New physics tutor to prepare for the Unified State Exam. Electromagnetism. Oscillations and waves. Optics. Elements of the theory of relativity. Physics of the atom and the atomic nucleus. Kasatkina I.L. History of Physics: Electromagnetism
The course "Electromagnetism" is a section of the course general physics, which sets out systematic knowledge about the basic concepts and laws of electromagnetism as generalizations of experimental facts expressed in mathematical form. The fundamental experiments underlying the fundamental laws of electricity, magnetism, and electrodynamics are studied and demonstrated. Theoretical models of the interaction of electric and magnetic fields with matter are analyzed and the areas of their applicability are analyzed. Modern technologies based on the laws of electromagnetism are explained. The discipline develops in students the foundations of a natural science worldview and is the basis for further study of general professional and special disciplines.
Format
The form of study is correspondence (distance). Weekly classes will include watching thematic video lectures, accompanied by video recordings of lecture experiments, and performing test tasks With automated check results. An important element of studying the discipline is independent decision physical tasks. The solution will have to contain rigorous and logically correct reasoning leading to the correct answer.
Requirements
The course is designed for 1st year bachelors. Knowledge of physics and mathematics at the level of high school (grade 11) is required.
Course program
Lecture 1. Electromagnetic interaction and its place among other interactions in nature. Development of the physics of electricity in the works of M.V. Lomonosov. Electric charge. Microscopic charge carriers. Millikan's experience. Law of conservation of electric charge. Electrostatics. Coulomb's law and its field interpretation. Electric field strength vector. The principle of superposition of electric fields.
Lecture 1. Electric field strength vector flux. Ostrogradsky–Gauss electrostatic theorem, its representation in differential form. Electrostatic field potential. Potential. Normalization of potential. Relationship between the vector of electrostatic field strength and potential. Work of electrostatic field forces. Charge system potential.
Lecture 3. Circulation of the electric field strength vector. The circulation theorem, its representation in differential form. Poisson and Laplace equations. Electric dipole. Potential and field strength of a dipole.
Lecture 4. Conductors in an electrostatic field. Electrostatic induction. Field strength at the surface and inside the conductor. Distribution of charge over the surface of a conductor. Electrostatic protection. Relationship between charge and potential of a conductor. Electrical capacity. Capacitors. Capacity of flat, spherical and cylindrical capacitors. A conducting ball in a uniform electrostatic field.
Lecture 5. Dielectrics. Free and bound charges. Polarization vector. Relationship between the polarization vector and bound charges. Vector of electrical induction in a dielectric. Dielectric susceptibility and dielectric constant and substances. Material equation for electric field vectors. Ostrogradsky–Gauss theorem for dielectrics. Its differential form. Boundary conditions for voltage vectors and electrical induction. Dielectric ball in a uniform electric field.
Lecture 6. Energy of a system of electric charges. Interaction energy and self-energy. Electrostatic field energy and its volumetric density. Energy of an electric dipole in an external field. Ponderomotive forces in an electric field and methods for their calculations. Relationship between ponderomotive forces and the energy of the charge system.
Lecture 7. Electronic theory of polarization of dielectrics. Local field. Non-polar dielectrics. Clausius–Mossotti formula. Polar dielectrics. Langevin function. Polarization of ionic crystals. Electrical properties of crystals. Pyroelectrics. Piezoelectrics. Direct and inverse piezoelectric effect and their application. Ferroelectrics. Domain structure of ferroelectrics. Hysteresis. Curie point. Application of ferroelectrics.
Lecture 8. Constant electric current. Current strength and density. Current lines. Electric field in a current-carrying conductor and its sources. Continuity equation. Condition for the current to be stationary. Electrical voltage. Ohm's law for a section of a circuit. Electrical resistance. Ohm's law in differential form. Specific electrical conductivity of a substance.
Lecture 9. Currents in continuous media. Grounding. Work and power DC. Joule–Lenz law and its differential form. Outside forces. Electromotive force. Ohm's law for a closed circuit. Branched chains. Kirchhoff's rules. Examples of their application.
Lecture 10. Magnetostatics. Interaction of currents. Current element. The Biot-Savart-Laplace law and its field interpretation. Magnetic field induction vector. The effect of a magnetic field on a current. Ampere's law. Theorem on the circulation of the magnetic field induction vector. Differential form of the circulation theorem. Vortex nature of the magnetic field. Equation div B = 0. Concept of vector potential. Relativistic nature of magnetic interactions.
Lecture 11. Elementary current and its magnetic moment. Magnetic field of an elementary current. Elementary current in a magnetic field. Magnetic field of a moving charge. Interaction of moving charges. Lorentz force. Hall effect.
Lecture 12. Magnetic induction vector flux (magnetic flux). Self-inductance coefficient (inductance). The coefficient of mutual induction of two circuits. Potential current function. Forces acting on a current-carrying circuit. Interaction of two circuits with current.
Lecture 13. Electromagnetic induction. Faraday's law of electromagnetic induction and its differential form. Lenz's rule.
Lecture 14. Magnetics. The concept of molecular currents. The magnetization vector of a substance and its connection with molecular currents. Magnetic field strength vector.
Lecture 15. Classification of magnetic materials. Diamagnets, paramagnets and ferromagnets. Classic description of diamagnetism. Larmor precession.
Lecture 16. Ferromagnets. Spontaneous magnetization and Curie temperature. Domain structure. Magnetization hysteresis, Stoletov curve.
Lecture 17. Quasi-stationary currents. Conditions for quasi-stationarity. Transient processes in RC and LC circuits.
Lecture 18. Forced oscillations in the circuit. The process of establishing forced oscillations.
Lecture 19. Voltage resonance. Voltages and currents at resonance.
Lecture 20. Technical application of alternating currents. Generators and electric motors. Three-phase current.
Lecture 21. High frequency currents. Skin effect. Skin layer thickness.
Lecture 22. Classical theory of electronic conductivity Drude – Lorentz.
Lecture 23. Semiconductors.
Learning outcomes
As a result of mastering the discipline, the student must know the basic phenomena of electricity and magnetism, methods of their theoretical description and methods of their use in physical devices, and be able to solve problems from the “Electromagnetism” section of the general physics course section.
Formed competencies
Competencies required to master the discipline: ONK-1, PC-1; Competencies formed as a result of mastering the discipline: PC-2; ONK-5.
