IV Yakovlev | Materials on physics | MathUs.ru
Electrodynamics
This manual is devoted to the third section "Electrodynamics" of the USE codifier in physics. It covers the following topics.
Electrification of tel. Interaction of charges. Two types of charge. The law of conservation of electric charge. Coulomb's law.
The action of an electric field on electric charges. Electric field strength. The principle of superposition of electric fields.
Potentiality of the electrostatic field. Electric field potential. Voltage (potential difference).
conductors in an electric field. Dielectrics in an electric field.
electrical capacity. Capacitor. The energy of the electric field of the capacitor.
Constant electric current. Current strength. Voltage. Electrical resistance. Ohm's law for a circuit section.
Parallel and series connection of conductors. Mixed connection of conductors.
The work of electric current. Joule-Lenz law. Electric current power.
Electromotive force. Internal resistance of the current source. Ohm's law for a complete electrical circuit.
Carriers of free electric charges in metals, liquids and gases.
Semiconductors. Intrinsic and impurity conductivity of semiconductors.
Interaction of magnets. The magnetic field of a current-carrying conductor. Ampere power. Lorentz force.
The phenomenon of electromagnetic induction. magnetic flux. Faraday's law of electromagnetic induction. Lenz's rule.
Self-induction. Inductance. The energy of the magnetic field.
Free electromagnetic oscillations. Oscillatory circuit. Forced electromagnetic oscillations. Resonance. Harmonic electromagnetic oscillations.
Alternating current. Production, transmission and consumption of electrical energy.
Electromagnetic field.
Properties of electromagnetic waves. Various types of electromagnetic radiation and their application.
The manual also contains some additional material that is not included in the USE codifier (but included in the school curriculum!). This material allows you to better understand the topics covered.
1.2 Electrification of bodies . . . . . . . 7
2.1 Superposition principle . 11
2.2 Coulomb's law in a dielectric . . 12
3.1 Long range and close range 13
3.2 Electric field . . 13
3.3 Field strength of a point charge 14
3.4 The principle of superposition of electric fields . . . . . . . . . . . . . . . . . . . . . 16
3.5 Field of a uniformly charged plane. . . . . . . . . . . . . . . . . . . . . . . . 17
3.6 Electric field strength lines. . . . . . . . . . . . . . . . . . . . . . 18
4.1 Conservative forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Potentiality of the electrostatic field. . . . . . . . . . . . . . . . . . . . . . 20
4.3 Potential charge energy in a uniform field. . . . . . . . . . . . . . . . . . 20
4.6 Potential difference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.7 Superposition principle for potentials. . . . . . . . . . . . . . . . . . . . . . . . 24
4.8 Homogeneous field: the relationship between stress and tension. . . . . . . . . . . . . . . . 24
5.2 Charge inside a conductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.1 The dielectric constant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.2 Polar dielectrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.3 Non-polar dielectrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.1 solitary conductor capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.2 Flat capacitor capacitance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3 Energy of a charged capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7.4 Electric field energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
8.1 Direction of electric current. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8.2 The action of electric current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
8.5 Stationary electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
9 Ohm's Law |
9.1 Ohm's law for a circuit section. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
9.2 Electrical resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Resistivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Conductor connections | |||
Resistors and lead wires. . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
serial connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Parallel connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
mixed connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Work and current power | |||
11.1 Current work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.2 Current power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.3 Joule-Lenz law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
12.3 Electric circuit efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
12.4 Ohm's law for a heterogeneous area. . . . . . . . . . . . . . . . . . . . . . . . . 61
13.1 free electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
13.2 Rikke's experience. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
14.1 Electrolytic dissociation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
14.2 Ionic conduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
14.3 Electrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
15.1 Free charges in a gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
15.2 Non-self discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
16.1 covalent bond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
16.2 Crystal structure of silicon. . . . . . . . . . . . . . . . . . . . . . . . . . 78
16.3 Own conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
16.4 Impurity conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
16.5 p–n junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
17.1 Interaction of magnets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
