Electrodynamics is a branch of physics that studies the electromagnetic field in the most general case. Definition in electrodynamics What electrodynamics studies

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Pyatigorsk branch of the Volgograd State Medical University of the Ministry of Health of the Russian Federation

Abstract on the topicat:

"Electrodynamics"

Performed:

Student of group 211

Monina Marina

1. History of electrodynamics

2. Electrostatics

3. DC laws

1. History of electrodynamics

Electrodynamics is the science of the properties and patterns of behavior of a special type of matter - the electromagnetic field that interacts between electrically charged bodies and particles.

In electrodynamics there are four types of interaction:

Gravitational

Electromagnetic

Weak (interaction between elementary particles)

Electromagnetic interaction is the most important thing on earth.

Electrodynamics has its origins in Ancient Greece. The translation of the word electron is amber. Besides amber, many other bodies are also attracted. Both light and heavy objects are attracted to electrified bodies. In 1729, Gray discovered the transfer of charges over a distance. Charles Dufrais discovers two types of charges: glass and resin. Glass appears as a positive charge, and resin as a negative charge. Subsequently, James Clerk Maxwell completed the creation of the theory of electrodynamics, but the use of electrodynamics began only in the second half of the 19th century. Maxwell drew attention to the shortcomings of classical electrodynamics. The inconsistency with the law of conservation of charge was a sufficient argument to doubt its truth, since the laws of conservation are of a very general nature.

The mathematical consequences of Maxwell's modified system of equations were the statement about the conservation of energy in electromagnetic processes and the theoretical conclusion about the possibility of the existence of a field in the form of electromagnetic waves in empty space, independent of charges and currents. This last prediction found brilliant experimental confirmation in the famous experiments of Hertz and Popov, which laid the foundation for modern radio communications. The speed of propagation of electromagnetic waves calculated from the system turned out to be equal to the experimentally measured speed of propagation of light in a vacuum, which meant the unification of the practically previously independent sections of the physics of electromagnetism and optics into one complete theory.

The most important step forward in the development of the doctrine of electrical and magnetic phenomena was the invention of the first source of direct current - a galvanic cell. The history of this invention begins with the work of the Italian physician Luigi Galvani, dating back to the end of the 18th century. Galvani was interested in the physiological effects of electrical discharge. Since the 80s. XVIII century, he undertook a series of experiments to determine the effect of an electric discharge on the muscles of a dissected frog. He once discovered that when a spark flashed in an electric machine or when a Leyden jar was discharged, the frog's muscles contracted if they were touched at that time with a metal scalpel.

Interested in the observed effect, Galvani decided to check whether atmospheric electricity would have the same effect on the frog's legs. Indeed, having connected one end of the nerve of the frog's leg with a conductor to an insulated pole placed on the roof, and the other end of the nerve to the ground, he noticed that during a thunderstorm, the frog's muscles contracted from time to time.

Galvani then hung the dissected frogs by copper hooks hooked to their spinal cords near the garden's iron railing. He discovered that sometimes when the frog's muscles touched the iron fence, a muscle contraction occurred. Moreover, these phenomena were observed in clear weather. Consequently, Galvani decided, in this case it is no longer the thunderstorm that is the cause of the observed phenomenon.

To confirm this conclusion, Galvani performed a similar experiment in the room. He took a frog, whose spinal nerve was connected to a copper hook, and placed it on an iron plate. It turned out that when the copper hook touched the iron, the frog's muscles contracted.

Galvani decided that he had discovered “animal electricity,” that is, electricity that is produced in the body of a frog. When a frog's nerve is closed using a copper hook and an iron plate, a closed circuit is formed through which an electric charge (electric fluid or matter) runs, which causes muscle contraction.

Both physicists and doctors became interested in Galvani's discovery. Among the physicists was Galvani's compatriot, Alessandro Volta. Volta repeated Galvani’s experiments, and then decided to test how the frog’s muscles would behave if not (“animal electricity”), but electricity obtained by any of the known methods was passed through them. At the same time, he discovered that the frog's muscles contracted in the same way as in Galvani's experiment.

Having done this kind of research, Volta came to the conclusion that the frog is only a “device” that registers the flow of electricity, that no special “animal electricity” exists.

Volt proposed that the cause of electricity was the contact of two different metals.

It should be noted that Galvani already noticed the dependence of the force of convulsive contraction of the frog’s muscles on the type of metals that form the circuit through which electricity flows. However, Galvani did not pay serious attention to this. Volta, on the contrary, saw in it the possibility of constructing a new theory.

Disagreeing with the theory of “animal electricity,” Volta put forward the theory of “metallic electricity.” According to this theory, the cause of galvanic electricity is the contact of different metals.

Every metal, Volta believed, contains an electric fluid - a fluid that, when the metal is not charged, is at rest and does not manifest itself. But if you combine two different metals, the balance of electricity inside them will be disrupted, and the electric fluid will begin to move. In this case, the electrical fluid will move in some quantity from one metal to another, after which equilibrium will be restored again. But as a result of this, the metals become electrified: one is positive, the other is negative.

Volta confirmed these considerations experimentally. He was able to show that, indeed, when two metals simply come into contact, one of them acquires a positive charge and the other a negative one. Thus, Volta discovered the so-called contact potential difference. Volta performed the following experiment. On a copper disk attached to an ordinary electroscope instead of a ball, he placed the same disk, made of a different metal and having a handle. When applied, the discs came into contact in a number of places.

As a result of this, a contact potential difference appeared between the disks (in Volta’s terminology, a “voltage difference” arose between the disks).

In order to detect the “voltage difference” that appears when different metals come into contact, which, generally speaking, is small, Volta raised the upper disk and then the leaves of the electroscope noticeably diverged. This was caused by the fact that the capacitance of the capacitor formed by the disks decreased, and the potential difference between them increased by the same amount.

But the discovery of contact potential differences between different metals could not yet explain Galvani’s experiments with frogs. Additional assumptions were needed.