Certificate
A certificate of participation is usually issued upon reaching 60% of the overall rating, provided that the work is submitted before a strict deadline. A certificate of honors is usually issued upon reaching 90% of the overall rating, provided the work is submitted before the soft deadline.
The first law of electromagnetism describes the flow of an electric field:
where ε 0 is some constant (read epsilon-zero). If there are no charges inside the surface, but there are charges outside it (even very close), then it’s all the same average the normal component of E is zero, so there is no flow through the surface. To show the usefulness of this type of statement, we will prove that equation (1.6) coincides with Coulomb's law, if only we take into account that the field of an individual charge must be spherically symmetric. Let's draw a sphere around a point charge. Then the average normal component is exactly equal to the value of E at any point, because the field must be directed along the radius and have the same value at all points on the sphere. Our rule then states that the field on the surface of a sphere multiplied by the area of the sphere (i.e., the flux flowing out of the sphere) is proportional to the charge inside it. If you increase the radius of a sphere, its area increases as the square of the radius. The product of the average normal component of the electric field by this area must still be equal to the internal charge, which means that the field must decrease as the square of the distance; This is how a field of “inverse squares” is obtained.
If we take an arbitrary curve in space and measure the circulation of the electric field along this curve, it turns out that in the general case it is not equal to zero (although in a Coulomb field this is so). Instead, the second law holds true for electricity, stating that
And finally, the formulation of the laws of the electromagnetic field will be completed if we write two corresponding equations for the magnetic field B:
And for the surface S,
limited curve WITH:
The constant c 2 that appears in equation (1.9) is the square of the speed of light. Its appearance is justified by the fact that magnetism is essentially a relativistic manifestation of electricity. And the constant ε 0 is set so that the usual units of force arise electric current.
Equations (1.6) - (1.9), as well as equation (1.1) are all the laws of electrodynamics. As you remember, Newton's laws were very simple to write, but many complex consequences followed from them, so it took a lot of time to study them all. The laws of electromagnetism are incomparably more difficult to write, and we should expect that the consequences from them will be much more complicated, and now we will have to understand them for a very long time.
We can illustrate some laws of electrodynamics with a series of simple experiments that can show us, at least qualitatively, the relationship between the electric and magnetic fields. You become familiar with the first term in equation (1.1) when combing your hair, so we won’t talk about it. The second term in equation (1.1) can be demonstrated by passing a current through a wire hanging over a magnetic bar, as shown in Fig. 1.6. When the current is turned on, the wire moves due to the force acting on it F = qvXB. When current flows through a wire, the charges inside it move, that is, they have a speed v, and they are acted upon by the magnetic field of the magnet, as a result of which the wire moves to the side.
When the wire is pushed to the left, you can expect the magnet itself to experience a push to the right. (Otherwise the whole device could be mounted on a platform and get a reactive system in which momentum would not be conserved!) Although the force is too small to notice the movement of a magnetic rod, the movement of a more sensitive device, say a compass needle, is quite noticeable.
How does current in a wire push a magnet? The current flowing through the wire creates its own magnetic field around it, which acts on the magnet. In accordance with the last term in equation (1.9), the current should lead to circulations vector B; in our case, the field lines B are closed around the wire, as shown in Fig. 1.7. It is this field B that is responsible for the force acting on the magnet.
Equation (1.9) tells us that for a given amount of current flowing through the wire, the circulation of the field B is the same for any curve surrounding the wire. For those curves (circles, for example) that lie far from the wire, the length turns out to be greater, so the tangent component B should decrease. You can see that you would expect B to decrease linearly with distance from a long straight wire.
We said that current flowing through a wire creates a magnetic field around it and that if there is a magnetic field, then it acts with some force on the wire through which the current flows. This means that one should think that if a magnetic field is created by a current flowing in one wire, then it will act with some force on the other wire, which also carries current. This can be shown by using two freely suspended wires (Fig. 1.8). When the direction of the currents is the same, the wires attract, and when the directions are opposite, they repel.
In short, electric currents, like magnets, create magnetic fields. But then what is a magnet? Since magnetic fields are created by moving charges, could it be that the magnetic field created by a piece of iron is actually the result of currents? Apparently this is true. In our experiments, we can replace the magnetic rod with a coil of wound wire, as shown in Fig. 1.9. When current passes through the coil (as well as through the straight wire above it), exactly the same movement of the conductor is observed as before when there was a magnet instead of the coil. Everything looks as if current were continuously circulating inside a piece of iron. Indeed, the properties of magnets can be understood as a continuous current within the iron atoms. The force acting on the magnet in Fig. 1.7 is explained by the second term in equation (1.1).
Where do these currents come from? One source is the movement of electrons in atomic orbits. This is not the case with iron, but in some materials this is the origin of magnetism. In addition to rotating around the nucleus of an atom, the electron also rotates around its own axis(something similar to the rotation of the Earth); It is from this rotation that a current arises, creating a magnetic field in the iron. (We said “something like the rotation of the Earth” because in fact in quantum mechanics the question is so deep that it does not fit well enough into classical ideas.) In most substances, some electrons rotate in one direction, others in the other, so magnetism disappears, and in iron (for a mysterious reason which we will talk about later) many electrons rotate so that their axes point in the same direction and this serves as a source of magnetism.
Since the fields of magnets are generated by currents, there is no need to insert additional terms into equations (1.8) and (1.9) that take into account the existence of magnets. These equations are about everyone currents, including circular currents from rotating electrons, and the law turns out to be correct. It should also be noted that, according to equation (1.8), magnetic charges similar to the electric charges on the right side of equation (1.6) do not exist. They were never discovered.
The first term on the right side of equation (1.9) was discovered theoretically by Maxwell; he is very important. He says change electrical fields causes magnetic phenomena. In fact, without this term the equation would lose its meaning, because without it the currents in open circuits would disappear. But in reality such currents exist; The following example illustrates this. Imagine a capacitor made up of two flat plates. It is charged by a current flowing into one of the plates and flowing out from the other, as shown in Fig. 1.10. Let's draw a curve around one of the wires WITH and stretch a surface over it (surface S 1) that will intersect the wire. In accordance with equation (1.9), the circulation of field B along the curve WITH is given by the magnitude of the current in the wire (multiplied by from 2). But what happens if we pull on a curve another surface S 2
in the shape of a cup, the bottom of which is located between the plates of the capacitor and does not touch the wire? No current, of course, passes through such a surface. But a simple change in the position and shape of an imaginary surface should not change the real magnetic field! The circulation of field B should remain the same. Indeed, the first term on the right side of equation (1.9) is combined with the second term in such a way that for both surfaces S 1
and S 2 the same effect occurs. For S 2
the circulation of vector B is expressed through the degree of change in the flow of vector E from one plate to another. And it turns out that the change in E is related to the current precisely in such a way that equation (1.9) turns out to be satisfied. Maxwell saw the need for this and was the first to write the complete equation.
