Physical processes occurring in nature are not always explained by the laws of molecular kinetic theory, mechanics or thermodynamics. There are also electromagnetic forces that act at a distance and do not depend on the mass of the body.
Their manifestations were first described in the works of ancient Greek scientists, when they attracted light, small particles of individual substances with amber rubbed on wool.
Historical contribution of scientists to the development of electrodynamics
Experiments with amber were studied in detail by an English researcher William Gilbert. In the last years of the 16th century, he made a report on his work, and designated objects capable of attracting other bodies at a distance with the term “electrified.”
The French physicist Charles Dufay determined the existence of charges with opposite signs: some were formed by the friction of glass objects on silk fabric, and others by resins on wool. That’s what he called them: glass and resin. After completing the research Benjamin Franklin The concept of negative and positive charges was introduced.
Charles Coulomb realized the possibility of measuring the force of charges with the design of torsion balances of his own invention.
Robert Millikan, based on a series of experiments, established the discrete nature of the electrical charges of any substance, proving that they consist of a certain number of elementary particles. (Not to be confused with another concept of this term - fragmentation, discontinuity.)
The works of these scientists served as the foundation of modern knowledge about the processes and phenomena occurring in electric and magnetic fields created by electric charges and their movement, studied by electrodynamics.
Definition of charges and principles of their interaction
Electric charge characterizes the properties of substances that provide them with the ability to create electric fields and interact in electromagnetic processes. It is also called the amount of electricity and is defined as a physical scalar quantity. To denote charge, the symbols “q” or “Q” are used, and in measurements they use the “Coulomb” unit, named after the French scientist who developed a unique technique.
He created a device whose body used balls suspended on a thin thread of quartz. They were oriented in space in a certain way, and their position was recorded relative to a graduated scale with equal divisions.
Through a special hole in the lid, another ball with an additional charge was brought to these balls. The emerging interaction forces caused the balls to deflect and turn their rocker arm. The magnitude of the difference in readings on the scale before and after the introduction of a charge made it possible to estimate the amount of electricity in the test samples.
A charge of 1 coulomb is characterized in the SI system by a current of 1 ampere passing through the cross-section of a conductor in a time equal to 1 second.
Modern electrodynamics divides all electric charges into:
positive;
negative.
When they interact with each other, they develop forces, the direction of which depends on the existing polarity.
Charges of the same type, positive or negative, always repel in opposite directions, trying to move as far away from each other as possible. And charges of opposite signs have forces that tend to bring them closer together and unite them into one whole.
Superposition principle
When there are several charges in a certain volume, the principle of superposition applies to them.
Its meaning is that each charge in a certain way, according to the method discussed above, interacts with all the others, being attracted to those of different types and repelled by those of the same type. For example, a positive charge q1 is affected by the force of attraction F31 to the negative charge q3 and repulsion force F21 from q2.
The resulting force F1 acting on q1 is determined by the geometric addition of the vectors F31 and F21. (F1= F31+ F21).
The same method is used to determine the resulting forces F2 and F3 on charges q2 and q3, respectively.
Using the principle of superposition, it was concluded that for a certain number of charges in a closed system, steady electrostatic forces act between all its bodies, and the potential at any specific point in this space is equal to the sum of the potentials from all individually applied charges.
The effect of these laws is confirmed by the created devices electroscope and electrometer, which have a general operating principle.
An electroscope consists of two identical blades of thin foil suspended in an isolated space by a conductive thread attached to a metal ball. In the normal state, charges do not act on this ball, so the petals hang freely in the space inside the device’s bulb.
How can charge be transferred between bodies?
If you bring a charged body, for example, a stick, to the electroscope ball, the charge will pass through the ball along a conductive thread to the petals. They will receive the same charge and begin to move away from each other by an angle proportional to the applied amount of electricity.
The electrometer has the same basic device, but it has slight differences: one petal is fixed permanently, and the second extends from it and is equipped with an arrow that allows you to take a reading from a graduated scale.
To transfer charge from a remote, stationary and charged body to an electrometer, you can use intermediate carriers.
Measurements made with an electrometer do not have a high accuracy class and on their basis it is difficult to analyze the forces acting between charges. Coulomb torsional balances are more suitable for their study. They use balls with diameters significantly smaller than their distance from each other. They have the properties of point charges - charged bodies, the dimensions of which do not affect the accuracy of the device.