17.2 Magnetic field lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
17.5 The magnetic field of a coil with current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
17.6 The magnetic field of a coil with current. . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Ampère's hypothesis. Elementary currents. . . . . . . . . . . . . . . . . . . . . . . . . | |||
A magnetic field. Forces | |||
Lorentz force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Ampere power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Frame with current in a magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Electromagnetic induction | |||
magnetic flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
19.2 EMF of induction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
19.3 Faraday's law of electromagnetic induction. . . . . . . . . . . . . . . . . . . . . . 99
19.4 Lenz's rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
19.7 Vortex electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
19.8 EMF of induction in a moving conductor. . . . . . . . . . . . . . . . . . . . . . . 104
self induction | |||
Inductance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 |
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Electromechanical analogy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Magnetic field energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110 |
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Electromagnetic vibrations | |||
Oscillatory circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Energy transformations in an oscillatory circuit. . . . . . . . . . . . . . . | |||
Electromechanical analogies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
21.4 Harmonic law of oscillations in the circuit. . . . . . . . . . . . . . . . . . . . . . . 116
21.5 Forced electromagnetic oscillations. . . . . . . . . . . . . . . . . . . . . . 119
Alternating current. one | |||
Quasi-stationarity condition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Resistor in AC circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 |
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Capacitor in AC circuit. . . . . . . . . . . . . . . . . . . . . . . . . | |||
Coil in AC circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 |
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Alternating current. 2 | |||
Auxiliary angle method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Oscillatory circuit with resistor. . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Resonance in an oscillatory circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
AC power | |||
24.1 Current power through the resistor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
24.2 Current power through the capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
24.3 Current power through the coil. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
26.1 Maxwell's hypothesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
26.2 The concept of an electromagnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
27.1 Open oscillating circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
27.2 Properties of electromagnetic waves. . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
27.3 Radiation Flux Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
27.4 Types of electromagnetic radiation. . . . . . . . . . . . . . . . . . . . . . . . . . . 154
1 Electric charge
Electromagnetic interactions are among the most fundamental interactions in nature. Forces of elasticity and friction, pressure of liquid and gas, and much more can be reduced to electromagnetic forces between particles of matter. The electromagnetic interactions themselves are no longer reduced to other, deeper types of interactions.
An equally fundamental type of interaction is gravitational attraction of any two bodies. However, there are several important differences between electromagnetic and gravitational interactions.
1. Not everyone can participate in electromagnetic interactions, but only charged
bodies (having an electric charge).
2. Gravitational interaction is always the attraction of one body to another. Electromagnetic interactions can be both attraction and repulsion.
3. The electromagnetic interaction is much more intense than the gravitational one. For example, the electrical repulsion between two electrons is 10 42 times the force of their gravitational attraction to each other.
Every charged body has some amount of electric charge q. Electric charge is a physical quantity that determines the strength of the electromagnetic interaction between objects of nature. The unit of charge is the pendant (C)1.
1.1 Two types of charge
Since the gravitational interaction is always an attraction, the masses of all bodies are non-negative. But this is not the case for charges. It is convenient to describe two types of electromagnetic interaction attraction and repulsion by introducing two types of electric charges: positive and negative.
Charges of different signs attract each other, and charges of the same sign repel each other. This is illustrated in fig. one ; balls suspended on threads are given charges of one sign or another.
Rice. 1. Interaction of two types of charges
The ubiquitous manifestation of electromagnetic forces is explained by the fact that charged particles are present in the atoms of any substance: positively charged protons are part of the atomic nucleus, and negatively charged electrons move in orbits around the nucleus. The charges of a proton and an electron are equal in absolute value, and the number of protons in the nucleus is equal to the number of electrons in orbits, and therefore it turns out that the atom as a whole is electrically neutral. That is why, under normal conditions, we do not notice the electromagnetic influence from others.