Using the device shown in FIG. 1.6, another law of electromagnetism can be demonstrated. Let's disconnect the ends of the hanging wire from the battery and connect them to a galvanometer - a device that records the passage of current through the wire. Stands only in the field of a magnet swing wire, and current will immediately flow through it. This is a new consequence of equation (1.1): the electrons in the wire will feel the action of the force F=qv X B. Their speed is now directed to the side, because they are deflected along with the wire. This v, together with the vertically directed field B of the magnet, results in a force acting on the electrons along wires and electrons are sent to the galvanometer.
Suppose, however, that we left the wire alone and began to move the magnet. We feel that there should be no difference, because the relative motion is the same, and indeed current flows through the galvanometer. But how does a magnetic field act on charges at rest? In accordance with equation (1.1) there should arise electric field. A moving magnet must create an electric field. The question of how this happens is answered quantitatively by equation (1.7). This equation describes many practically very important phenomena occurring in electrical generators and transformers.
The most remarkable consequence of our equations is that by combining equations (1.7) and (1.9), we can understand why electromagnetic phenomena spread over long distances. The reason for this, roughly speaking, is something like this: suppose that somewhere there is a magnetic field that increases in magnitude, say, because a current is suddenly passed through a wire. Then from equation (1.7) it follows that circulation of the electric field should arise. When the electric field begins to gradually increase for circulation to occur, then, according to equation (1.9), magnetic circulation should also arise. But increasing this magnetic field will create a new circulation of the electric field, etc. In this way, the fields propagate through space without the need for charges or currents anywhere other than the source of the fields. This is the way we we see each other! All this is hidden in the electromagnetic field equations.
In physics for grade 11 (Kasyanov V.A., 2002),
task №49
to the chapter " Electromagnetism. BASIC POINTS».
At the ends of a conductor of length l, moving at speed in a magnetic field with induction perpendicular to the speed of movement, a potential difference arises
Electromagnetic induction - a physical phenomenon consisting in the occurrence of electric current in a closed circuit when the flux of magnetic induction changes through the surface limited by this circuit
Law of electromagnetic induction (Faraday's law): The emf of electromagnetic induction in a circuit is numerically equal and opposite in sign to the rate of change of magnetic flux through the surface bounded by this circuit
Lenz's rule: the induced current in the circuit has such a direction that the magnetic flux it creates through the surface bounded by the circuit prevents a change in the magnetic flux that caused this current
Self-induction- the occurrence of induced emf in a conductive circuit when the current strength changes, self-induction emf in the coil 
where L is the inductance of the coil
Transformer- a device used to increase or decrease alternating voltage Transformation ratio K - a value equal to the ratio of voltages in the primary and secondary windings of the transformer 
Step-up transformer - transformer that increases voltage (TO<
1).
Step-down transformer - voltage reducing transformer (K> 1)
Instantaneous voltage value- voltage in at the moment time
Oscillation phase- argument of the function describing harmonic oscillations
The voltage and current in the resistor are in phase at any time.
Effective force value AC is equal to the strength of a direct current that releases the same amount of heat in a conductor as an alternating current in the same period of time. If the alternating current changes according to a harmonic law, the period of change in the current is chosen as the time interval.
Current (effective) value of alternating current in 
times less than its amplitude 
Active resistance- element resistance electrical circuit, in which electrical energy is irreversibly converted into internal (thermal) energy. The electric field that changes over time is the source of the magnetic field.
Magnetoelectric induction - the phenomenon of the appearance of a magnetic field in an alternating electric field. Current fluctuations in the capacitor circuit are ahead in phase of voltage fluctuations on its plates by π/2. Reactance- circuit element for which the average alternating current power is zero
Capacitance- reactance of the capacitor. The current fluctuations in the capacitor are π/2 ahead in phase of the voltage fluctuations on its plates
Inductive reactance- coil reactance. The current fluctuations in the inductor lag in phase by π/2 from the voltage fluctuations across it. Thomson formula:
Impedance oscillatory circuit alternating current depends on current frequency
Resonance in the oscillatory circuit- the physical phenomenon of a sharp increase in the amplitude of current oscillations in the circuit when the frequency of forced oscillations coincides with the frequency of natural oscillations in the circuit
Resonance curve- a graph of the dependence of the amplitude of forced oscillations of current strength on the frequency of voltage applied to the circuit. In semiconductors, there are two mechanisms of intrinsic conductivity: electron and hole.
Electronic conductivity- the result of the directed movement in the interatomic space of free electrons that left the valence shell of the atom as a result of heating the semiconductor or under the influence of external fields.
Hole conductivity- the result of the directed movement of valence electrons between the electron shells of neighboring atoms to vacant places - holes.
Impurities in a semiconductor- foreign atoms chemical elements contained in the main semiconductor. There are donor and acceptor impurities. Atoms of the donor impurity have a valence greater than that of the main semiconductor. Atoms of the acceptor impurity have a valence less than the valence of the main semiconductor.
n-type semiconductor- semiconductor with donor impurity
p-type semiconductor- semiconductor with acceptor impurity
p-n-junction- contact layer of two p- and n-type impurity semiconductors
Barrier layer- a double layer of opposite electric charges, creating an electric field at the p-n junction, preventing the free separation of charges
Semiconductor diode- element electrical diagram containing a p-n junction and two terminals for inclusion in an electrical circuit
Transistor- a semiconductor device with two p-n junctions and three terminals for inclusion in an electrical circuit. A transistor is used to amplify and generate electrical signals.
Gain- the ratio of the change in output voltage to the change in input Emission and reception of electromagnetic waves in the radio and microwave range
Phenomena resulting from the interaction of electricity and magnetism are called electromagnetism.
Discovery of electromagnetism
Hans Christian Oersted
The discoverer of electromagnetism is considered to be the Danish physicist Hans Christian Ørsted, who discovered the effect of electric current on a magnet.
Until the beginning of the 19th century, no one assumed that electricity and magnetism were connected in any way. And even the branches of physics in which they were considered were different. Proof of the existence of such a connection was obtained by Oersted in 1820 during an experiment at a lecture at the university. On the experimental table next to the current conductor there was magnetic compass. At the moment of closing the electrical circuit, the magnetic needle of the compass deviated from its original position. Repeating the experiment, Oersted obtained the same result.