Measurements performed by Coulomb confirmed his guess that a point charge is transferred from a charged body to a body of the same properties and mass, but uncharged, in such a way as to be evenly distributed between them, decreasing by a factor of 2 at the source. In this way, it was possible to reduce the amount of charge by two, three, or other times.
The forces that exist between stationary electric charges are called Coulomb or static interaction. They are studied by electrostatics, which is one of the branches of electrodynamics.
Types of electric charge carriers
Modern science considers the smallest negatively charged particle to be the electron, and the positron to be the smallest positively charged particle. They have the same mass 9.1·10-31 kg. The elementary particle proton has only one positive charge and a mass of 1.7·10-27 kg. In nature, the number of positive and negative charges is balanced.
In metals, the movement of electrons creates, and in semiconductors, the carriers of its charges are electrons and holes.
In gases, current is generated by the movement of ions - charged non-elementary particles (atoms or molecules) with positive charges, called cations or negative charges - anions.
Ions are formed from neutral particles.
A positive charge is created by a particle that has lost an electron under the influence of a powerful electrical discharge, light or radioactive irradiation, wind flow, movement of water masses or a number of other reasons.
Negative ions are formed from neutral particles that have additionally received an electron.
Use of ionization for medical purposes and everyday life
Researchers have long noticed the ability of negative ions to affect the human body, improve the consumption of oxygen in the air, deliver it faster to tissues and cells, and accelerate the oxidation of serotonin. All this together significantly improves immunity, improves mood, and relieves pain.
The first ionizer used to treat people was called Chizhevsky chandeliers, in honor of the Soviet scientist who created a device that has a beneficial effect on human health.
In modern household electrical appliances you can find built-in ionizers in vacuum cleaners, humidifiers, hair dryers, dryers...
Special air ionizers purify the air and reduce the amount of dust and harmful impurities.
Water ionizers can reduce the amount of chemical reagents in its composition. They are used to clean pools and ponds, saturating the water with copper or silver ions, which reduce the growth of algae and destroy viruses and bacteria.
Electric charge is a physical quantity that determines the intensity of electromagnetic interactions. Electromagnetic interactions are interactions between charged particles or bodies.
Electric charges are divided into positive and negative. Stable elementary particles have a positive charge - protons And positrons, as well as ions of metal atoms, etc. Stable negative charge carriers are electron And antiproton.
There are electrically uncharged particles, that is, neutral ones: neutron, neutrino. These particles do not participate in electrical interactions, since their electric charge is zero. There are particles without an electric charge, but an electric charge does not exist without a particle.
Positive charges appear on glass rubbed with silk. Ebonite rubbed on fur has negative charges. Particles repel when charges have the same signs ( charges of the same name), and with different signs ( unlike charges) particles are attracted.
All bodies are made of atoms. Atoms consist of a positively charged atomic nucleus and negatively charged electrons that move around the atomic nucleus. The atomic nucleus consists of positively charged protons and neutral particles - neutrons. The charges in an atom are distributed in such a way that the atom as a whole is neutral, that is, the sum of the positive and negative charges in the atom is zero.
Electrons and protons are part of any substance and are the smallest stable elementary particles. These particles can exist in a free state for an unlimited time. The electric charge of an electron and a proton is called the elementary charge.
Elementary charge- this is the minimum charge that all charged elementary particles have. The electric charge of a proton is equal in absolute value to the charge of an electron:
E = 1.6021892(46) * 10 -19 C
The interaction forces between stationary charges are directly proportional to the product of the charge moduli 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 stationary electric charges is called electrostatic or Coulomb interaction. The branch 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 sizes of charged bodies are much smaller than the distance between them.
Proportionality factor k in Coulomb's law depends on the choice of system of units. In the International SI System, the unit of charge is taken to be pendant(Cl).
Pendant is a charge passing through the cross-section of a conductor in 1 s at a current of 1 A. The unit of current (ampere) in SI is, along with units of length, time and mass basic unit of measurement.
Coefficient k in the SI system it is usually written as:
Experience shows that the Coulomb interaction forces obey the principle of superposition.
Like the concept of 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 represented by the letters q or Q.
The totality of all known experimental facts allows us to draw the following conclusions:
There are two types 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 integral characteristic of a given body. The same body under different conditions can have a different charge.
Like charges repel, unlike charges attract. This also reveals the fundamental difference between electromagnetic forces and gravitational ones. Gravitational forces are always attractive forces.
