interaction of the body carrying the charge and the field.
Electromagnetic potential is a physical quantity that completely determines the distribution of the electromagnetic field in space.
Basic equations of electrodynamics
Maxwell's equations are the basic laws of classical macroscopic electrodynamics. They are obtained as a result of generalization of empirical data. In brief form, these equations reflect the entire content of electrodynamics for a stationary medium. There are structural and material Maxwell equations. These equations can be represented in differential and integral forms. Let us write Maxwell's structural equations in integral form (SI system):
where is the magnetic field strength vector; is the electric current density vector; - electric displacement vector. Equation (1) reflects the law of creation of magnetic fields. A magnetic field occurs when a charge moves (electric current) or when an electric field changes. This equation is a generalization of the Biot-Savart-Laplace law. Equation (1) is called the magnetic field circulation theorem.
where is the magnetic field induction vector; - electric field strength vector; L is a closed loop along which the electric field strength vector circulates. Otherwise, equation (2) can be called the law of electromagnetic induction. This equation shows that the vortex electric field arises due to an alternating magnetic field.
where is the electric charge; - charge density. This equation is also called the Ostrogradsky-Gauss theorem. Electric charges are sources of electric field; there are free electric charges.
Equation (4) says that the magnetic field is of a vortex nature and there are no magnetic charges.
Maxwell's system of structural equations is supplemented with material equations that reflect the relationship of vectors with parameters characterizing the electrical and magnetic properties of matter.
where is the relative dielectric constant, is the relative magnetic permeability, is the specific electrical conductivity, is the electrical constant, is the magnetic constant. The medium in this case is considered isotropic, non-ferromagnetic, non-ferroelectric.
When solving applied problems in electrodynamics, Maxwell's equations are supplemented with initial and boundary conditions.
Examples of problem solving
EXAMPLE 1
| Exercise | Determine what will be the flow of the electric field strength vector () through the surface of a hypothetical sphere of radius R, if the electric field is created by an infinite uniformly charged thread, the charge distribution density on the thread is equal to? The center of the sphere is located on the thread. |
| Solution | In accordance with one of Maxwell’s equations (Gauss’s theorem), we have:
where for an isotropic medium: hence:
Considering that the charge on the thread is distributed uniformly with density , and the sphere cuts off a piece of thread with a length of 2R, we obtain that the charge inside the selected surface is equal to: Taking into account (1.3) and (1.4) we finally obtain (we assume that the field exists in a vacuum):
|
| Answer |
EXAMPLE 2
| Exercise | Write down the displacement current density function depending on the distance from the solenoid axis (), if the magnetic field of the solenoid varies according to the law: . R is the radius of the solenoid. The solenoid is direct. Consider the case when |
| Solution | As a basis for solving the problem, we use the equation from Maxwell’s system of equations:
|
Definition 1
Electrodynamics is a theory that examines electromagnetic processes in a vacuum and various media.
Electrodynamics covers a set of processes and phenomena in which the key role is played by the actions between charged particles, which are carried out through an electromagnetic field.
History of the development of electrodynamics
The history of the development of electrodynamics is the history of the evolution of traditional physical concepts. Even before the mid-18th century, important experimental results were established that were due to electricity:
- repulsion and attraction;
- dividing matter into insulators and conductors;
- existence of two types of electricity.
Considerable results have also been achieved in the study of magnetism. The use of electricity began in the second half of the 18th century. The emergence of the hypothesis about electricity as a special material substance is associated with the name of Franklin (1706-1790). And in 1785, Coulomb established the law of interaction of point charges.
Volt (1745-1827) invented many electrical measuring instruments. In 1820, a law was established that determined the mechanical force with which a magnetic field acts on an element of electric current. This phenomenon became known as Ampere's law. Ampere also established the law of the force action of several currents. In 1820, Oersted discovered the magnetic effect of electric current. Ohm's law was established in 1826.
In physics, the hypothesis of molecular currents, which was proposed by Ampere back in 1820, is of particular importance. Faraday discovered the law of electromagnetic induction in 1831. James Clerk Maxwell (1831-1879) in 1873 set out the equations that later became the theoretical basis of electrodynamics. A consequence of Maxwell's equations is the prediction of the electromagnetic nature of light. He also predicted the possibility of the existence of electromagnetic waves.
Over time, physical science developed the idea of the electromagnetic field as an independent material entity, which is a kind of carrier of electromagnetic interactions in space. Various magnetic and electrical phenomena have always aroused people's interest.