Oersted's experience
In subsequent experiments, the scientist pulled a metal wire between two posts. The magnetic needle was located under it. Before current was passed through the wire, the arrow was oriented from north to south. After closing the electrical circuit, it was installed perpendicular to the wire. Experiments were carried out in different conditions. The magnetic needle was placed under a cap from which air was pumped out. But regardless of the environment, it stubbornly deviated from its original position as soon as current flowed through the conductor. This meant that a magnetic needle located near a current-carrying conductor was acted upon by forces tending to turn it. Oersted found an explanation for this. He proposed that an electric current flowing through a conductor creates a magnetic field. Thus, the connection between electrical and magnetic phenomena was discovered experimentally.
Magnetic field of a straight conductor carrying current
Power lines of conductor with current
Like the magnetic field formed by a permanent magnet, the magnetic field of a current-carrying conductor is characterized by lines of force.
If a straight conductor carrying current is passed through a hole in a sheet of cardboard on which small iron or steel filings are scattered, then they form concentric circles, the center of which is located on the axis of the conductor. These circles represent the magnetic field lines of a current-carrying conductor.
But if you give the conductor a different shape, the picture will be different.
Magnetic field of a current coil
Solenoid magnetic field
By bending a current-carrying conductor into a spiral, we get solenoid (from the Greek “pipe”). The lines of force of the magnetic field it creates are closed lines. Most often they are located inside the turns.
If you wind the insulated wire around the frame so that the turns are located close to each other, you will get a coil. When current is passed through it, a magnetic field is created, and the coil begins to attract metal objects. This attraction is greatly enhanced by inserting a steel or iron rod into the coil, which is called core . The current creates a magnetic field that magnetizes the core. The magnetic field of the core then adds to the magnetic field of the solenoid itself, thereby increasing it. A coil with a core is called electromagnet .
Simplegreatest electromagnet
The magnetic field of an electromagnet can be adjusted by increasing or decreasing the current or the number of turns in the winding. Each turn creates its own magnetic field. And the more turns there are in an electromagnet, the stronger its field. Accordingly, if you reduce the number of turns, the magnetic field is weakened.
The first electromagnet was created English engineer William Sturgeon in 1825. His device was a curved rod made of soft iron and coated with varnish to insulate the wire. A thick copper wire was wound around the rod.
Drawing of Sturgeon's electromagnet
In modern electromagnets, the cores are made of ferromagnets - substances that have high magnetization at temperatures below the Curie point, even in the absence of an external magnetic field. Insulated aluminum or copper wire is used for winding.
Application of electromagnets
Electromagnetic tap
Typically an electromagnet is a coil of wire wound around a ferromagnetic core. The core may have the most different shapes. It is part of a magnetic circuit through which a magnetic flux excited by an electric current passes. The other, moving part of the magnetic circuit is the armature, which transmits force.
Electromagnets are used in various electrical devices, telephones, cars, televisions, electric bells, etc. Using an electromagnet, you can attract, hold and move heavy metal parts and objects, sort magnetic and non-magnetic substances. Metallurgical plants use electromagnetic cranes and machines with magnetic tables , on which the product is fixed with electromagnets. In medicine, they are used to remove metal filings that have gotten into the eye.
Parallel conductors in a magnetic field
Conductors carrying current in a magnetic field
Continuing Oersted's research, Ampere confirmed the magnetic effect of electric current, discovering that current-carrying conductors interact with each other. Moreover, if the currents are in parallel conductors x flow in one direction, then the conductors attract. If same the direction of currents in such conductors is opposite, then they repel. Moreover, Ampere developed a law, later named after him (Ampere's law), which allows one to determine the magnitude of the force with which conductors interact with current.
It should be noted that Ampere examined a conductor in a magnetic field created not by a permanent magnet, but by another conductor carrying current.
Two parallel conductors carrying current interact with a force proportional to the magnitude of the currents in elementary segments and inversely proportional to the distance between them.
Combining electricity and magnetism, Ampère called the new field of physics electrodynamics.
The effect of a magnetic field on a current-carrying conductor
Conductor carrying current in a magnetic field
Oersted's experiment demonstrates the effect of electric current on a magnet. But can a magnet exert an effect on a current-carrying conductor? It turns out yes.
Let's suspend the conductor between the poles permanent magnet. As soon as current flows through it, the conductor will be pulled into the magnet or pushed out of it, depending on the direction of the current and the location of the magnet's poles. The force acting on a conductor is called Ampere force . Its value depends on the current I , length of a conductor section in a magnetic field l , magnitude of magnetic field induction B and angle values α between the direction of the current and the magnetic induction vector:
F= I l ·B·sinα
As we see, highest value force will occur if the conductor is located in such a way that the direction of the current in it is perpendicular to the direction of the magnetic induction vector. In this casesinα = 1 .
If the directions of the current and the magnetic induction vector coincide, then the Ampere force is zero, and the magnetic field does not act on the current-carrying conductor in this case.
The direction of the Ampere force is determined using the left-hand rule: If the current-carrying conductor is positioned so that the magnetic field lines enter the palm of the left hand, and the direction of the current coincides with the direction of 4 fingers, then the bent thumb will show the direction of the Ampere force.
The effect of a magnetic field on a current-carrying frame
Frame with current in a magnetic field
Electric current is always closed, so a straight conductor can be considered as part of an electrical circuit.
How does a closed circuit behave in a magnetic field?
If, instead of a flexible conductor, a wire bent in the form of a rigid frame is placed between the poles of a magnet, then at the initial moment such a frame will be installed parallel to the line connecting the poles of the magnet. At this moment, the magnetic induction vector is parallel to the two sides of the frame and is located in its plane. After turning on the current, the frame will begin to rotate and position itself in such a way that the magnetic field lines will penetrate its plane.
The rotation of the frame is explained by the action of Ampere forces on it.
Each side of the frame individually can be considered as a conductor carrying current. According to Ampere's law, the Ampere force acts on them. Its direction is determined using the left-hand rule.
Obviously, the forces acting on opposite sides of the rectangular frame will be equal in magnitude and opposite in direction due to the different directions of the currents in them.
Forces do not act on the sides of the frame located parallel to the lines of magnetic induction, since the angle α between the magnetic induction vector and the direction of the current is 0, therefore, sinα is also zero.