1 The unit of charge is determined by the unit of current. 1 C is the charge passing through the cross section of the conductor in 1 s at a current of 1 A.
bodies: the total charge of each of them is equal to zero, and the charged particles are evenly distributed over the volume of the body. But if electrical neutrality is violated (for example, as a result of electrification), the body immediately begins to act on the surrounding charged particles.
Why there are exactly two types of electric charges, and not some other number of them, is not currently known. We can only assert that the acceptance of this fact as primary gives an adequate description of electromagnetic interactions.
The proton charge is 1;6 10 19 C. The charge of an electron is opposite to it in sign and is equal to
1;6 10 19 Cl. Value
e = 1;6 10 19 C
called the elementary charge. This is the minimum possible charge: free particles with a smaller charge were not found in the experiments. Physics cannot yet explain why nature has the smallest charge and why its magnitude is precisely that.
The charge of any body q always consists of an integer number of elementary charges:
If q< 0, то тело имеет избыточное количество N электронов (по сравнению с количеством протонов). Если же q >0, then vice versa, the body lacks electrons: there are more protons by N.
1.2 Electrification of bodies
In order for a macroscopic body to exert an electrical influence on other bodies, it must be electrified. Electrification is a violation of the electrical neutrality of the body or its parts. As a result of electrification, the body becomes capable of electromagnetic interactions.
One of the ways to electrify a body is to impart an electric charge to it, that is, to achieve an excess of charges of the same sign in a given body. This is easy to do with friction.
So, when rubbing a glass rod with silk, part of its negative charges goes to the silk. As a result, the stick is charged positively, and the silk is negatively charged. But when rubbing an ebonite stick with wool, part of the negative charges transfers from the wool to the stick: the stick is charged negatively, and the wool is positively charged.
This method of electrification of bodies is called friction electrification. You encounter electrification by friction every time you take off a sweater over your head ;-)
Another type of electrification is called electrostatic induction, or electrification through influence. In this case, the total charge of the body remains equal to zero, but is redistributed so that positive charges accumulate in some parts of the body, and negative charges in others.
Rice. 2. Electrostatic induction
Let's look at fig. 2. At some distance from the metal body there is a positive charge q. It attracts the negative charges of the metal (free electrons), which accumulate on the areas of the body surface closest to the charge. Uncompensated positive charges remain in the far regions.
Despite the fact that the total charge of the metallic body remained equal to zero, a spatial separation of charges occurred in the body. If we now divide the body along the dotted line, then the right half will be negatively charged, and the left half positively.
You can observe the electrification of the body using an electroscope. A simple electroscope is shown2 in Fig.3.
Rice. 3. Electroscope
What happens in this case? A positively charged rod (for example, previously rubbed) is brought to the electroscope disk and collects a negative charge on it. Below, on the moving leaves of the electroscope, uncompensated positive charges remain; pushing away from each other, the leaves diverge in different directions. If you remove the wand, then the charges will return to their place and the leaves will fall back.
The phenomenon of electrostatic induction on a grandiose scale is observed during a thunderstorm. On fig. 4 we see a thundercloud moving over the earth3.
Rice. 4. Electrification of the earth by a thundercloud
Inside the cloud there are ice floes of different sizes, which are mixed by ascending air currents, collide with each other and become electrified. In this case, it turns out that a negative charge accumulates in the lower part of the cloud, and a positive charge accumulates in the upper part.
The negatively charged lower part of the cloud induces positive charges on the surface of the earth. A giant capacitor with a colossal voltage appears
2 Image from en.wikipedia.org.
3 Image from elementy.ru.
between cloud and earth. If this voltage is sufficient to break through the air gap, then a discharge of lightning, well known to you, will occur.
1.3 Law of conservation of charge
Let's go back to the example of electrification by rubbing a stick with a cloth. In this case, the stick and the piece of cloth acquire charges equal in magnitude and opposite in sign. Their total charge, as it was equal to zero before the interaction, remains equal to zero after the interaction.