But in Galvani's experience, not only metals were combined. The chain also included frog muscles, which also contained fluid.

He suggested that all conductors should be divided into two classes: conductors of the first kind - metals and some other solids, and conductors of the second kind - liquids. At the same time, Volta decided that a potential difference arises only when conductors of the first kind come into contact.

This assumption explained Galvani's experiment. As a result of the contact of two different metals, the balance of electricity in them is disrupted. This balance is restored as a result of the metals being combined through the frog's body. Thus, the electrical balance is constantly disturbed and restored all the time, which means that electricity is moving all the time.

This explanation of Galvani's experience is incorrect, but it gave Volta the idea of creating a direct current source - a galvanic battery. And in 1800 Volta built the first galvanic battery - the Voltaic Pole.

The Voltaic column consisted of several dozen round silver and zinc plates stacked on top of each other. Cardboard mugs soaked in salt water were placed between pairs of plates. Such a device served as a source of continuous electric current.

It is interesting that Volta used direct human sensations as an argument for the existence of a continuous electric current. He wrote that if the outer plates are closed through the human body, then at first, as in the case of the Leyden jar, the person experiences a shock and tingling sensation. Then there is a feeling of continuous burning, “which not only does not subside, but becomes stronger and stronger, soon becoming unbearable, until the chain opens.”

The invention of the Voltaic Column, the first source of direct current, was of great importance for the development of the doctrine of electricity and magnetism. As for the explanation of the action of this Volta device, it was erroneous. This was soon noticed by some scientists.

Indeed, according to Volta's theory, it turned out that no changes occur to the galvanic element during its operation. An electric current flows through a wire, heats it, can charge a Leyden jar, etc., but the galvanic cell itself remains unchanged. Such a device is nothing more than a perpetual motion machine, which, without changing, produces a change in the surrounding bodies, including mechanical work.

By the end of the 18th century. Among scientists there is already a widespread opinion about the impossibility of the existence of a perpetual motion machine. Therefore, many of them rejected the theory of the action of the galvanic element invented by Volta.

In contrast to Volta's theory, the chemical theory of the galvanic element was proposed. Soon after its invention, it was noticed that chemical reactions occur in a galvanic cell, in which metals and liquids enter. The correct chemical theory of the action of the galvanic element replaced Volta's theory.

After the discovery of the Voltaic Column, scientists from different countries began to study the effects of electric current. At the same time, the galvanic element itself was improved. Already Volta, along with the “pillar”, began to use a more convenient cup battery of galvanic cells. To study the effects of electric current, they began to build batteries with more and more elements.

The largest battery at the very beginning of the 19th century. built by Russian physicist Vasily Vladimirovich Petrov in St. Petersburg. His battery consisted of 4,200 zinc and copper circles. The mugs were placed horizontally in the box and separated by paper spacers soaked in ammonia.

The first steps in the study of electric current related to its chemical actions. Already in the same year in which Volta invented the galvanic battery, the property of electric current to decompose water was discovered. Following this, solutions of some salts were decomposed by electric current. In 1807, the English chemist Davy discovered new elements by electrolysis of caustic alkali melts: potassium and sodium.

The study of the chemical effect of current and the elucidation of the chemical processes occurring in galvanic cells led scientists to develop the theory of the passage of electric current through electrolytes.

Following the study of the chemical effects of current, scientists turned to its thermal and optical effects. The most interesting result of these studies was at the very beginning of the 19th century. was the discovery of the electric arc by Petrov.

The discovery made by Petrov was forgotten. Many, especially foreign, scientists did not know about him, since Petrov’s book was written in Russian. Therefore, when Davy rediscovered the electric arc in 1812, he was considered the author of this discovery.

The most important event, which soon led to new ideas about electrical and magnetic phenomena, was the discovery of the magnetic action of electric current.

2. Electrostatics

Electrostatics is a part of electrodynamics that studies stationary electric charges.

Electric charge

Particles interacting with each other with forces that decrease with increasing distance in the same way as the forces of universal gravity, but exceeding the gravitational forces many times, then these particles are said to have an electric charge. There are particles without an electric charge, but an electric charge does not exist without a particle. The interaction between charged particles is called electromagnetic. The presence of an electric charge on particles means the existence of certain force interactions between them. In a free state, only electrons and protons can exist for an unlimited time. If an elementary particle has a charge, then its value is strictly defined.

Charged bodies

Electromagnetic forces play a huge role in nature due to the fact that all bodies contain electrically charged particles. The action of electromagnetic forces between bodies is not detected, because bodies in their normal state are electrically neutral. Positively and negatively charged particles are connected to each other by electrical forces and form neutral systems.

A macroscopic body is electrically charged if it contains an excess amount of elementary particles with any one sign of charge.

In order to electrify a body, it is necessary to separate part of the negative charge from the positive charge associated with it. This can be done using friction.

Law of conservation of electric charge

When bodies are electrified, the law of conservation of electric charge is satisfied. This law is valid for a closed system. The validity of the law of conservation of electric charge is confirmed by observations of a huge number of transformations of elementary particles.

Coulomb's law

The fundamental law of electrostatics is the experimentally established law of the French physicist Charles Coulomb in 1785. XVIII

However, the story of its discovery begins earlier. This story shows one of the ways in which physics develops - the way of using analogy. Epinus already guessed that the force of interaction between electric charges is inversely proportional to the square of the distance between them. And this guess arose on the basis of some analogy between the forces of gravity and electrical forces. But analogy is not proof. The conclusion from an analogy always requires verification. Relying only on analogy can lead to incorrect results. Epinus did not check the validity of this analogy, and therefore his statement was only speculative.

Coulomb's law applies to point charges. Point charges are the sizes of bodies that are many times smaller than the distance between them. The interaction forces between two stationary point charged bodies in a vacuum are directly proportional to the product of the charge modules and inversely proportional to the square of the distance between them.