The angle between the induction vector and the direction of the current in the vertical sides of the frame is 90 o. Hence, sinα = 1, and the modulus of the force acting on each of them is equal to
F = I · B·a , Where A – length of the side of the frame.
Forces create torque scalar quantity which is equal to
M = I · S · B
Under the influence of this moment, the frame begins to rotate. At any time in between M = I · S · B · sinβ , Where β – the angle between the magnetic induction vector and the normal (perpendicular) to the plane of the frame. When turning, this angle changes, the magnitude of the force decreases, and gradually the frame takes a position perpendicular to the magnetic induction vector. In this case, the torque becomes equal to zero. (M = 0 ) .
The operation of a simple electric motor is based on the principle of rotating a frame with current in a magnetic field. If you turn off the current at a time when the frame has not yet reached a stable position, it will rotate by inertia and stop. When the current is turned on, it will begin to rotate again. By turning the current on and off at the right moment, you can achieve continuous rotation of the frame. The operation of the simplest DC electric motor is based on this principle.
In order for the frame to rotate continuously, it is necessary that current flows every half turn. In an engine, this function is performed by a device called collector . It consists of two metal half rings. The ends of the frame are soldered to them. When the current is connected, the frame makes half a revolution. The half-rings of the collector rotate along with it. As a result, the contacts of the frame switch, the current in it changes its direction, and the frame continues to rotate non-stop.
DC motors are used in traction electric drives of electric locomotives, trams, diesel locomotives, and motor ships. An electric car starter is also a DC motor. Micromotors power children's toys, power tools, computer devices, sewing machines, vacuum cleaners, drills, etc.
History of Physics: Electromagnetism
In the 18th century, work on the electrification of bodies, begun by Gilbert, continued. Numerous experiments carried out in various laboratories made it possible to discover not only new materials capable of becoming electrified by friction, but also to discover a number of new properties of this phenomenon. The Englishman Stephen Gray (1670-1735) showed that electricity can spread through certain bodies, i.e. introduced the concepts of conductor and insulator. Devices for generating electricity were improved - electrostatic machines, and capacitors (Leyden jar) were created.
Interest in new phenomena spread widely in society through various tricks and public demonstrations. Franklin conducted systematic studies of electrical phenomena and formulated his theory in 1747 using the concept of an electrical fluid, the excess or deficiency of which causes the electrification of bodies.
Franklin Benjamin (17.01.1706-17.04.1790) - American physicist, member of the Royal Society of London (1756), St. Petersburg Academy of Sciences (1789), prominent political and public figure, Copley Medal (1753). Born in Boston in the family of an entrepreneur. I received my education on my own. In 1727 he organized his own printing house in Philadelphia, in 1731 - the first public library in America, in 1743 - the American Philosophical Society (the first scientific research institution in America), in 1751 - the University of Pennsylvania. 1737-53 - postmaster of Pennsylvania, 1753-74 - North American colonies. Participated in the drafting of the Declaration of Independence and the US Constitution.
In 1746-54 he conducted experimental research on electricity, explained the action of the Leyden jar, built the first flat capacitor, invented the lightning rod in 1750, proved in 1753 the identity of earthly and atmospheric electricity, the electrical nature of lightning. Developed (1750) a theory of electrical phenomena and introduced the concepts of positive and negative electricity. He studied the thermal conductivity of metals and the propagation of sound in air and water. Author of a number of inventions (using sparks to explode gunpowder, etc.).
Franklin's works were deemed unworthy of publication by the Royal Society of London, and they were published by his friend, the English physicist Peter Collinson (1694-1768), at his own expense. The success of the publication was enormous, and after his experiment with a lightning rod was carried out in 1752, confirming the equivalence of an electric spark and lightning, scientific enthusiasm for the study of electrical phenomena spread very widely. The Royal Society awarded Franklin the Copley Medal in 1753, and elected him a member in 1756.
General, already established by that time methodology scientific research required quantitative measurements. And the founder of electrical metrology was Volta, who also designed very accurate electrometers.
Volta Alessandro (02/18/1745-03/05/1827) - Italian physicist, chemist and physiologist, member of the Royal Society of London and the Paris Academy of Sciences, Copley Medal (1794). Born in Como into a noble noble family. He studied at the school of the Jesuit Order. In 1774-79 he taught physics at the gymnasium in Como, from 1779 - professor at the University of Pavia, in 1815-19 - director of the Faculty of Philosophy at the University of Padua.
Works in the field of electricity, molecular physics. He developed the theory of the Leyden jar (1769), built a resin electrophore (1775), an electroscope with straws (1781), a capacitor (1783), an electrometer and other instruments, and described the operation of the telegraph. In 1792, L. Galvani began repeating experiments with “animal” electricity and came to the conclusion that the cause of short-term current was the presence of a circuit of two classes of dissimilar conductors (two metals and a liquid). At the end of 1799 he designed the first source of long-term galvanic current - a voltaic column. He discovered (1795) the mutual electrification of dissimilar metals upon contact and compiled a series of voltages for metals (1801). He studied the thermal expansion of air, observed diffusion, and established the conductivity of flame (1787). Discovered methane (1776) and explained its formation by the decomposition of animal and plant remains.
The unit of voltage, the volt, is named after him.
Coulomb conducted brilliant research in the field of electricity.
Pendant Charles Auguste (06/14/1736-08/23/1806) - French physicist and military engineer, member of the Paris Academy of Sciences (1803). Born in Angoulême in the family of an official. He graduated from the military engineering school in Mézières (1761), after which he spent several years in military service in Martinique, where he supervised the construction of the fleet. After returning to France, he served in the military engineering corps, devoting all his time to more attention scientific research.
Works in the field of mechanics, electricity and magnetism. The first scientific work, begun in Martinique, “On the application of the rules of maxima and minima to certain problems of statics relating to architecture,” determined the progress of structural mechanics in the 18th and 19th centuries. Formulated the laws of sliding and rolling friction in 1781. In 1784 he researched and designed torsion balances, with the help of which he established the fundamental law of electrostatics in 1785, and in 1788 extended it to the interactions of magnetic poles. He put forward the hypothesis of magnetism, according to which magnetic fluids are not free, but are associated with individual molecules that are polarized during the magnetization process. Constructed a magnetometer (1785).
The unit of charge, the pendant, is named after him.
