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.
Publications based on materials by D. Giancoli. "Physics in two volumes" 1984 Volume 2.
There is a force between electric charges. How does it depend on the magnitude of the charges and other factors?
This question was explored in the 1780s by the French physicist Charles Coulomb (1736-1806). He used torsion balances very similar to those used by Cavendish to determine the gravitational constant.
If a charge is applied to a ball at the end of a rod suspended on a thread, the rod is slightly deflected, the thread twists, and the angle of rotation of the thread will be proportional to the force acting between the charges (torsion balance). Using this device, Coulomb determined the dependence of force on the size of charges and the distance between them.
At that time, there were no instruments to accurately determine the amount of charge, but Coulomb was able to prepare small balls with a known charge ratio. If a charged conducting ball, he reasoned, is brought into contact with exactly the same uncharged ball, then the charge present on the first ball, due to symmetry, will be distributed equally between the two balls.
This gave him the ability to receive charges of 1/2, 1/4, etc. from the original one.
Despite some difficulties associated with the induction of charges, Coulomb was able to prove that the force with which one charged body acts on another small charged body is directly proportional to the electric charge of each of them.
In other words, if the charge of any of these bodies is doubled, the force will also be doubled; if the charges of both bodies are doubled at the same time, the force will become four times greater. This is true provided that the distance between the bodies remains constant.
By changing the distance between bodies, Coulomb discovered that the force acting between them is inversely proportional to the square of the distance: if the distance, say, doubles, the force becomes four times less.
So, Coulomb concluded, the force with which one small charged body (ideally a point charge, i.e. a body like a material point that has no spatial dimensions) acts on another charged body is proportional to the product of their charges Q 1 and Q 2 and is inversely proportional to the square of the distance between them:
Here k- proportionality coefficient.
This relationship is known as Coulomb's law; its validity has been confirmed by careful experiments, much more accurate than Coulomb's original, difficult to reproduce experiments. The exponent 2 is currently established with an accuracy of 10 -16, i.e. it is equal to 2 ± 2×10 -16.
Since we are now dealing with a new quantity - electric charge, we can select a unit of measurement so that the constant k in the formula is equal to one. Indeed, such a system of units was widely used in physics until recently.
We are talking about the CGS system (centimeter-gram-second), which uses the electrostatic charge unit SGSE. By definition, two small bodies, each with a charge of 1 SGSE, located at a distance of 1 cm from each other, interact with a force of 1 dyne.
Now, however, charge is most often expressed in the SI system, where its unit is the coulomb (C).
We will give the exact definition of a coulomb in terms of electric current and magnetic field later.
In the SI system the constant k has the magnitude k= 8.988×10 9 Nm 2 / Cl 2.
The charges arising during electrification by friction of ordinary objects (combs, plastic rulers, etc.) are in the order of magnitude a microcoulomb or less (1 µC = 10 -6 C).
The electron charge (negative) is approximately 1.602×10 -19 C. This is the smallest known charge; it has a fundamental meaning and is represented by the symbol e, it is often called the elementary charge.
e= (1.6021892 ± 0.0000046)×10 -19 C, or e≈ 1.602×10 -19 Cl.
Since a body cannot gain or lose a fraction of an electron, the total charge of the body must be an integer multiple of the elementary charge. They say that the charge is quantized (that is, it can take only discrete values). However, since the electron charge e is very small, we usually do not notice the discreteness of macroscopic charges (a charge of 1 µC corresponds to approximately 10 13 electrons) and consider the charge to be continuous.
The Coulomb formula characterizes the force with which one charge acts on another. This force is directed along the line connecting the charges. If the signs of the charges are the same, then the forces acting on the charges are directed in opposite directions. If the signs of the charges are different, then the forces acting on the charges are directed towards each other.
Note that, in accordance with Newton's third law, the force with which one charge acts on another is equal in magnitude and opposite in direction to the force with which the second charge acts on the first.
Coulomb's law can be written in vector form, similar to Newton's law of universal gravitation:
Where F 12 - vector of force acting on the charge Q 1 charge side Q 2,
- distance between charges,
- unit vector directed from Q 2 k Q 1.