We see here the law of conservation of charge, which says: in a closed system of bodies, the algebraic sum of charges remains unchanged in any processes that occur with these bodies:
q1 + q2 + : : : + qn = const:
Closedness of a system of bodies means that these bodies can exchange charges only among themselves, but not with any other objects external to the given system.
When the stick is electrified, there is nothing surprising in the conservation of charge: how many charged particles left the stick, the same amount came to a piece of cloth (or vice versa). It is surprising that in more complex processes, accompanied by mutual transformations of elementary particles and a change in the number of charged particles in the system, the total charge is still preserved!
For example, in fig. 5 shows the process! e + e+ , at which a portion of electromagnetic radiation (the so-called photon) turns into two charged particles, an electron e and a positron e+ . Such a process is possible under certain conditions, for example, in the electric field of an atomic nucleus.
Rice. 5. Creation of an electron–positron pair
The charge of the positron is equal in absolute value to the charge of the electron and is opposite to it in sign. The law of conservation of charge is fulfilled! Indeed, at the beginning of the process we had a photon whose charge is zero, and at the end we got two particles with zero total charge.
The law of conservation of charge (along with the existence of the smallest elementary charge) is today the primary scientific fact. Physicists have not yet succeeded in explaining why nature behaves in this way and not otherwise. We can only state that these facts are confirmed by numerous physical experiments.
Electric charges, their interaction.
DC electric circuit, its basic laws.
Electronic theory of the structure of matter.
All substances in nature are made up of molecules, molecules of atoms.
Molecule is the smallest particle that has the chemical properties of a given substance.
Atom is the smallest particle that has the chemical and physical properties of a given element.
It consists of:
a positively charged nucleus
negative electrons rotating in allowed orbits.
The nucleus consists of positive protons and neutral neutrons.
The charge of an electron is equal to the charge of a proton, but the signs are opposite. These elementary particles are not equal in size and mass, the proton is larger than the electron.
An atom is an electrically neutral particle (not charged), that is, as many protons are in the nucleus, so many electrons revolve around the nucleus, since one proton can hold one electron.
Thus, the diversity of the world around us is formed from various combinations of only three particles: a neutron, a proton and an electron, which in turn also have an internal structure.
Valence electrons are the electrons that are in the extreme orbit. They determine the chemical properties of a substance and its electrical conductivity.
Electrical conductivity is the ability of a substance to conduct an electric current.
Electric charges, their interaction.
Even in ancient times, it was known that amber, worn on wool, acquires the ability to attract light objects. Later it was found that many other substances have a similar property. Bodies capable, like amber, after rubbing attract light objects, are called electrified. On bodies in this state there are electric charges, and the bodies themselves are called charged.
In nature, there are only two types of charges - positive and negative. Charges of the same sign (like charges) repel, charges of opposite signs (opposite charges) attract.
Elementary particles have the smallest (elementary) charge. For example, a proton and a positron are positively charged, while an electron and an antiproton are negatively charged.
The elementary negative charge is equal in magnitude to the elementary positive charge. In the SI system, charge is measured in pendants(CL). The value of the elementary charge e \u003d 1.6-10-19 C. In nature, nowhere and never does an electric charge of the same sign arise and disappear. The appearance of a positive electric charge + q is always accompanied by the appearance of an equal negative electric charge - q. Neither positive nor negative charges can disappear separately from one another, they can only mutually neutralize each other if they are equal.
To get a charge from a neutral atom, you need to act with some kind of force and tear off electrons, or attach foreign electrons to a neutral atom. As a result, upon separation (for example, during friction), a positively charged atom is obtained, which is called positive ion, and when attached - negative ion.
Ionization is the process of formation of charges from a neutral atom.
Like the concept of the gravitational mass of a body in Newtonian mechanics, the concept of charge in electrodynamics is the primary, basic concept.
Electric charge is a physical quantity that characterizes the property of particles or bodies to enter into electromagnetic force interactions.
Electric charge is usually denoted by the letters q or Q.
The totality of all known experimental facts allows us to draw the following conclusions:
There are two kinds of electric charges, conventionally called positive and negative.