Coulomb designed a highly sensitive torsion scale, having previously established that the force of twisting a thread depends on the substance of the thread, is proportional to the angle of twist and the fourth power of the diameter of the thread, and is inversely proportional to its length. Using these scales, Coulomb experimentally established that the forces of attraction and repulsion of charges are inversely proportional to the squares of the distances. Coulomb postulated the proportionality of the interaction force to the product of electric charges, i.e. during 4 years of intensive work from 1785 to 1789, he laid the foundation of modern electrostatics. Since electrostatic forces depend on distance in the same way as Newtonian forces, all the properties of Newtonian forces found in theoretical mechanics can be used here.
It should be noted that using also torsion balances, Cavendish in 1798 proved the validity of the law of gravity for ordinary (not celestial) bodies.
Cavendish Henry (10.10.1731-24.02.1810) – English physicist and chemist, member of the Royal Society of London (1760). Born in Nice into the family of a lord. In 1749-53 he studied at Cambridge University. He spent most of his life alone, completely devoting himself to scientific work in his own laboratory.
He published only those articles in which he was completely confident, which is why many works on electricity remained unknown. These works, published in 1879 by J. Maxwell, showed that back in 1771 he came to the conclusion that the force of electrostatic interaction is inversely proportional to the square of the distance. He introduced the concept of electrical capacity, discovered the influence of the environment on the capacitance of a capacitor, and determined the dielectric constant of a number of substances. In 1798 he measured gravitational force attraction of two small spheres, determined the gravitational constant, mass and average density Earth. He obtained hydrogen in 1766 and determined its properties, established the composition of water and showed that it can be obtained artificially, and determined the oxygen content in the air (1781).
From the very first cases of electric shock, speculation arose about “animal electricity”, the regulator of animal life. In 1773, John Walsh's memoir about the electric stingray appeared, and physiologists arose a hypothesis about the “animal essence”, which, like the electrical fluid, is responsible for the transfer of nerve signals.
Professor of anatomy at the University of Bologna Luigi Galvani (1737-1798) conducted electro-physiological experiments and came to the conclusion that the effect of frog muscle contraction from physiological and electrical influences is the same. The results amazed Volt, special attention who was attracted by one feature of the galvanic experiment: the transmission of a signal for muscle contraction by conductors homogeneous or composed of different metals was carried out in different ways.
Volta first conducted an experiment with the detection of a sour taste on the tongue if one end was applied to its tip, and the other end of an arc made of different metals was applied to the middle. He then began purely physical studies of contact electricity and obtained the law of contact voltages, arranging metals in a “series of voltages.” As a result, Volta invented a new device, which he first called an “artificial electric organ” and then an “electromotive apparatus.” The French later began to call it "galvanic or voltaic column".
The invention of galvanic cells (much more convenient electrical sources than electrostatic machines) significantly expanded the range of research on electricity. First of all, the identity of the electrical and galvanic “fluids” was shown, the difference between which first manifested itself in a number of physiological and chemical processes (electric shock, chemical action of current, etc.).
Even after the first studies in the field of electricity and magnetism, assumptions arose about the connection between them. The search for this connection intensified after the discovery of Coulomb's laws. The decisive experiment in this area was carried out in 1820 by Oersted, who discovered the deflection of a magnetic needle by a current-carrying conductor.
Oersted Hans Christian (08/14/1777–03/09/1851) - Danish physicist, permanent secretary of the Royal Danish Society (since 1815), honorary member of the St. Petersburg (1830) and other academies of sciences. Born in Rudkøbing in the family of a pharmacist. Graduated from the University of Copenhagen: pharmacist diploma (1797), doctorate (1799). From 1806 he was a professor at this university, and from 1829 he was also the director of the Copenhagen Polytechnic School.
Works in the field of electricity, acoustics, molecular physics. Oersted's scientific creativity is characterized by the search for relationships between various natural phenomena. His discovery of the effect of electric current on a magnetic needle led to the emergence of a new field of physics - electromagnetism. In 1822-23, independently of J. Fourier, he rediscovered the thermoelectric effect and built the first thermoelement. He experimentally studied the compressibility and elasticity of liquids and gases and invented the piezometer.
He was a brilliant lecturer and popularizer, organized the Society for the Propagation of Natural Science in 1824, and created the first physics laboratory in Denmark.
The unit of magnetic field strength, the oersted, is named after him.
One thing to note important fact in Oersted's experiment: the discovered effect did not fit into the Newtonian concept of interaction, where all forces were central. In the same 1820, the French physicists Biot and Felix Savard (1791-1836) experimentally studied the dependence of the magnetic field on the distance from the current-carrying conductor to the observation point. However, they were unable to obtain such a dependence in general form. This problem was solved by Laplace and the general law he obtained is called the Biot-Savart-Laplace law.
At the same time, Ampere discovered the interaction of currents, which he called electrodynamic.
Ampere Andre Marie (01/22/1775–06/10/1836) - French physicist, mathematician and chemist, member of the Paris (1814), St. Petersburg (1830) and other academies of sciences. Born in Lyon in the family of a businessman. Received home education. In 1801 he began teaching physics and chemistry at the central school of Burg. In 1805-24 he worked at the Polytechnic School in Paris (from 1809 - professor), from 1824 - professor at the Collège de France.
Physical works are devoted to electromagnetism. He established the law of interaction of electric currents (Ampere's law) and developed the theory of magnetism. According to this theory, all magnetic interactions are reduced to the interaction of circular electric molecular currents, each of which is equivalent to a flat magnet - a magnetic sheet. Ampère was the first to point out the close connection between electrical and magnetic processes. He discovered (1822) the magnetic effect of a coil with current - a solenoid, which is the equivalent of a permanent magnet, and put forward the idea of strengthening the magnetic field by placing an iron core inside the solenoid. In 1820 he proposed using electromagnetic phenomena to transmit signals, invented the commutator, and the electromagnetic telegraph. Formulated the concept of “kinematics”, conducted research in the field of philosophy and botany.
The unit of current, the ampere, is named after him.
Ampere also proposed a hypothesis according to which a magnet is a collection of currents, and derived a formula for the interaction of current elements. The theory he developed made it possible to explain various types of interactions: magnetostatic, electromagnetic and electrodynamic. The studies of the effect of magnets on current-carrying conductors conducted by Oersted, Ampere and other scientists and the rotation of a current-carrying conductor in a magnetic field discovered in 1821 by Faraday formed the basis for the creation of galvanometers, which in various modifications were widely used in the study of electromagnetic phenomena.