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 creation or disappearance of charges of only one sign cannot be observed.
From a modern point of view, charge carriers are elementary particles. All ordinary bodies consist 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 a proton and an electron are exactly the same in magnitude 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 may lose one or more electrons or gain an extra electron. In these cases, the neutral atom turns into a positively or negatively charged ion.
Charge can be transferred from one body to another only in portions containing an integer number of elementary charges. Thus, the electric charge of a body is a discrete quantity:
Physical quantities that can only take 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 physics of elementary particles the existence of so-called quarks is assumed - particles with a fractional charge and However, quarks have not yet been observed in a free state.
In common laboratory experiments, a electrometer ( or electroscope) - a device consisting of a metal rod and a pointer that can rotate around a horizontal axis (Fig. 1.1.1). The arrow rod is isolated from the metal body. When a charged body comes into contact with the electrometer rod, electric charges of the same sign are distributed over the rod and the pointer. Electrical repulsion forces cause the needle to rotate through a certain angle, by which one can judge the charge transferred to the electrometer rod.
The electrometer is a rather crude instrument; it does not allow one to study the forces of interaction between charges. The law of interaction of stationary charges was first 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 distinguished by extremely high sensitivity. For example, the balance beam was rotated 1° under the influence of a force of the order of 10 -9 N.
The idea of the 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 way was indicated to change the charge of the ball by two, three, etc. times. In Coulomb's experiments, the interaction between balls whose dimensions were much smaller than the distance between them was measured. Such charged bodies are usually called point charges.
Point charge called a charged body, the dimensions of which can be neglected in the conditions of this problem.
Based on numerous experiments, Coulomb established the following law:
The interaction forces between stationary charges are directly proportional to the product of the charge moduli 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 stationary electric charges is called electrostatic or Coulomb interaction. The branch 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 sizes of charged bodies are much smaller than the distance between them.
Proportionality factor k in Coulomb's law depends on the choice of system of units. In the International SI System, the unit of charge is taken to be pendant(Cl).
Pendant is a charge passing in 1 s through the cross section of a conductor at a current strength of 1 A. The unit of current (Ampere) in SI is, along with units of length, time and mass basic unit of measurement.
Coefficient k in the SI system it is usually written as:
Where 
- electrical constant
.
In the SI system, the elementary charge e equal to:
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 a given 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 we are talking about the interaction of charged bodies of finite sizes (for example, two conducting charged balls 1 and 2). If a third charged ball is brought 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.
By hanging light balls of foil on two threads and touching each of them with a glass rod rubbed on silk, you can see that the balls will repel each other. If you then touch one ball with a glass rod rubbed on silk, and the other with an ebonite rod rubbed on fur, the balls will attract each other. This means that glass and ebonite rods, when rubbed, acquire charges of different signs , i.e. exist in nature two types of electric charges, having opposite signs: positive and negative. We agreed to assume that a glass rod rubbed on silk acquires positive charge , and an ebonite stick, rubbed on fur, acquires negative charge .
From the described experiment it also follows that charged bodies interact with each other. This interaction of charges is called electrical. Wherein charges of the same name, those. charges of the same sign , repel each other, and unlike charges attract each other.
The device is based on the phenomenon of repulsion of similarly charged bodies electroscope- a device that allows you to determine whether a given body is charged, and electrometer, a device that allows you to estimate the value of electric charge.
If you touch the rod of an electroscope with a charged body, the leaves of the electroscope will disperse, since they will acquire a charge of the same sign. The same thing will happen to the needle of an electrometer if you touch its rod with a charged body. In this case, the greater the charge, the greater the angle the arrow will deviate from the rod.
From simple experiments it follows that the force of interaction between charged bodies can be greater or less depending on the magnitude of the acquired charge. Thus, we can say that the electric charge, on the one hand, characterizes the body’s ability to interact electrically, and on the other hand, is a quantity that determines the intensity of this interaction.
The charge is indicated by the letter q , taken as a unit of charge pendant: [q ] = 1 Cl.
If you touch one electrometer with a charged rod, and then connect this electrometer with a metal rod to another electrometer, then the charge on the first electrometer will be divided between the two electrometers. You can then connect the electrometer to several more electrometers, and the charge will be divided between them. Thus, the electric charge has property of divisibility . The charge divisibility limit, i.e. the smallest charge existing in nature is the charge electron. The electron charge is negative and equal to 1.6*10 -19 Cl. Any other charge is a multiple of the electron charge.