With the help of torsion balances, it was possible to establish stationary charged bodies with each other. Coulomb found a simple way to change the charge of one of the balls by 2, 4 or more times by connecting it with the same uncharged ball. In this case, the charge is distributed equally between the balls, which reduced the charge under study in a certain ratio.

One Coulomb is a charge passing through the cross-section of a conductor at a current strength of one Ampere in one second.

Electric field

After the discovery of Coulomb's law, the theory of long-range action completely replaces the theory of short-range action. And only in the 19th century. Faraday revives the theory of short-range action. However, its general recognition begins in the second half of the 19th century, after the experimental proof of Maxwell’s theory.

According to Faraday's idea, electric charges do not act on each other directly. Each of them creates an electric field in the surrounding space. The field of one charge acts on another charge, and vice versa. As you move away from the charge, the field weakens.

Success in the theory of short-range interaction came after studying the electronic interactions of moving charged particles. First, the existence of time-varying fields was proven, and only after that a conclusion was made about the reality of the electric field of stationary charges. Based on Faraday's ideas, Maxwell was able to theoretically prove that electromagnetic interactions must propagate in space with a finite speed. This means that if you move one charge slightly, the force acting on the other charge will change, but not at the same instant, but only after some time.

The existence of a certain process in the space between interacting bodies, which is divided by finite time, is the main thing that distinguishes the theory of short-range action from the theory of action at a distance. The main property of the electric field is its action on electric charges with some force. The electric field of stationary charges is called electrostatic. It doesn't change over time. An electrostatic field is created only by an electric charge. It exists in the space surrounding these charges and is inextricably linked with them.

According to the theory of short-range interaction, the interaction between charged particles is carried out through an electric field.

An electric field is a special form of matter that exists regardless of our ideas about it. Proof of the reality of the electric field is the finite speed of propagation of electromagnetic interactions.

Electric field strength

An electric field is detected by the forces acting on a charge. If you alternately place small charged bodies at the same point in the field and measure the forces, you will find that the force acting on the charge from the field is directly proportional to this charge. The ratio of the force acting on a charge placed at a given point in the field to this charge for each point in the field does not depend on the charge and can be considered as a characteristic of the field. This characteristic is called electric field strength. Like force, field strength is a vector quantity. The field strength is equal to the ratio of the force with which the field acts on a point charge to this charge.

Electric field lines

The electric field is invisible to the human eye. Nevertheless, the distribution of the field in space can be made visible. Continuous lines whose tangents at each point through which they pass coincide with the tension vectors. These lines are called electric field lines or tension lines. An electric field whose strength is the same at all points in space is called homogeneous.

3. DC laws

Electricity

When charged particles move in a conductor, they are transferred from one place to another. If charged particles undergo random thermal motion, like free electrons in a metal, then charge transfer does not occur. Electric charge moves through the cross-section of a conductor only if, in addition to random motion, electrons participate in ordered motion. In this case, they say that an electric current is established in the conductor.

Electric current is the ordered movement of charged particles. Electric current arises from the ordered movement of free electrons or ions. Electric current has a certain direction. The direction of current is taken to be the direction of movement of positively charged particles. If the current is formed by the movement of negatively charged particles, then the direction of the current is considered opposite to the direction of movement of the particles.

Electric current exists due to the actions or phenomena that accompany it:

a) the conductor through which current flows heats up

b) electric current can change the chemical composition of the conductor

c) current shows the force effect on neighboring currents and magnetized bodies

The magnetic effect of current, in contrast to chemical and thermal, is the main one.

If an electric current is established in a circuit, this means that an electric charge is constantly being transferred through the cross-section of the conductor. The charge transferred per unit time serves as the main quantitative characteristic of current, called current strength.

The current strength is equal to the ratio of the charge transferred through the cross section of the conductor during a time interval to this time interval. If the current strength does not change over time, then the current is called constant. Current strength is a scalar quantity. It can be both negative and positive. The strength of the current depends on the charge carried by each particle, the concentration of the particles, the speed of their directional movement and the cross-sectional area of the conductor. Current strength is expressed in amperes. This unit is established on the basis of the magnetic interaction of currents. Current strength is measured with ammeters. The speed of ordered movement of electrons is very low (about 0.1 mm/s). Current strength is the main quantitative characteristic of electric current.

For the existence and occurrence of a constant electric current in a substance, the presence of free charged particles is necessary. To create and maintain the ordered movement of charged particles, a force is required that acts on them in a certain direction. Typically, it is the electric field inside the conductor that causes and maintains the ordered movement of charged particles. If there is an electric field inside a conductor, then there is a potential difference between the ends of the conductor. When the potential difference does not change over time, a constant electric current is established in the conductor.

Ohm's law for a circuit section

For each conductor, there is a certain dependence of the current strength on the applied potential difference at the ends of the conductor. This dependence is expressed by the current-voltage characteristic of the conductor.

It is found by measuring the current in a conductor at various voltage values. The simplest form is the current-voltage characteristic of metal conductors and electrolyte solutions. For the first time, the current-voltage characteristic for metals was established by the German scientist Georg Ohm.

According to Ohm's law, for a section of a circuit, the current strength is directly proportional to the applied voltage and inversely proportional to the resistance of the conductor.

The main electrical characteristic of a conductor is resistance. The current strength in the conductor at a given voltage depends on this value. Conductor resistance is a measure of the conductor's resistance to the establishment of electric current in it. Resistance depends on the material of the conductor and its geometric dimensions. The resistivity is numerically equal to the resistance of a conductor shaped like a cube with an edge of one meter, if the current is directed along the normal to two opposite faces of the cube. The unit of conductor resistance, based on Ohm's law, is called an ohm. The unit of resistivity is Ohm * m. Ohm's law allows us to determine the resistance of a conductor.

Current measurement

To measure the current in a conductor, an ammeter is connected in series with this conductor. If you connect an ammeter to an outlet, a short circuit will occur.

In order to measure the voltage on a section of a circuit with resistance, a voltmeter is connected in parallel to it. The voltage on the voltmeter matches the voltage on the circuit section.