Michael Faraday (09/22/1791–08/25/1867) - English physicist, member of the Royal Society of London (1824), St. Petersburg Academy of Sciences (1830). Born in London into the family of a blacksmith. From the age of 12 he worked as a newspaper delivery boy, then as an apprentice in a bookbinding shop. I studied on my own. In 1813 he became an assistant to G. Davy at the Royal Institution in London, in 1825 - director of the laboratory, replacing G. Davy in this post, in 1833-62 - professor of the department of chemistry.
Work in the field of electricity, magnetism, magnetooptics, electrochemistry. Faraday's discovery of the rotation of a magnet around a current-carrying conductor and a current-carrying conductor around a magnet became the basis for a laboratory model of an electric motor and clearly revealed the connection between electrical and magnetic phenomena, which ultimately led to the discovery and establishment of the laws of electromagnetic induction. In 1835 he discovered extracurrents during closure and opening. Proved identity various types electricity: “animal”, “magnetic”, galvanic, thermoelectricity and electricity arising from friction. As a result of work on the study of the nature of electric current in solutions of acids, salts and alkalis, he discovered in 1833 the laws of electrolysis (Faraday's laws), which were an important argument in favor of the discreteness of electricity. Introduced the concepts of mobility, cathode, anode, ions, electrolysis, electrolytes, electrodes, and acquired a voltmeter. In 1845 he discovered diamagnetism, in 1847 - paramagnetism. He discovered the rotation of the plane of polarization of light in a magnetic field (Faraday effect), which was proof of the connection between light and magnetism and marked the beginning of magnetooptics.
Faraday was the first to introduce the concept of field, the idea of electric and magnetic lines of force. The idea of a field radically changed the idea of long-range action and space, which existed among Newton and his followers, as a passive container of bodies and electric charges. In 1837 he discovered the influence of dielectrics on electrical interaction and introduced the concept of dielectric constant. He expressed the idea of the propagation of electrical and magnetic interactions through an intermediate medium, the idea of the unity of the forces of nature (various types of energy) and their mutual transformation.
The unit of capacitance, the farad, is named in his honor.
Early research in the field of electricity was mainly focused on active elements - sources of electromotive force, and virtually no attention was paid to passive conductors. Ohm conducted systematic experimental and theoretical studies of conductivity and formulated his laws in integral and differential forms in 1827, introducing the concepts and precise definitions of electromotive force, electrical conductivity and current.
Ohm Georg Simon (03/16/1789-07/06/1854) - German physicist, corresponding member of the Berlin Academy (1839), member of the Turin and Bavarian Academy of Sciences, the Royal Society of London (1842), Copley Medal (1841). Born in Erlangen in the family of a mechanic. Graduated from the University of Erlangen, Doctor of Philosophy (1811). He taught mathematics, then physics in a number of gymnasiums. From 1833 - professor at the Nuremberg Higher Polytechnic School (from 1839 - rector), 1849-52 - at the University of Munich.
Work in the field of electricity, acoustics, optics. In 1826 he experimentally discovered the basic law of an electrical circuit (Ohm's law), and in 1827 he derived it theoretically. He established that the ear perceives as a simple tone only the sound caused by a simple harmonic vibration, other sounds - as the main tone and additional ones - overtones (Ohm's acoustic law).
The unit of electrical resistance, the ohm, is named after him.
At the same time, Ohm carried out his work using the analogy of electric current with heat flows of the French mathematician and physicist Jean Baptiste Joseph Fourier (1768-1830) between two bodies with different temperatures. However, his work went unnoticed for ten years. Simultaneously with Ohm's experiments, research was carried out in France by Antoine Cesar Becquerel (1788-1878), who determined the dependence of resistance on the length and cross-section of the conductor, and in England by Peter Barlow (1776-1862), who confirmed the constancy of the current throughout the entire circuit. A number of private laws, obtained at this time independently of Ohm, were summarized by Kirchhoff in his rules in 1845.
The first practical use of electrical phenomena in telegraphy gave a great impetus to electrical measurements. The creation of airborne and underwater telegraphs required the development of new methods of electrical measurements. In 1840, Wheatstone proposed his bridge method for accurate resistance measurements. Gauss laid the foundations of electromagnetic metrics, taking as the main three mechanical units (time, length and mass) and expressing all the others through them, as well as developing a number of new instruments.
Gauss Karl Friedrich (04/30/1777-02/23/1855) - German mathematician, astronomer and physicist, member of the Royal Society of London (1804), Paris (1820) and St. Petersburg Academy of Sciences (1824). Born in Braunschweig in the family of a plumber. He studied at the University of Göttingen in 1795-98, in 1799 he received an assistant professorship in Braunschweig, and from 1807 he was a professor at the University of Göttingen and director of the astronomical observatory.
Works in many areas of physics. In 1832 he created the absolute system of measures, in 1833, together with V. Weber, he built the first electromagnetic telegraph in Germany. In 1839 in the essay " General theory forces of attraction and repulsion acting inversely proportional to the square of the distance" laid out the foundations of potential theory (Ostrogradsky-Gauss theorem). In 1840, in the work "Dioptric Research" he developed the theory of constructing images in complex optical systems. In 1845 he came to the idea of the finiteness of the propagation of electromagnetic interactions. In 1829 he formulated the principle of least coercion (Gauss's principle). In 1818, he was one of the first to propose a hypothesis about the existence of non-Euclidean geometry.
The unit of magnetic induction - gauss - is named after him.
Work on metrology was continued by the German physicist Wilhelm Eduard Weber (1804-1891) and Maxwell. As a result, the idea of creating a unified system of measures arose and in 1881 the International Congress in Paris established international units of measurement.
A huge contribution to the development of electromagnetism was made by the work of Michael Faraday. One of the leading philosophical ideas physics of the 19th century was that all physical phenomena are manifestations of the same essence. Following this principle, in 1831 Faraday discovered the phenomenon of electromagnetic induction. He proposed a theory of this phenomenon, for the first time introducing the concepts of magnetic force lines and electromagnetic fields and expressing the idea of the propagation of magnetic disturbances in time. In 1833, the American physicist Joseph Henry (1797-1878) discovered the phenomenon of self-induction, and the Russian scientist Emil Christianovich Lenz (1804-1865) formulated his rule on the direction of induction currents in 1834.
In the mid-40s, German scientists Franz Ernst Neumann (1798-1895), Weber and Helmholtz developed induction theories that take into account that the interaction of electric charges depends on both the distance between them and the speeds.