I. V. Yakovlev | Physics materials | MathUs.ru
Electrodynamics
This manual is devoted to the third section “Electrodynamics” of the Unified State Examination codifier in physics. It covers the following topics.
Electrification of bodies. Interaction of charges. Two types of charge. Law of conservation of electric charge. Coulomb's law.
The effect of an electric field on electric charges. Electric field strength. The principle of superposition of electric fields.
Electrostatic field potential. Electric field potential. Voltage (potential difference).
Conductors in an electric field. Dielectrics in an electric field.
Electrical capacity. Capacitor. Electric field energy of a capacitor.
Constant electric current. Current strength. Voltage. Electrical resistance. Ohm's law for a section of a circuit.
Parallel and series connection of conductors. Mixed connection of conductors.
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. 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. Magnetic field energy.
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 applications.
The manual also contains some additional material that is not included in the Unified State Examination codifier (but is 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 dielectrics . . 12
3.1 Long-range and short-range 13
3.2 Electric field . . 13
3.3 Point charge field strength 14
3.4 The principle of superposition of electric fields . . . . . . . . . . . . . . . . . . . . . 16
3.5 Field of a uniformly charged plane. . . . . . . . . . . . . . . . . . . . . . . . 17
3.6 Electric field lines. . . . . . . . . . . . . . . . . . . . . . 18
4.1 Conservative forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Electrostatic field potential. . . . . . . . . . . . . . . . . . . . . . 20
4.3 Potential energy of a charge in a uniform field. . . . . . . . . . . . . . . . . . 20
4.6 Potential difference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.7 Superposition principle for potentials. . . . . . . . . . . . . . . . . . . . . . . . 24
4.8 Homogeneous field: the relationship between voltage and intensity. . . . . . . . . . . . . . . . 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 Capacitance of a solitary conductor. . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.2 Capacitance of a parallel plate capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.3 Energy of a charged capacitor. . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7.4 Electric field energy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
8.1 Direction of electric current. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
8.2 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 compound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Work and current power | |||
11.1 Current work. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.2 Current power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
11.3 Joule-Lenz law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
12.3 Electrical circuit efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
12.4 Ohm's law for a heterogeneous area. . . . . . . . . . . . . . . . . . . . . . . . . 61
13.1 Free electrons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
13.2 Rikke's experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
14.1 Electrolytic dissociation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
14.2 Ionic conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
14.3 Electrolysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
15.1 Free charges in gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
15.2 Non-self-sustaining discharge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
16.1 Covalent bond. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
16.2 Crystal structure of silicon. . . . . . . . . . . . . . . . . . . . . . . . . . 78
16.3 Self conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
16.4 Impurity conductivity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
16.5 p–n junction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
17.1 Magnet interaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
17.2 Magnetic field lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
17.5 Magnetic field of a coil with current. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
17.6 Magnetic field of a current coil. . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Ampere's hypothesis. Elementary currents. . . . . . . . . . . . . . . . . . . . . . . . . | |||
A magnetic field. Powers | |||
Lorentz force. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Ampere power. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Frame with current in a magnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
Electromagnetic induction | |||
Magnetic flux. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
19.2 Induction emf. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
19.3 Faraday's law of electromagnetic induction. . . . . . . . . . . . . . . . . . . . . . 99
19.4 Lenz's rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
19.7 Vortex electric field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
19.8 Induction emf 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 a circuit. . . . . . . . . . . . . . . . . . . . . . . 116
21.5 Forced electromagnetic oscillations. . . . . . . . . . . . . . . . . . . . . . 119
Alternating current. 1 | |||
Quasi-stationary 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 the oscillatory circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . | |||
AC power | |||
24.1 Current power through 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 Concept of electromagnetic field. . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
27.1 Open oscillatory 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. The forces of elasticity and friction, the pressure of liquid and gas, and much more can be reduced to electromagnetic forces between particles of matter. Electromagnetic interactions themselves are no longer reduced to other, deeper types of interactions.
An equally fundamental type of interaction is gravitation—the 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 ones.
bodies (having an electric charge).
2. Gravitational interaction is always the attraction of one body to another. Electromagnetic interactions can be either attractive or repulsive.