Charges can be transferred (for example, by direct contact) from one body to another. Unlike body mass, electric charge is not an inherent characteristic of a given body. The same body in different conditions can have a different charge.
Like charges repel, unlike charges attract. This also shows the fundamental difference between electromagnetic forces and gravitational ones. Gravitational forces are always forces of attraction.
One of the fundamental laws of nature is the experimentally established law of conservation of electric charge .
In an isolated system, the algebraic sum of the charges of all bodies remains constant:
|
q 1 + q 2 + q 3 + ... +qn= const. |
The law of conservation of electric charge states that in a closed system of bodies processes of the birth or disappearance of charges of only one sign cannot be observed.
From the modern point of view, charge carriers are elementary particles. All ordinary bodies are composed of atoms, which include positively charged protons, negatively charged electrons and neutral particles - neutrons. Protons and neutrons are part of atomic nuclei, electrons form the electron shell of atoms. The electric charges of the proton and electron modulo are exactly the same and equal to the elementary charge e.
In a neutral atom, the number of protons in the nucleus is equal to the number of electrons in the shell. This number is called atomic number . An atom of a given substance can lose one or more electrons or gain an extra electron. In these cases, the neutral atom turns into a positively or negatively charged ion.
A charge can be transferred from one body to another only in portions containing an integer number of elementary charges. Thus, the electric charge of the body is a discrete quantity:
Physical quantities that can only take on a discrete series of values are called quantized . elementary charge e is a quantum (smallest portion) of electric charge. It should be noted that in modern elementary particle physics, the existence of so-called quarks is assumed - particles with a fractional charge and However, quarks in the free state have not yet been observed.
In conventional laboratory experiments, electric charges are detected and measured using electrometer ( or electroscope) - a device consisting of a metal rod and an arrow that can rotate around a horizontal axis (Fig. 1.1.1). The arrowhead is insulated from the metal case. When a charged body comes into contact with the rod of an electrometer, electric charges of the same sign are distributed along the rod and the arrow. The forces of electrical repulsion cause the arrow to turn at a certain angle, by which one can judge the charge transferred to the rod of the electrometer.
The electrometer is a fairly crude instrument; it does not allow one to investigate the forces of interaction of charges. For the first time, the law of interaction of fixed charges was discovered by the French physicist Charles Coulomb in 1785. In his experiments, Coulomb measured the forces of attraction and repulsion of charged balls using a device he designed - a torsion balance (Fig. 1.1.2), which was extremely sensitive. So, for example, the balance beam was rotated by 1 ° under the action of a force of the order of 10 -9 N.
The idea of measurements was based on Coulomb's brilliant guess that if a charged ball is brought into contact with exactly the same uncharged one, then the charge of the first will be divided equally between them. Thus, a method was indicated to change the charge of the ball by two, three, etc. times. Coulomb's experiments measured the interaction between balls whose dimensions are much smaller than the distance between them. Such charged bodies are called point charges.
point charge called a charged body, the dimensions of which can be neglected under the conditions of this problem.
Based on numerous experiments, Coulomb established the following law:
The forces of interaction of fixed charges are directly proportional to the product of charge modules and inversely proportional to the square of the distance between them:
Interaction forces obey Newton's third law:
They are repulsive forces with the same signs of charges and attractive forces with different signs (Fig. 1.1.3). The interaction of fixed electric charges is called electrostatic or Coulomb interaction. The section of electrodynamics that studies the Coulomb interaction is called electrostatics .
Coulomb's law is valid for point charged bodies. In practice, Coulomb's law is well satisfied if the dimensions of the charged bodies are much smaller than the distance between them.
Proportionality factor k in Coulomb's law depends on the choice of the system of units. In the International SI system, the unit of charge is pendant(CL).
Pendant - this is the charge passing in 1 s through the cross section of the conductor at a current strength of 1 A. The unit of current strength (Ampere) in SI is, along with units of length, time and mass basic unit of measure.