With the ordered movement of charged particles in a conductor, the electric field does work; it is usually called the work of current. The work done by the current on a section of the circuit is equal to the product of the current, voltage and time during which the work was done.

Any electrical device is designed to consume a certain energy per unit of time. Therefore, along with the work of current, the concept of current power is very important.

Current power is equal to the ratio of current work over time to this time interval.

The electric field of charged particles is not capable of maintaining a constant current in the circuit. Any forces acting on electrically charged particles, with the exception of forces of electrostatic origin, are called external forces.

When a circuit is closed, an electric field is created in all conductors of the circuit. Inside the current source, charges move under the influence of external forces against Coulomb forces, and throughout the rest of the circuit they are driven by an electric field.

The action of external forces is characterized by an important physical quantity called electromotive force. Electromotive force in a closed loop is the ratio of the work done by external forces when moving a charge along the loop to the charge. The electromotive force of a galvanic cell is the work done by external forces when moving a single positive charge inside the element from one pole to the other. The work of external forces cannot be expressed through a potential difference, since external forces are non-potential and their work depends on the shape of the trajectory. Direct current cannot exist in a closed circuit unless external forces act in it.

Joule-Lenz law

The Joule-Lenz law is a law that determines the amount of heat that a current-carrying conductor releases into the environment.

The Joule-Lenz law is formulated as follows: the amount of heat released by a conductor carrying current is equal to the product of the square of the current strength, the resistance of the conductor and the time the current passes through the conductor.

Ohm's law for a complete circuit

Source resistance is often called internal resistance in contrast to the external resistance of a circuit. Ohm's law for a closed circuit relates the current in the circuit, the emf and the total resistance of the circuit. This connection can be established theoretically if we use the law of conservation of energy and the Joule-Lenz law. The product of the current and the resistance of a section of a circuit is called the voltage drop across that section. Thus, the EMF is equal to the sum of the voltage drops in the internal and external sections of the closed circuit.

The current strength in a complete circuit is equal to the ratio of the circuit's emf to its total resistance. The current strength depends on three quantities: EMF, resistance of the external and internal sections of the circuit. The internal resistance of the current source does not have a noticeable effect on the current strength if it is small compared to the resistance of the external part of the circuit.

Conclusion

electrodynamics conductor resistance

Having considered all of the above, we see that the laws of electrodynamics mainly depend on each other and to discover a new law we have to consider and check all the laws almost from the very beginning. We also understand that in our time, we can’t live without all these laws, so to speak. They apply everywhere. Each person has his own magnetic field. But except for scientists, no one thinks about the fact that if all this had not happened, people would have stopped at the first stages of development.

The goal set for the work, to consider one of the main branches of physics - electrodynamics, can be said to be fulfilled, and everyone who reads it will be able to understand the importance and essence of physics, in general, and each law or any discovery separately.

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Basic equations of electrodynamics

The main formulas that describe the behavior of the electromagnetic field and its direct interaction with charged bodies are Maxwell’s equations, which determine the probable actions of a free electromagnetic field in a medium and vacuum, as well as the general generation of the field by sources.

Among these provisions in physics it is possible to highlight:

Gauss's theorem for the electric field - intended to determine the generation of an electrostatic field by positive charges;
hypothesis of closed field lines - promotes the interaction of processes within the magnetic field itself;
Faraday's law of induction - establishes the generation of electric and magnetic fields by the variable properties of the environment.

In general, the Ampere-Maxwell theorem is a unique idea about the circulation of lines in a magnetic field with the gradual addition of displacement currents introduced by Maxwell himself, which precisely determines the transformation of the magnetic field by moving charges and the alternating action of the electric field.

Charge and force in electrodynamics

In electrodynamics, the interaction of force and charge of the electromagnetic field comes from the following joint definition of the electric charge $q$, energy $E$ and magnetic $B$ fields, which are established as a fundamental physical law based on the entire set of experimental data. The formula for the Lorentz force (within the idealization of a point charge moving at a certain speed) is written with the replacement of the speed $v$.

Conductors often contain a huge amount of charges, therefore, these charges are fairly well compensated: the number of positive and negative charges is always equal to each other. Consequently, the total electric force that constantly acts on the conductor is also zero. The magnetic forces operating on individual charges in a conductor are ultimately not compensated, because in the presence of current, the speeds of movement of the charges are always different. The equation for the action of a conductor with current in a magnetic field can be written as follows: $G = |v ⃗ |s \cos(a) $

If we study not a liquid, but a full and stable flow of charged particles as a current, then the entire energy potential passing linearly through the area for $1s$ will be the current strength equal to: $I = ρ| \vec (v) |s \cos(a) $, where $ρ$ is the charge density (per unit volume in the total flow).

Note 2

If the magnetic and electric field systematically changes from point to point on a specific site, then in the expressions and formulas for partial flows, as in the case of liquid, the average values $E ⃗ $ and $B ⃗$ on the site must be entered.

The special position of electrodynamics in physics

The significant position of electrodynamics in modern science can be confirmed through the famous work of A. Einstein, in which the principles and foundations of the special theory of relativity were outlined in detail. The scientific work of the outstanding scientist is called “On the electrodynamics of moving bodies,” and includes a huge number of important equations and definitions.

As a separate field of physics, electrodynamics consists of the following sections:

the doctrine of the field of stationary but electrically charged physical bodies and particles;
the doctrine of the properties of electric current;
the doctrine of the interaction of magnetic field and electromagnetic induction;
the study of electromagnetic waves and oscillations.

All of the above sections are united into one by the theorem of D. Maxwell, who not only created and presented a coherent theory of the electromagnetic field, but also described all its properties, proving its real existence. The work of this particular scientist showed the scientific world that the electric and magnetic fields known at that time are just a manifestation of a single electromagnetic field operating in different reference systems.