3. Electromagnetic interaction is much more intense than gravitational interaction. For example, the electrical repulsion force of two electrons is 10 42 times the force of their gravitational attraction to each other.
Each charged body has a certain amount of electric charge q. Electric charge is a physical quantity that determines the strength of electromagnetic interaction between natural objects. The unit of charge is the coulomb (C)1.
1.1 Two types of charge
Since gravitational interaction is always attraction, the masses of all bodies are non-negative. But this is not true 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. 1 ; The balls suspended on threads are given charges of one or another sign.
Rice. 1. Interaction of two types of charges
The widespread manifestation of electromagnetic forces is explained by the fact that the atoms of any substance contain charged particles: the nucleus of an atom contains positively charged protons, and negatively charged electrons move in orbits around the nucleus. The charges of a proton and an electron are equal in magnitude, 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. This is why under normal conditions we do not notice electromagnetic influence from others
1 The charge unit is determined through the current unit. 1 C is the charge passing through the cross section of a conductor in 1 s at a current of 1 A.
bodies: the total charge of each of them is zero, and charged particles are evenly distributed throughout 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, is currently not known. We can only assert that accepting this fact as primary provides an adequate description of electromagnetic interactions.
The charge of a proton is 1.6 10 19 C. The charge of an electron is opposite in sign and is equal to
1;6 10 19 Cl. Magnitude
e = 1;6 10 19 Cl
called the elementary charge. This is the minimum possible charge: free particles with a smaller charge were not detected in experiments. Physics cannot yet explain why nature has the smallest charge and why its magnitude is exactly 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 on the contrary, the body lacks electrons: there are N more protons.
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 using friction.
Thus, when a glass rod is rubbed with silk, part of its negative charges goes to the silk. As a result, the stick becomes positively charged and the silk negatively charged. But when rubbing an ebonite stick with wool, some of the negative charges are transferred from the wool to the stick: the stick is charged negatively, and the wool is charged positively.
This method of electrifying bodies is called electrification by friction. You encounter electrified 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 negative metal charges (free electrons), which accumulate on the areas of the body surface closest to the charge. Uncompensated positive charges remain in distant areas.
Despite the fact that the total charge of the metal 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 will be positively charged.
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 stick (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 move in different directions. If you remove the stick, the charges will return to their place and the leaves will fall back.
The phenomenon of electrostatic induction on a grand scale is observed during a thunderstorm. In Fig. 4 we see a thundercloud passing over the earth3.
Rice. 4. Electrification of the earth by a thundercloud
Inside the cloud there are pieces of ice of different sizes, which are mixed by rising air currents, collide with each other and become electrified. It turns out that a negative charge accumulates at the bottom of the cloud, and a positive charge at the top.
The negatively charged lower part of the cloud induces positive charges below it on the surface of the earth. A giant capacitor with colossal voltage appears
2 Image from en.wikipedia.org.
3 Image from elementy.ru.
between the cloud and the ground. If this voltage is sufficient to break down the air gap, then the well-known lightning discharge will occur.
1.3 Law of conservation of charge
Let's return to the example of electrification by friction 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 was equal to zero before the interaction and remains equal to zero after the interaction.
We see here the law of conservation of charge, which states: in a closed system of bodies, the algebraic sum of charges remains unchanged during any processes occurring with these bodies:
q1 + q2 + : : : + qn = const:
The closedness of a system of bodies means that these bodies can exchange charges only among themselves, but not with any other objects external to this system.
When electrifying a stick, there is nothing surprising in the conservation of charge: as many charged particles left the stick as many came to the piece of fabric (or vice versa). The surprising thing is 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 conserved!
For example, in Fig. 5 shows the process! e + e+, in which a portion of electromagnetic radiation (the so-called photon) turns into two charged particles electron e and positron e+. Such a process turns out to be possible under certain conditions, for example, in the electric field of the atomic nucleus.
Rice. 5. Birth of an electron–positron pair
The charge of a positron is equal in magnitude to the charge of an electron and opposite in sign. The law of conservation of charge is fulfilled! Indeed, at the beginning of the process we had a photon whose charge was zero, and at the end we got two particles with a total charge of zero.
The law of conservation of charge (along with the existence of the smallest elementary charge) is a primary scientific fact today. Physicists have not yet been able to explain why nature behaves this way and not otherwise. We can only state that these facts are confirmed by numerous physical experiments.