Coefficient k in the SI system is usually written as:
Where 
- electrical constant
.
In the SI system, the elementary charge e equals:
Experience shows that the Coulomb interaction forces obey the superposition principle:
If a charged body interacts simultaneously with several charged bodies, then the resulting force acting on this body is equal to the vector sum of the forces acting on this body from all other charged bodies.
Rice. 1.1.4 explains the principle of superposition using the example of the electrostatic interaction of three charged bodies.
The principle of superposition is a fundamental law of nature. However, its use requires some caution when it comes to the interaction of charged bodies of finite size (for example, two conductive charged balls 1 and 2). If a third charged ball is raised to a system of two charged balls, then the interaction between 1 and 2 will change due to charge redistribution.
The principle of superposition states that when given (fixed) charge distribution on all bodies, the forces of electrostatic interaction between any two bodies do not depend on the presence of other charged bodies.
Electric charge. Two types of charges
ELECTRIC CHARGE. TWO TYPES OF CHARGES.
THE LAW OF CONSERVATION OF CHARGE. PENDANT'S LAW
Electric charge. Two types of charges
Let us begin our acquaintance with electrical phenomena with very simple experiments.
1st experience. We rub the ebonite stick with a piece of woolen cloth, and then touch this stick to a light paper sleeve. We will see that the paper sleeve will be repelled by the ebonite stick (Fig. 1.1, a). If you touch the second paper sleeve with the same stick, and then hang both sleeves side by side, they will repel each other (Fig. 1.1, b), which means that repulsive forces arise between the shells. We denote the sleeves in this figure with the number 1.
Rice. 1.2
3rd experience. Now we hang two paper sleeves side by side (Fig. 1.3): 1 (which was in contact with an ebonite rod worn on wool) and 2 (which was in contact with a glass rod worn on silk). The sleeves are attracted, which means that an attractive force arises between sleeves 1 and 2.
The type of interaction considered by us was known in antiquity and was called electric interactions.
With friction are charged with electricity(or acquire charges) bodies, which then interact. It has been experimentally established that there are two types of charges conventionally called positive and negative. Like charges repel, and unlike charges attract.
Historically, it was customary to call the charges that a glass rod receives when rubbing against silk positive, and the charges that an ebonite stick receives when rubbing against wool - negative. (You could also call it the other way around.)
Basic concepts of electrostatics
Charge is an inherent property of some elementary particles, the most important of which are the electron and proton.
The charges of electrons and protons are the same in magnitude and are called elementary charges.
There are two types of charges, conventionally called positive and negative . Like charges repel, and unlike charges attract.
The charge of a proton is considered positive and is denoted by + e, and the charge of the electron is negative and is denoted by - e.
The charge of the body is equal to the algebraic sum of the charges of the elementary particles that make up the body. If this sum is zero, the body is called electrically neutral .
Usually electrons and protons are distributed in the body in equal quantities and with the same density. Therefore, the algebraic sum of charges in each elementary volume of the body is zero, and each such volume (and the body as a whole) is electrically neutral.
If you create an excess of particles of any sign in the body, then the body will be charged. Note that when an ebonite stick is rubbed against wool on a stick, it creates Xia excess of electrons, and it is negatively charged. On a glass rod, when rubbed against silk, excess protons(or lack of electrons, since it was the electrons that left the glass in the silk), so the glass is positively charged.
Any charge is formed by a combination of elementary charges, so you can always write:
q =± Ne, (1.1)
where N- natural number.
It has been experimentally established that the magnitude of the charge does not depend on the speed with which it moves. In addition, elementary charges can appear and disappear. But! Two elementary charges of different signs always appear and disappear simultaneously.
For example, an electron and a positron (a positively charged electron) in a collision annihilate, i.e. turn into neutral particles called g-photons. In turn, the g-photon, flying near the atomic nucleus, can turn into an electron + positron pair.
The system is called electrically isolated, if charged particles do not penetrate through the boundary surface.
Law of conservation of elementary charge:
The net charge of an electrically isolated system cannot change.