A significant part of physics is devoted to the study of electrodynamics and electromagnetic phenomena. This area largely lays claim to the status of a separate science, since it not only explores all the patterns of electromagnetic interactions, but also describes them in detail through mathematical formulas. Deep and long-term research in electrodynamics has opened new ways for the use of electromagnetic phenomena in practice, for the benefit of all mankind.

Electrodynamics- a branch of physics that studies the electromagnetic field in the most general case (that is, time-dependent variable fields are considered) and its interaction with bodies that have an electric charge (electromagnetic interaction). The subject of electrodynamics includes the connection between electrical and magnetic phenomena, electromagnetic radiation (in different conditions, both free and in various cases of interaction with matter), electric current (generally speaking, variable) and its interaction with the electromagnetic field (electric current can be considered when this is like a collection of moving charged particles). Any electrical and magnetic interaction between charged bodies is considered in modern physics as occurring through an electromagnetic field, and, therefore, is also the subject of electrodynamics.

Most often, the term electrodynamics by default means classical (not affecting quantum effects) electrodynamics; To denote the modern quantum theory of the electromagnetic field and its interaction with charged particles, the stable term quantum electrodynamics is usually used.

Sections of electrodynamics

Basic concepts and laws of electrostatics

Electrostatics- a section of the study of electricity that studies the interaction of stationary electric charges.

Electrostatic (or Coulomb) repulsion occurs between similarly charged bodies, and electrostatic attraction occurs between oppositely charged bodies. The phenomenon of repulsion of like charges underlies the creation of an electroscope - a device for detecting electric charges.

Coulomb's Law: the force of interaction between two stationary point charges in a vacuum is directly proportional to the product of the charge moduli and inversely proportional to the square of the distance between them:

The proportionality coefficient k in this law is equal to:

In SI, the coefficient k is written as

where ε0 = 8.85·10−12 F/m (electric constant).

Electric field strength

Point charges are those charges the distances between which are much larger than their sizes.

Electric charges interact with each other using an electric field. To qualitatively describe the electric field, a force characteristic is used, which is called the electric field strength. The electric field strength is equal to the ratio of the force acting on a test charge placed at a certain point in the field to the magnitude of this charge:

The direction of the voltage vector coincides with the direction of the force acting on the positive test charge. [E] = B/m. From Coulomb’s law and the definition of field strength it follows that the field strength of a point charge is equal to

where q is the charge creating the field; r is the distance from the point where the charge is located to the point where the field is created. If the electric field is created not by one, but by several charges, then to find the strength of the resulting field, the principle of superposition of electric fields is used: the strength of the resulting field is equal to the vector sum of the field strengths created by each of the source charges separately:

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Let's find the work of moving a positive charge by Coulomb forces in a uniform electric field. Let the field move charge q from point 1 to point 2:

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It follows that:

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Ohm's law for a section of a circuit has the form:

The proportionality coefficient R, called electrical resistance, is a characteristic of the conductor [R] = Ohm. The resistance of a conductor depends on its geometry and material properties.

where l is the length of the conductor, ρ is the resistivity, S is the cross-sectional area. ρ is a characteristic of the material and its state. [ρ] = Ohm m.

Conductors can be connected in series. The resistance of such a connection is found as the sum of the resistances:

With a parallel connection, the reciprocal of the resistance is equal to the sum of the inverse resistances:

In order for electric current to flow in a circuit for a long time, the circuit must contain current sources. Current sources are quantitatively characterized by their electromotive force (EMF). This is the ratio of the work done by external forces when transferring electrical charges through a closed circuit to the amount of charge transferred:

If a load resistance R is connected to the terminals of the current source, then a current will flow in the resulting closed circuit, the strength of which can be calculated using the formula:

This relationship is called Ohm's law for a complete circuit.

An electric current running through conductors heats them, doing work:

where t is time, I is current strength, U is potential difference, q is the passed charge.

Basic concepts and laws of magnetostatics

A characteristic of a magnetic field is magnetic induction B. Since this is a vector, both the direction of this vector and its magnitude should be determined. The direction of the magnetic induction vector is associated with the orienting effect of the magnetic field on the magnetic needle. The direction of the magnetic induction vector is taken to be the direction from the south pole S to the north pole N of the magnetic needle, which is freely established in the magnetic field.

The direction of the magnetic induction vector of a straight conductor carrying current can be determined using the gimlet rule: if the direction of the translational movement of the gimlet coincides with the direction of the current in the conductor, then the direction of rotation of the gimlet handle coincides with the direction of the magnetic induction vector.

The magnitude of the magnetic induction vector is the ratio of the maximum force acting from the magnetic field on a section of a conductor carrying current to the product of the current strength and the length of this section:

The unit of magnetic induction is called tesla (1 Tesla).

Magnetic flux Φ through a contour surface of area S is a quantity equal to the product of the magnitude of the magnetic induction vector by the area of this surface and the cosine of the angle between the magnetic induction vector B and the normal to the surface n:

The unit of magnetic flux is the weber (1 Wb).

A current-carrying conductor placed in a magnetic field is acted upon by an Ampere force.

Ampere's law:

A section of conductor with a current of strength I and length l, placed in a uniform magnetic field with induction B, is acted upon by a force whose modulus is equal to the product of the modulus of the magnetic induction vector by the current strength, by the length of the section of the conductor located in the magnetic field, and by the sine of the angle between direction of vector B and conductor with current:

The direction of the Ampere force is determined using the left-hand rule:

if the left hand is positioned so that the component of the magnetic induction vector perpendicular to the conductor enters the palm, and four extended fingers indicate the direction of the current, then the thumb bent by 90◦ will indicate the direction of the Ampere force.

An electric charge moving in a magnetic field is affected by Lorentz force. The Lorentz force modulus is equal to the product of the charge modulus and the magnetic induction vector modulus and the sine of the angle between the magnetic induction vector and the velocity vector of the moving charge:

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where L is the inductance of the conductor creating the field; I is the current flowing through this conductor.

Electromagnetic oscillations and waves

An oscillating circuit is an electrical circuit consisting of a capacitor with capacitance C and a coil with inductance L connected in series (see figure).