Often the term “electrodynamics” refers to traditional electrodynamics, which describes only the continuous properties of the electromagnetic field.
The electromagnetic field is the main subject of study of electrodynamics, as well as a special type of matter that manifests itself when interacting with charged particles.
Popov A.S. In 1895 he invented radio. It was this that had a key impact on the further development of technology and science. Maxwell's equations can be used to describe all electromagnetic phenomena. The equations establish the relationship between quantities that characterize magnetic and electric fields, distributing currents and charges in space.
Figure 1. Development of the doctrine of electricity. Author24 - online exchange of student work
Formation and development of traditional electrodynamics
The key and most significant step in the development of electrodynamics was the discovery of Faraday - the phenomenon of electromagnetic induction (excitation of electromotive force in conductors using an alternating electromagnetic field). This is what became the basis of electrical engineering.
Michael Faraday is an English physicist who was born into the family of a blacksmith in London. He graduated from primary school and worked as a newspaper delivery boy from the age of 12. In 1804, he became a student of the French emigrant Ribot, who encouraged Faraday's desire for self-education. At lectures, he sought to expand his knowledge of the natural sciences of chemistry and physics. In 1813, he was given a ticket to Humphry Davy's lectures, which played a decisive role in his fate. With his help, Faraday received a position as an assistant at the Royal Institution.
Faraday's scientific career took place at the Royal Institution, where he first assisted Davy in his chemical experiments, after which he began to conduct them independently. Faraday obtained benzene by reducing chlorine and other gases. In 1821, he discovered how a magnet rotates around a current-carrying conductor, creating the first model of an electric motor.
Over the next 10 years, Faraday studied the connections between magnetic and electrical phenomena. All his research was crowned with the discovery of the phenomenon of electromagnetic induction, which happened in 1831. He studied this phenomenon in detail, and also formed its basic law, during which he revealed the dependence of the induction current. Faraday also investigated the phenomena of closure, opening and self-induction.
The discovery of electromagnetic induction produced scientific significance. This phenomenon underlies all alternating and direct current generators. Since Faraday constantly sought to identify the nature of electric current, this led him to conduct experiments on the passage of current through solutions of salts, acids and alkalis. As a result of these studies, the law of electrolysis appeared, which was discovered in 1833. This year he opens a voltmeter. In 1845, Faraday discovered the phenomenon of polarization of light in a magnetic field. This year he also discovered diamagnetism, and in 1847 paramagnetism.
Note 1
Faraday's ideas about magnetic and electric fields had a key influence on the development of all physics. In 1832, he proposed that the propagation of electromagnetic phenomena is a wave process that occurs at a finite speed. In 1845, Faraday first used the term “electromagnetic field.”
Faraday's discoveries gained wide popularity throughout the scientific world. In his honor, the British Chemical Society established the Faraday Medal, which became an honorary scientific award.
Explaining the phenomena of electromagnetic induction and encountering difficulties, Faraday suggested the implementation of electromagnetic interactions using an electric and magnetic field. This all laid the foundation for the creation of the concept of the electromagnetic field, which was formalized by James Maxwell.
Maxwell's contribution to the development of electrodynamics
James Clerk Maxwell is an English physicist who was born in Edinburgh. It was under his leadership that the Cavendish Laboratory in Cambridge was created, which he headed throughout his life.
Maxwell's works are devoted to electrodynamics, general statistics, molecular physics, mechanics, optics, and the theory of elasticity. He made his most significant contributions to electrodynamics and molecular physics. One of the founders of the kinetic theory of gases is Maxwell. He established the velocity distribution functions of molecules, which are based on the consideration of reverse and direct collisions. Maxwell developed the theory of transfer in a general form and applied it to the processes of diffusion, internal friction, thermal conductivity, and also introduced the concept of relaxation.
In 1867, he first showed the statistical nature of thermodynamics, and in 1878 he introduced the concept of “statistical mechanics”. Maxwell's most significant scientific achievement is the theory of the electromagnetic field he created. In his theory, he uses a new concept “displacement current” and gives a definition of the electromagnetic field.
Note 2
Maxwell predicts a new important effect: the existence of electromagnetic radiation and electromagnetic waves in free space, as well as their propagation at the speed of light. He also formulated a theorem in the theory of elasticity, establishing the relationship between key thermophysical parameters. Maxwell develops the theory of color vision and studies the stability of Saturn's rings. It shows that the rings are not liquid or solid, but are a swarm of meteorites.