Coulomb's law
If the dimensions of a charged body can be neglected in comparison with the distances to other bodies, then such a body is called point charge.
Coulomb's law:
Two stationary point charges interact in vacuum with each other with a force directly proportional to the magnitude of each of the charges and inversely proportional to the square of the distance between them.
The force is directed along the straight line connecting the charges (Fig. 1.4).
In scalar form, Coulomb's law has the form
, . (1.2)
In vector form, Coulomb's law has the form
. (1.3)
Note that formula (1.3) uniquely determines not only the magnitude, but also the direction of the force!
The vector is equal to unity in absolute value, and coincides with the vector in direction. (In mathematics, such a vector is called ortom vector .)
A body which, after being rubbed, attracts other bodies to itself, is said to be electrified, or that an electric charge has been imparted to it.
Charge is the property of bodies to enter into electromagnetic interactions. A charged body is often called a charge, although a charge cannot exist in the absence of a body.
Bodies made of different substances can be electrified. The electrification of bodies occurs when the bodies come into contact and then separate (for example, during friction).
Two bodies are involved in the electrification. In this case, both bodies are electrified.
There are two types of electric charges: "+" and "-". The charge is denoted q, measured in Coulomb [C].
The charge obtained on glass rubbed with silk was called positive, and the charge obtained on amber rubbed with wool was called negative.
Electrification is explained by the movement of electrons from one body to another. If a body loses 1 or more electrons, it acquires a positive charge. If a body acquires 1 or more electrons, it acquires a negative charge.
Experience shows that the electric charge can have different meanings. However, this value is a multiple of the charge 1.6 ·10 -19 C, which was called elementary. The charge of an electron is equal to the elementary charge, taken with the "-" sign.
When electrified by friction, both bodies acquire an electric charge, while the charges are equal in magnitude, but opposite in sign. So, during friction, amber acquires a negative charge, and wool acquires an equal positive charge.
Bodies with electric charges of the same sign repel each other, and bodies with electric charges of the opposite sign attract each other.
The interaction of charges is explained by the fact that an electric field arises around any charge, which acts on another charge with a certain force. This force is proportional to the magnitude of the charges and decreases with distance.
In the process of interaction of charges, one of the fundamental laws of nature is fulfilled - the law of conservation of electric charge: the algebraic sum of electric charges in a closed system remains constant, i.e.
q 1 + q 2 + q 3 + ... + q n = const
To determine the presence of a charge on the body, an instrument called an electroscope is used, the operation of which is based on the interaction of charged bodies. In an electroscope, a metal rod is passed through a plastic stopper inserted into a metal frame, at the end of which two sheets of thin paper are fixed. The frame is covered with glass on both sides. The greater the charge of the electroscope, the greater the repulsive force of the leaves, and the greater the angle they will disperse. This means that by changing the angle of the divergence of the leaves of the electroscope, one can judge whether its charge has increased or decreased.
Electrization of bodies is used for electrostatic painting of metal products, for printing in printers, for air purification from dust and light particles, etc.
The electrostatic painting method allows you to apply paint on the part to be painted in a more even layer. To do this, use a spray gun. If you place the part to be painted on the side of the paint jet, apply a positive charge to it, and apply a negative charge to the metal spray gun tube by connecting it to an electrophore machine, you will notice that the dye droplets become smaller, the color is more even.
In production and in everyday life, there are cases when electrification must be eliminated: in a pulp and paper mill, electrification can cause frequent breaks in a fast-moving paper tape. When rubbing against the air, the aircraft becomes electrified. Therefore, after landing, a metal ladder cannot be immediately attached to the aircraft: a discharge may occur that will cause a fire.
Ways to combat electrification: careful grounding of machine tools, machines; the use of conductive plastics for floors, air humidification, the use of various kinds of “neutralizers”, air ionizers. In everyday life, to combat electrification, it is enough to increase the relative humidity of the apartment up to 60-70%; or apply the drug "Antistatic".