DEFINITION

Electromagnetic field- this is a type of matter that manifests itself in the interaction of charged bodies.

Electrodynamics for dummies

The electromagnetic field is often divided into electric and magnetic fields. The properties of electromagnetic fields and the principles of their interaction are studied by a special branch of physics called electrodynamics. In electrodynamics itself, the following sections are distinguished:

electrostatics;
magnetostatics;
electrodynamics of continuum;
relativistic electrodynamics.

Electrodynamics is the basis for the study and development of optics (as a branch of science) and the physics of radio waves. This branch of science is the foundation for radio engineering and electrical engineering.

Classical electrodynamics, in describing the properties of electromagnetic fields and the principles of their interaction, uses Maxwell’s system of equations (in integral or differential forms), supplementing it with a system of material equations, boundary and initial conditions. According to Maxwell, there are two mechanisms for the emergence of a magnetic field. This is the presence of conduction currents (moving electric charge) and a time-varying electric field (presence of displacement currents).

Maxwell's equations

The basic laws of classical electrodynamics (Maxwell's system of equations) are the result of a generalization of experimental data and have become the quintessence of the electrodynamics of a stationary medium. Maxwell's equations are divided into structural and material. Structural equations are written in two forms: integral and differential form. Let's write Maxwell's equations in differential form (SI system):

where is the electric field strength vector; - vector of magnetic induction.

where is the magnetic field strength vector; - dielectric displacement vector; - current density vector.

where is the electric charge distribution density.

Maxwell's structural equations in differential form characterize the electromagnetic field at each point in space. If charges and currents are distributed continuously in space, then the integral and differential forms of Maxwell's equations are equivalent. However, if there are discontinuity surfaces, then the integral form of writing Maxwell's equations is more general. (The integral form of writing Maxwell’s equations can be found in the “Electrodynamics” section). To achieve mathematical equivalence of the integral and differential forms of Maxwell's equations, the differential notation is supplemented with boundary conditions.

From Maxwell's equations it follows that an alternating magnetic field generates an alternating electric field and vice versa, that is, these fields are inseparable and form a single electromagnetic field. The sources of the electric field can be either electric charges or a time-varying magnetic field. Magnetic fields are excited by moving electric charges (currents) or alternating electric fields. Maxwell's equations are not symmetric with respect to electric and magnetic fields. This happens because electric charges exist, but magnetic charges do not.

Material equations

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.

Examples of problem solving

EXAMPLE 1

Exercise

Write down Maxwell's system of structural equations for stationary fields.

Solution

If we are talking about stationary fields, then we mean that: . Then Maxwell’s system of equations takes the form:

The sources of the electric field in this case are only electric charges. The sources of the magnetic field are conduction currents. In our case, the electric and magnetic fields are independent of each other. This makes it possible to study separately a constant electric field and a separate magnetic field.

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 where Draw a graph).

Solution

As a basis for solving the problem, we use the equation from Maxwell’s system of equations in integral form:

Let's define the bias current as:

Let's find the partial derivative using the given dependence B(t):

FUNDAMENTALS OF ELECTRODYNAMICS. ELECTROSTATICS

FUNDAMENTALS OF ELECTRODYNAMICS

Electrodynamics- the science of the properties of the electromagnetic field.

Electromagnetic field- determined by the movement and interaction of charged particles.

Manifestation of electric/magnetic field- this is the action of electric/magnetic forces:
1) frictional forces and elastic forces in the macrocosm;
2) the action of electric/magnetic forces in the microcosm (atomic structure, coupling of atoms into molecules,
transformation of elementary particles)

Discovery of the electric/magnetic field- J. Maxwell.

ELECTROSTATICS

The branch of electrodynamics studies electrically charged bodies at rest.

Elementary particles may have email charge, then they are called charged;
- interact with each other with forces that depend on the distance between particles,
but exceed many times the forces of mutual gravity (this interaction is called
electromagnetic).

Email charge- physical value determines the intensity of electric/magnetic interactions.
There are 2 signs of electric charges: positive and negative.
Particles with like charges repel, and particles with unlike charges attract.
A proton has a positive charge, an electron has a negative charge, and a neutron is electrically neutral.

Elementary charge- a minimum charge that cannot be divided.
How can we explain the presence of electromagnetic forces in nature?
- All bodies contain charged particles.
In the normal state of the body, el. neutral (since the atom is neutral), and electric/magnetic. powers are not manifested.

Body is charged, if it has an excess of charges of any sign:
negatively charged - if there is an excess of electrons;
positively charged - if there is a lack of electrons.

Electrification of bodies- this is one of the ways to obtain charged bodies, for example, by contact).
In this case, both bodies are charged, and the charges are opposite in sign, but equal in magnitude.

Law of conservation of electric charge.

In a closed system, the algebraic sum of the charges of all particles remains unchanged.
(... but not the number of charged particles, since there are transformations of elementary particles).

Closed system

A system of particles into which charged particles do not enter from the outside and do not exit.

Coulomb's law

Basic law of electrostatics.

The force of interaction between two point fixed charged bodies in a vacuum is directly proportional
the product of the charge modules and is inversely proportional to the square of the distance between them.

When bodies are considered point bodies? - if the distance between them is many times greater than the size of the bodies.
If two bodies have electric charges, then they interact according to Coulomb's law.

Unit of electric charge
1 C is a charge passing through the cross-section of a conductor in 1 second at a current of 1 A.
1 C is a very large charge.
Elemental charge:

ELECTRIC FIELD

There is an electrical charge around, materially.
The main property of the electric field: the action with force on the electric charge introduced into it.

Electrostatic field- the field of a stationary electric charge does not change with time.

Electric field strength.- quantitative characteristics of el. fields.
is the ratio of the force with which the field acts on the introduced point charge to the magnitude of this charge.
- does not depend on the magnitude of the introduced charge, but characterizes the electric field!

Tension vector direction
coincides with the direction of the force vector acting on a positive charge, and opposite to the direction of the force acting on a negative charge.