It should be borne in mind that the formula is applicable only to bodies the distance between which is significantly greater than their own dimensions. Ideally, these are point charges. For bodies of finite size, it is not always clear how to calculate the distance r between them, especially since the charge distribution may be non-uniform. If both bodies are spheres with a uniform charge distribution, then r means the distance between the centers of the spheres. It is also important to understand that the formula determines the force acting on a given charge from a single charge. If the system includes several (or many) charged bodies, then the resulting force acting on a given charge will be the resultant (vector sum) of the forces acting on the part of the remaining charges. The constant k in the Coulomb Law formula is usually expressed in terms of another constant, ε 0
, the so-called electrical constant, which is related to k ratio k = 1/(4πε 0). Taking this into account, Coulomb's law can be rewritten as follows:
where with the highest accuracy today
or rounded
Writing most other equations of electromagnetic theory is simplified by using ε 0 , because the 4π the final result is often shortened. Therefore, we will generally use Coulomb's Law, assuming that:
Coulomb's law describes the force acting between two charges at rest. When charges move, additional forces are created between them, which we will discuss in subsequent chapters. Here only charges at rest are considered; This section of the study of electricity is called electrostatics.
To be continued. Briefly about the following publication:
Electric field is one of two components of the electromagnetic field, which is a vector field that exists around bodies or particles with an electric charge, or that arises when the magnetic field changes.
Comments and suggestions are accepted and welcome!
The basic law of interaction of electric charges was found experimentally by Charles Coulomb in 1785. Coulomb found that the force of interaction between two small charged metal balls is inversely proportional to the square of the distance 
between them and depends on the magnitude of the charges 
And 
:
,
Where 
-proportionality factor
.
Forces acting on charges, are central
, that is, they are directed along the straight line connecting the charges. 
Coulomb's law can be written down in vector form:
,
Where 
-
charge side 
,
- radius vector connecting the charge 
with charge 
;
- module of the radius vector.
Force acting on the charge 
from the outside 
equal to 
,
.
Coulomb's law in this form
fair only for the interaction of point electric charges, that is, such charged bodies whose linear dimensions can be neglected in comparison with the distance between them.
expresses the strength of interaction between stationary electric charges, that is, this is the electrostatic law.
Formulation of Coulomb's law:
The force of electrostatic interaction between two point electric charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Proportionality factor
in Coulomb's law depends
from the properties of the environment
selection of units of measurement of quantities included in the formula.
That's why 
can be represented by the relation 
,
Where 
-coefficient depending only on the choice of system of units of measurement;
- a dimensionless quantity characterizing the electrical properties of the medium is called relative dielectric constant of the medium
. It does not depend on the choice of system of measurement units and is equal to one in a vacuum.
Then Coulomb's law will take the form: 
,
for vacuum 
,
Then 
-the relative dielectric constant of a medium shows how many times in a given medium the force of interaction between two point electric charges is 
And 
, located at a distance from each other 
, less than in a vacuum.
In the SI system coefficient 
, And
Coulomb's law has the form:
.
This rationalized notation of the law K catch.
- electrical constant, 
.
In the SGSE system
,
.
In vector form, Coulomb's law takes the form 
Where 
-vector of force acting on the charge 
charge side
,
- radius vector connecting the charge 
with charge
r–modulus of the radius vector 
.
Any charged body consists of many point electric charges, therefore the electrostatic force with which one charged body acts on another is equal to the vector sum of the forces applied to all point charges of the second body by each point charge of the first body.
1.3. Electric field. Tension.
Space, in which the electric charge is located has certain physical properties.
Just in case another the charge introduced into this space is acted upon by electrostatic Coulomb forces.
If a force acts at every point in space, then a force field is said to exist in that space.
The field, along with matter, is a form of matter.
If the field is stationary, that is, does not change over time, and is created by stationary electric charges, then such a field is called electrostatic.
Electrostatics studies only electrostatic fields and interactions of stationary charges.
To characterize the electric field, the concept of intensity is introduced
.
Tensionyu at each point of the electric field is called the vector 
, numerically equal to the ratio of the force with which this field acts on a test positive charge placed at a given point and the magnitude of this charge, and directed in the direction of the force.
Test charge, which is introduced into the field, is assumed to be a point charge and is often called a test charge.
- He does not participate in the creation of the field, which is measured with its help.
It is assumed that this charge does not distort the field being studied, that is, it is small enough and does not cause a redistribution of charges that create the field.
If on a test point charge 
the field acts by force 
, then the tension 
.
Tension units:
SI: 
SSSE: 
In the SI system expression
For 
point charge fields:
.
In vector form: 
Here 
– radius vector drawn from the charge q, creating a field at a given point.
T 
in this way electric field strength vectors of a point chargeq
at all points of the field are directed radially(Fig. 1.3)
- from the charge, if it is positive, “source”
- and to the charge if it is negative"drain"
For graphical interpretation electric field is introduced concept of a line of force orlines of tension . This
curve , the tangent at each point to which coincides with the tension vector.