In 1833-34 Faraday established the basic laws of electrolysis, laying the foundation for electrochemistry. He also experimentally proved that the electrical action propagates not only along straight lines, but also along curved lines, and the intermediate medium significantly affects this action. Thus, he confirmed that the interaction of two bodies occurs through the medium, and does not occur in accordance with the theory of long-range action at a distance, which was used in the simplest models for the mathematical interpretation of phenomena.
As a result of experiments with spherical capacitors with various insulating pads, Faraday formulated his theory of dielectric polarization, which was developed by the Italian physicist Ottaviano Fabrizio Mossotti (1791-1863).
In 1845, when passing light through an electromagnet, Faraday discovered a rotation of the plane of polarization, which he explained by the presence of magnetic fields in the light. He also discovered the phenomenon of diamagnetism.
In addition to numerous experimental discoveries, at the end of his life Faraday, in the fight against atomistic ideas about the continuity of only space, put forward an original idea: developing the concept of Boscovich, he introduced the concept of field. He says that not only is matter interpenetrable, but each atom of it extends throughout the entire solar system, maintaining its own center.
Also great practical significance Faraday's discoveries, because All machines in the modern electrical industry - generators (the first current generator was created by Faraday himself), transformers, electric motors - are based on electromagnetic induction. This also includes the telephone.
By the 60s of the 19th century, thanks to the work of Neumann, Weber and Helmholtz, electrodynamics was considered a fully formed science with clearly defined boundaries. However original ideas Faraday interested Maxwell, and he decided to give them a mathematical form. Introducing the concepts of displacement currents and field strengths, Maxwell first created the electrodynamics of dielectrics using Mossotti's theory. Extending these ideas with amendments to magnetism, he creates the theory of electromagnetic induction. As a result, the entire construction comes down to Maxwell’s famous six equations. These equations establish the continuity of phenomena and determine changes in the field, in contrast to the Newtonian model, where laws determine changes in the behavior of material particles. They connect events adjacent in space and time. Many saw a number logical errors and inconsistencies in Maxwell's theory. But it explained a lot, and by the end of the 19th century, the largest physicists adhered to the opinion expressed by Hertz: it is necessary to accept Maxwell’s equations as a hypothesis, postulates on which the entire theory of electromagnetism will be based.
Hertz Heinrich Rudolf (02.22.1857-01.01.1894) - German physicist, corresponding member of the Berlin Academy of Sciences (1889), member of a number of academies of sciences and scientific societies, awards of the Vienna, Paris, Turin Academy of Sciences, the Royal Society of London, etc. Born in Hamburg in the family of a lawyer. He graduated from the University of Berlin, doctorate (1880) and was an assistant to G. Helmholtz. From 1883 - privatdozent at the University of Kiel, in 1885-89 - professor at the Higher Technical School in Karlsruhe, from 1889 - at the University of Bonn.
The main works relate to electrodynamics and mechanics. In 1887, in his work “On Very Fast electrical vibrations"proposed a successful design of a generator of electromagnetic oscillations (Hertz vibrator) and a method for their detection (Hertz resonator), for the first time developing the theory of a vibrator emitting electromagnetic waves in space. He experimentally proved the existence of electromagnetic waves propagating in free space in accordance with Maxwell's theory. He gave the equations of electrodynamics symmetrical form, which clearly demonstrated the complete relationship between electrical and magnetic phenomena (Maxwell-Hertz electrodynamics). In 1887 he observed the external photoelectric effect, noting that the electric discharge is more intense when the electrodes are irradiated with ultraviolet light. "(1891) discovered the permeability of metals to cathode rays, laying the foundation for the study of these rays and the structure of matter. He built mechanics with the introduction of nonholonomic connections, the interpretation of a mechanical system as a system with a large number of degrees of freedom and the application of the principle shortest path or the least curvature.
The unit of frequency, the hertz, is named after him.
Following his equations and Faraday's ideas about the nature of light, Maxwell builds an electromagnetic theory of light, which describes the propagation of transverse electromagnetic waves. Additional prerequisites for this were also obtained by Weber and Kirchhoff when determining the speed of propagation of electromagnetic induction through a wire: it turned out to be equal to the speed of light. By this time, oscillations of the electrical discharge of a capacitor in a circuit with an induction coil had been discovered and studied, and in 1884 Hertz showed that these oscillations cause in space the appearance of waves consisting of electric and magnetic oscillations polarized perpendicular to each other. He also discovered reflection, refraction and interference of such waves. An important confirmation of the electromagnetic theory were the experiments of the Russian physicist Pyotr Nikolaevich Lebedev (1866-1912), who in 1900 measured the value of light pressure in full accordance with Maxwell's theory.
The Italian physicist Augusto Righi (1850-1920) developed these works and their results were summarized by him in 1897 in the book “Optics of Electrical Phenomena,” the very name of which speaks of the revolutionary nature of such a conclusion in the development of physics.
One of the most remarkable results practical application electromagnetic waves was the invention of radiotelegraphy in 1895 by Popov and the Italian researcher Guglielmo Marconi (1874-1937).
Popov Alexander Stepanovich (03/16/1859-01/13/1906) - Russian physicist and electrical engineer. Born in the village of Turinskie Rudniki (Ekaterinburg province) in the family of a priest. Graduated from St. Petersburg University (1882). In 1883-1901 he taught at military institutions in Kronstadt. Since 1901 - professor at the St. Petersburg Electrotechnical Institute (since 1905 - rector).
Work in the field of electrical engineering and radio engineering. In 1888 he repeated the experiments of G. Hertz and in 1889 he first pointed out the possibility of using electromagnetic waves to transmit signals. In 1894 he designed a generator of electromagnetic oscillations and a receiver with a sensitive element - a coherer, and also invented the first receiving antenna. He established that the antenna receiver responds to lightning discharges and created a lightning detector. On May 7, 1895, he demonstrated his lightning detector at a meeting of the physics department of the Russian Physicochemical Society and expressed the idea of the possibility of using it to transmit signals over a distance. At a meeting on March 24, 1896, he demonstrated the transmission of signals over a distance of 250 m. Somewhat later, G. Marconi created similar devices, conducted experiments with them and laid the foundation for the widespread use of radio communications, and in 1909 he received the Nobel Prize for this work, when Popov had already died. In 1897 he discovered the reflection of electromagnetic waves from objects (ships) located in the path of their propagation, which was the basis for radar.
Thus, by the end of the 19th century, the construction of classical physics was basically completed.
References
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