Point charge field strength:

where q0 is the charge creating the electric field.
At any point in the field, the intensity is always directed along the straight line connecting this point and q0.

ELECTRIC CAPACITY

Characterizes the ability of two conductors to accumulate electrical charge.
- does not depend on q and U.
- depends on the geometric dimensions of the conductors, their shape, relative position, electrical properties of the medium between the conductors.

SI units: (F - farad)

CAPACITORS

Electrical device that stores charge
(two conductors separated by a dielectric layer).

Where d is much smaller than the dimensions of the conductor.

Designation on electrical diagrams:

The entire electric field is concentrated inside the capacitor.
The charge of a capacitor is the absolute value of the charge on one of the capacitor plates.

Types of capacitors:
1. by type of dielectric: air, mica, ceramic, electrolytic
2. according to the shape of the plates: flat, spherical.
3. by capacity: constant, variable (adjustable).

Electrical capacitance of a flat capacitor

where S is the area of the plate (plating) of the capacitor
d - distance between plates
eo - electrical constant
e - dielectric constant of the dielectric

Including capacitors in an electrical circuit

parallel

sequential

Then the total electrical capacity (C):

when connected in parallel

when connected in series

DC AC CONNECTIONS

Electricity- ordered movement of charged particles (free electrons or ions).
In this case, electricity is transferred through the cross section of the conductor. charge (during the thermal movement of charged particles, the total transferred electrical charge = 0, since positive and negative charges are compensated).

Email direction current- it is conventionally accepted to consider the direction of movement of positively charged particles (from + to -).

Email actions current (in conductor):

thermal effect of current- heating of the conductor (except for superconductors);

chemical effect of current - appears only in electrolytes. Substances that make up the electrolyte are released on the electrodes;

magnetic effect of current(main) - observed in all conductors (deflection of the magnetic needle near a conductor with current and the force effect of the current on adjacent conductors through a magnetic field).

OHM'S LAW FOR A CIRCUIT SECTION

where , R is the resistance of the circuit section. (the conductor itself can also be considered a section of the circuit).

Each conductor has its own specific current-voltage characteristic.

RESISTANCE

Basic electrical characteristics of a conductor.
- according to Ohm's law, this value is constant for a given conductor.

1 Ohm is the resistance of a conductor with a potential difference at its ends
at 1 V and the current strength in it is 1 A.

Resistance depends only on the properties of the conductor:

where S is the cross-sectional area of the conductor, l is the length of the conductor,
ro - resistivity characterizing the properties of the conductor substance.

ELECTRICAL CIRCUITS

They consist of a source, a consumer of electric current, wires, and a switch.

SERIES CONNECTION OF CONDUCTORS

I - current strength in the circuit
U - voltage at the ends of the circuit section

PARALLEL CONNECTION OF CONDUCTORS

I - current strength in an unbranched section of the circuit
U - voltage at the ends of the circuit section
R - total resistance of the circuit section

Remember how measuring instruments are connected:

Ammeter - connected in series with the conductor in which the current is measured.

Voltmeter - connected in parallel to the conductor on which the voltage is measured.

DC OPERATION

Current work- this is the work of the electric field to transfer electric charges along the conductor;

The work done by the current on a section of the circuit is equal to the product of the current, voltage and time during which the work was performed.

Using the formula of Ohm's law for a section of a circuit, you can write several versions of the formula for calculating the work of the current:

According to the law of conservation of energy:

The work is equal to the change in the energy of a section of the circuit, so the energy released by the conductor is equal to the work of the current.

In the SI system:

JOULE-LENZ LAW

When current passes through a conductor, the conductor heats up and heat exchange occurs with the environment, i.e. the conductor gives off heat to the bodies surrounding it.

The amount of heat released by a conductor carrying current into the environment is equal to the product of the square of the current strength, the resistance of the conductor and the time the current passes through the conductor.

According to the law of conservation of energy, the amount of heat released by a conductor is numerically equal to the work done by the current flowing through the conductor during the same time.

In the SI system:

[Q] = 1 J

DC POWER

The ratio of the work done by the current during time t to this time interval.

In the SI system:

The phenomenon of superconductivity

Discovery of low temperature superconductivity:
1911 - Dutch scientist Kamerling - Onnes
observed at ultra-low temperatures (below 25 K) in many metals and alloys;
At such temperatures, the resistivity of these substances becomes vanishingly small.

In 1957, a theoretical explanation of the phenomenon of superconductivity was given:
Cooper (USA), Bogolyubov (USSR)

1957 Collins's experiment: the current in a closed circuit without a current source did not stop for 2.5 years.

In 1986, high-temperature superconductivity (at 100 K) was discovered (for metal-ceramics).

Difficulty of achieving superconductivity:
- the need for strong cooling of the substance

Application area:
- obtaining strong magnetic fields;
- powerful electromagnets with superconducting winding in accelerators and generators.

Currently in the energy sector there is a big problem
- large losses of electricity during transmission her by wire.

Possible Solution Problems:
with superconductivity, the resistance of the conductors is approximately 0
and energy losses are sharply reduced.

Substance with the highest superconducting temperature
In 1988 in the USA, at a temperature of –148°C, the phenomenon of superconductivity was obtained. The conductor was a mixture of thallium, calcium, barium and copper oxides - Tl2Ca2Ba2Cu3Ox.

Semiconductor -

A substance whose resistivity can vary over a wide range and decreases very quickly with increasing temperature, which means that the electrical conductivity (1/R) increases.
- observed in silicon, germanium, selenium and some compounds.

Conduction mechanism in semiconductors

Semiconductor crystals have an atomic crystal lattice where outer electrons are bonded to neighboring atoms by covalent bonds.
At low temperatures, pure semiconductors have no free electrons and behave like an insulator.