The voltage line starts at a positive charge and ends at a negative charge.
The tension lines do not intersect, since at each point of the field the tension vector has only one direction.
The forces of electrostatic interaction depend on the shape and size of the electrified bodies, as well as on the nature of the charge distribution on these bodies. In some cases, we can neglect the shape and size of charged bodies and assume that each charge is concentrated at one point. Point charge is an electric charge when the size of the body on which this charge is concentrated is much less than the distance between the charged bodies. Approximately point charges can be obtained experimentally by charging, for example, fairly small balls.
The interaction of two point charges at rest determines the basic law of electrostatics - Coulomb's law. This law was experimentally established in 1785 by a French physicist Charles Augustin Pendant(1736 – 1806). The formulation of Coulomb's law is as follows:
The power of interaction two point stationary charged bodies in a vacuum is directly proportional to the product of the charge modules and inversely proportional to the square of the distance between them.
This interaction force is called Coulomb force, And Coulomb's law formula will be the following:
F = k (|q 1 | |q 2 |) / r 2
Where |q1|, |q2| – charge modules, r – distances between charges, k – proportionality coefficient.
The coefficient k in SI is usually written in the form:
K = 1 / (4πε 0 ε)
Where ε 0 = 8.85 * 10 -12 C/N*m 2 is the electrical constant, ε is the dielectric constant of the medium.
For vacuum ε = 1, k = 9 * 10 9 N*m/Cl 2.
The force of interaction between stationary point charges in a vacuum:
F = · [(|q 1 | · |q 2 |) / r 2 ]
If two point charges are placed in a dielectric and the distance from these charges to the boundaries of the dielectric is significantly greater than the distance between the charges, then the force of interaction between them is equal to:
F = · [(|q 1 | · |q 2 |) / r 2 ] = k · (1 /π) · [(|q 1 | · |q 2 |) / r 2 ]
Dielectric constant of the medium is always greater than unity (π > 1), therefore the force with which charges interact in a dielectric is less than the force of their interaction at the same distance in vacuum.
The forces of interaction between two stationary point charged bodies are directed along the straight line connecting these bodies (Fig. 1.8).
Rice. 1.8. Forces of interaction between two stationary point charged bodies.
Coulomb forces, like gravitational forces, obey Newton's third law:
F 1.2 = -F 2.1
The Coulomb force is a central force. As experience shows, like charged bodies repel, oppositely charged bodies attract.
The force vector F 2.1 acting from the second charge on the first is directed towards the second charge if the charges are of different signs, and in the opposite direction if the charges are of the same sign (Fig. 1.9).
Rice. 1.9. Interaction of unlike and like electric charges.
Electrostatic repulsive forces is considered to be positive gravity– negative. The signs of the interaction forces correspond to Coulomb's law: the product of like charges is a positive number, and the repulsive force has a positive sign. The product of opposite charges is a negative number, which corresponds to the sign of the force of attraction.
In Coulomb's experiments, the interaction forces of charged balls were measured, for which they used torsion scales(Fig. 1.10). A light glass rod is suspended from a thin silver thread. With, at one end of which a metal ball is attached A, and on the other there is a counterweight d. The upper end of the thread is fixed to the rotating head of the device e, the angle of rotation of which can be accurately measured. Inside the device there is a metal ball of the same size b, fixedly mounted on the lid of the scale. All parts of the device are placed in a glass cylinder, on the surface of which there is a scale that allows you to determine the distance between the balls a And b at their various positions.
Rice. 1.10. Coulomb experiment (torsion balance).
When the balls are charged with the same charges, they repel each other. In this case, the elastic thread is twisted at a certain angle to hold the balls at a fixed distance. The angle of twist of the thread determines the force of interaction between the balls depending on the distance between them. The dependence of the interaction force on the magnitude of the charges can be established as follows: give each of the balls a certain charge, place them at a certain distance and measure the angle of twist of the thread. Then you need to touch one of the balls with a charged ball of the same size, changing its charge, since when bodies of equal size come into contact, the charge is distributed equally between them. To maintain the same distance between the balls, it is necessary to change the angle of twist of the thread, and therefore, determine a new value of the interaction force with a new charge.
In 1785, the French physicist Charles Coulomb experimentally established the basic law of electrostatics - the law of interaction of two stationary point charged bodies or particles.
The law of interaction of stationary electric charges - Coulomb's law - is a basic (fundamental) physical law and can only be established experimentally. It does not follow from any other laws of nature.