Maxwell was a famous popularizer of physical knowledge. The contents of his four electromagnetic field equations are as follows:
- A magnetic field is generated with the help of moving charges and an alternating electric field.
- An electric field with closed lines of force is generated with the help of an alternating magnetic field.
- Magnetic field lines are always closed. This field does not have magnetic charges, which are similar to electric ones.
- An electric field, which has open lines of force, is generated by electric charges, which are the sources of this field.
The book is a course of lectures on classical electrodynamics, which the author read for many years at the undergraduate level of the Physics Faculty of St. Petersburg (Leningrad) State University. The course is based on fundamental principles such as Maxwell's equations and the principle of relativity, combined in the relativistic covariant form of the electrodynamics equations. On their basis, the basic ideas and methods of electrostatics, radiation theory, electrodynamics of continuous media and the theory of waveguides are consistently presented. The material is presented with a high degree of mathematical rigor, which is seamlessly combined with a clear presentation of the physical content. The book can be useful to anyone who, having basic knowledge in the field of electrical phenomena and mathematical analysis, would like to get a clear and mathematically rigorous understanding of both the theoretical foundations and methods for solving the most complex problems of electrodynamics.
Fragment from the book.
Summary: when considering radio engineering problems of the type “how does this antenna radiate,” we are, of course, only interested in the field created by it itself, and to exclude external free fields, it is natural to impose the necessary asymptotic conditions at infinity on the potentials. With this formulation, the above gauge conditions fix the potentials uniquely. But if we are interested in the free fields themselves (which is natural when formulating problems, for example, in quantum field theory), then we cannot impose conditions that exclude these very fields.
Preface
1 General introduction
1.1 Maxwell's equations.
1.2 Mathematical digression: notation conventions, reference formulas.
1.3 Integral form of Maxwell's equations.
1.4 The relationship between the differential and integral forms of Maxwell's equations in the presence of discontinuity surfaces. Boundary conditions (matching conditions).
1.5 Continuity equation, charge conservation law.
1.6 Transition from tensions to potentials. Maxwell's equations for potentials.
1.7 Calibration transformations and calibration conditions.
2 Relativistic-covariant formulation of electrodynamics
2.1 Designations.
2.2 Tensors on the SO3 rotation group and on the 03 group.
2.3 Tensor fields.
2.4 Electrodynamics and the principle of relativity.
2.5 Lorentz transformations, general properties.
2.6 Lorentz eigentransformations. Explicit form of transformations of the transition to a moving reference frame..
2.7 Relativistic law of addition of velocities. Reducing scale and stretching time.
2.8 Tensors and tensor fields on the Lorentz group.
2.9 Tensor nature of potentials and tensions.
2.10 Covariant formulation of Maxwell's equations for potentials.
2.11 Transversality K, continuity equation, gauge invariance of Maxwell’s equations, gauge conditions.
2.12 General considerations on the form of Maxwell’s equations for potentials.
2.13 Covariant recording of Maxwell's equations for tensions.
2.14 Transformations of potentials and tensions during the transition to a moving reference frame.
2.15 Electrodynamics from the standpoint of theoretical mechanics. Action functional for electromagnetic field.
2.16 Energy-momentum tensor. Laws of conservation of energy and momentum.
2.17 Elements of relativistic dynamics of a point particle. Lorentz force.
3 Statics
3.1 Basic relationships.
3.2 Solution of Poisson's equation.
3.3 Multipole expansion of the scalar potential
in electrostatics. Multipole moments and their properties.
3.4 Multifield expansion of the vector potential A in magnetostatics. Magnetic moment of an arbitrary current system.
3.5 Forces and moments of forces. acting on distributed sources.
3.6 Potential energy of a system of charges or currents
in a given external field.
3.7 Own potential energy of a system of charges or currents (energy in its own field).
3.8 Dielectrics and magnets (statics).
3.9 Fundamentals of thermodynamics of dielectrics and magnets. Volume forces in dielectrics and magnets.
3.10 Boundary value problems of electrostatics and methods for their solution....
4 Dynamics
4.1 Statement of the problem, general form of the solution.
4.2 Retarded Green's function of the wave operator....
4.3 Delayed potentials.
4.4 Field of an arbitrarily moving point charge. Liénard-Wiechert potentials. Radiation power and radiation pattern.
4.5 Radiation from localized sources, multipole decomposition.
4.6 Linear antenna with central excitation.
4.7 Maxwell's dynamic equations in a medium.
4.8 Waveguides.
Literature Subject index
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