ELECTRIC CURRENT IN VACUUM

What is a vacuum?
- this is the degree of rarefaction of a gas at which there are practically no collisions of molecules;

Electric current is not possible because the possible number of ionized molecules cannot provide electrical conductivity;
- it is possible to create electric current in a vacuum if you use a source of charged particles;
- the action of a source of charged particles can be based on the phenomenon of thermionic emission.

Thermionic emission

- this is the emission of electrons by solid or liquid bodies when they are heated to temperatures corresponding to the visible glow of hot metal.
The heated metal electrode continuously emits electrons, forming an electron cloud around itself.
In an equilibrium state, the number of electrons that left the electrode is equal to the number of electrons that returned to it (since the electrode becomes positively charged when electrons are lost).
The higher the temperature of the metal, the higher the density of the electron cloud.

Vacuum diode

Electric current in a vacuum is possible in vacuum tubes.
A vacuum tube is a device that uses the phenomenon of thermionic emission.

A vacuum diode is a two-electrode (A - anode and K - cathode) electron tube.
Very low pressure is created inside the glass container

H - filament placed inside the cathode to heat it. The surface of the heated cathode emits electrons. If the anode is connected to + of the current source, and the cathode is connected to -, then the circuit flows
constant thermionic current. The vacuum diode has one-way conductivity.
Those. current in the anode is possible if the anode potential is higher than the cathode potential. In this case, electrons from the electron cloud are attracted to the anode, creating an electric current in a vacuum.

Current-voltage characteristic of a vacuum diode.

At low anode voltages, not all the electrons emitted by the cathode reach the anode, and the electric current is small. At high voltages, the current reaches saturation, i.e. maximum value.
A vacuum diode is used to rectify alternating current.

Current at the input of the diode rectifier:

Rectifier output current:

Electron beams

This is a stream of rapidly flying electrons in vacuum tubes and gas-discharge devices.

Properties of electron beams:

Deflects in electric fields;
- deflect in magnetic fields under the influence of the Lorentz force;
- when a beam hitting a substance is decelerated, X-ray radiation appears;
- causes glow (luminescence) of some solids and liquids (luminophores);
- heat the substance by contacting it.

Cathode ray tube (CRT)

Thermionic emission phenomena and properties of electron beams are used.

A CRT consists of an electron gun, horizontal and vertical deflectors
electrode plates and screen.
In an electron gun, electrons emitted by a heated cathode pass through the control grid electrode and are accelerated by the anodes. An electron gun focuses an electron beam into a point and changes the brightness of the light on the screen. Deflecting horizontal and vertical plates allow you to move the electron beam on the screen to any point on the screen. The tube screen is coated with a phosphor that begins to glow when bombarded with electrons.

There are two types of tubes:

1) with electrostatic control of the electron beam (deflection of the electric beam only by the electric field);
2) with electromagnetic control (magnetic deflection coils are added).

Main applications of CRT:

picture tubes in television equipment;
computer displays;
electronic oscilloscopes in measuring technology.

ELECTRIC CURRENT IN GASES

Under normal conditions, gas is a dielectric, i.e. it consists of neutral atoms and molecules and does not contain free carriers of electric current.
The conductor gas is an ionized gas. Ionized gas has electron-ion conductivity.

Air is a dielectric in power lines, air capacitors, and contact switches.

Air is a conductor when lightning, an electric spark occurs, or when a welding arc occurs.

Gas ionization

It is the breakdown of neutral atoms or molecules into positive ions and electrons by removing electrons from the atoms. Ionization occurs when a gas is heated or exposed to radiation (UV, X-rays, radioactive) and is explained by the disintegration of atoms and molecules during collisions at high speeds.

Gas discharge

This is electric current in ionized gases.
The charge carriers are positive ions and electrons. Gas discharge is observed in gas-discharge tubes (lamps) when exposed to an electric or magnetic field.

Recombination of charged particles

- the gas ceases to be a conductor if ionization stops, this occurs as a result of recombination (reunion of oppositely charged particles).

There is a self-sustaining and non-self-sustaining gas discharge.

Non-self-sustaining gas discharge

If the action of the ionizer is stopped, the discharge will also stop.

When the discharge reaches saturation, the graph becomes horizontal. Here, the electrical conductivity of the gas is caused only by the action of the ionizer.

Self-sustaining gas discharge

In this case, the gas discharge continues even after the termination of the external ionizer due to ions and electrons resulting from impact ionization (= ionization of electric shock); occurs when the potential difference between the electrodes increases (an electron avalanche occurs).
A non-self-sustained gas discharge can transform into a self-sustained gas discharge when Ua = Uignition.

Electrical breakdown of gas

The process of transition of a non-self-sustaining gas discharge into a self-sustaining one.

Self-sustained gas discharge occurs 4 types:

1. smoldering - at low pressures (up to several mm Hg) - observed in gas-light tubes and gas lasers.
2. spark - at normal pressure and high electric field strength (lightning - current strength up to hundreds of thousands of amperes).
3. corona - at normal pressure in a non-uniform electric field (at the tip).
4. arc - high current density, low voltage between the electrodes (gas temperature in the arc channel -5000-6000 degrees Celsius); observed in spotlights and projection film equipment.

These discharges are observed:

smoldering - in fluorescent lamps;
spark - in lightning;
corona - in electric precipitators, during energy leakage;
arc - during welding, in mercury lamps.

Plasma

This is the fourth state of aggregation of a substance with a high degree of ionization due to the collision of molecules at high speed at high temperature; found in nature: ionosphere - weakly ionized plasma, Sun - fully ionized plasma; artificial plasma - in gas-discharge lamps.

Plasma can be:

Low temperature - at temperatures less than 100,000K;
high temperature - at temperatures above 100,000K.

Basic properties of plasma:

High electrical conductivity
- strong interaction with external electric and magnetic fields.

At a temperature

Any substance is in a plasma state.

Interestingly, 99% of the matter in the Universe is plasma

TEST QUESTIONS FOR TESTING

Electrodynamics is a branch of physics that studies the electromagnetic field in the most general case. Definition in electrodynamics What electrodynamics studies

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