If we denote the charge modules by | q 1 | and | q 2 |, then Coulomb’s law can be written in the following form:
\(~F = k \cdot \dfrac(|q_1| \cdot |q_2|)(r^2)\) , (1)
Where k– proportionality coefficient, the value of which depends on the choice of units of electric charge. In the SI system \(~k = \dfrac(1)(4 \pi \cdot \varepsilon_0) = 9 \cdot 10^9\) N m 2 / C 2, where ε 0 is the electrical constant equal to 8.85 ·10 -12 C 2 /N m 2.
Statement of the law:
the force of interaction between two point stationary charged bodies in a vacuum is directly proportional to the product of the charge modules and inversely proportional to the square of the distance between them.
This force is called Coulomb.
Coulomb's law in this formulation is valid only for point charged bodies, because only for them the concept of distance between charges has a certain meaning. There are no point charged bodies in nature. But if the distance between the bodies is many times greater than their size, then neither the shape nor the size of the charged bodies significantly, as experience shows, affects the interaction between them. In this case, the bodies can be considered as point bodies.
It is easy to find that two charged balls suspended on threads either attract each other or repel each other. It follows that the forces of interaction between two stationary point charged bodies are directed along the straight line connecting these bodies. Such forces are called central. If we denote by \(~\vec F_(1,2)\) the force acting on the first charge from the second, and by \(~\vec F_(2,1)\) the force acting on the second charge from the first (Fig. 1), then, according to Newton’s third law, \(~\vec F_(1,2) = -\vec F_(2,1)\) . Let us denote by \(\vec r_(1,2)\) the radius vector drawn from the second charge to the first (Fig. 2), then
\(~\vec F_(1,2) = k \cdot \dfrac(q_1 \cdot q_2)(r^3_(1,2)) \cdot \vec r_(1,2)\) . (2)
If the signs of the charges q 1 and q 2 are the same, then the direction of the force \(~\vec F_(1,2)\) coincides with the direction of the vector \(~\vec r_(1,2)\) ; otherwise, the vectors \(~\vec F_(1,2)\) and \(~\vec r_(1,2)\) are directed in opposite directions.
Knowing the law of interaction of point charged bodies, one can calculate the force of interaction of any charged bodies. To do this, bodies must be mentally broken down into such small elements that each of them can be considered a point. By adding geometrically the forces of interaction of all these elements with each other, we can calculate the resulting interaction force.
The discovery of Coulomb's law is the first concrete step in studying the properties of electric charge. The presence of an electric charge in bodies or elementary particles means that they interact with each other according to Coulomb's law. No deviations from the strict implementation of Coulomb's law have currently been detected.
Coulomb's experiment
The need to conduct Coulomb's experiments was caused by the fact that in the middle of the 18th century. A lot of high-quality data on electrical phenomena has accumulated. There was a need to give them a quantitative interpretation. Since the electrical interaction forces were relatively small, a serious problem arose in creating a method that would make it possible to make measurements and obtain the necessary quantitative material.
The French engineer and scientist C. Coulomb proposed a method for measuring small forces, which was based on the following experimental fact discovered by the scientist himself: the force arising during elastic deformation of a metal wire is directly proportional to the angle of twist, the fourth power of the diameter of the wire and inversely proportional to its length:
\(~F_(ynp) = k \cdot \dfrac(d^4)(l) \cdot \varphi\) ,
Where d– diameter, l– wire length, φ – twist angle. In the given mathematical expression, the proportionality coefficient k was determined empirically and depended on the nature of the material from which the wire was made.
This pattern was used in the so-called torsion balances. The created scales made it possible to measure negligible forces of the order of 5·10 -8 N.
Rice. 3 Torsion scales (Fig. 3, a) consisted of a light glass rocker 9 10.83 cm long, suspended on a silver wire 5 about 75 cm long, 0.22 cm in diameter. At one end of the rocker there was a gilded elderberry ball 8 , and on the other - a counterweight 6 - a paper circle dipped in turpentine. The upper end of the wire was attached to the head of the device 1 . There was also a sign here 2 , with the help of which the angle of twist of the thread was measured on a circular scale 3 . The scale was graduated. This entire system was housed in glass cylinders 4 And 11 . In the upper cover of the lower cylinder there was a hole into which a glass rod with a ball was inserted 7 at the end. In the experiments, balls with diameters ranging from 0.45 to 0.68 cm were used.
Before the start of the experiment, the head indicator was set to zero. Then the ball 7 charged from a pre-electrified ball 12 . When the ball touches 7 with movable ball 8 charge redistribution occurred. However, due to the fact that the diameters of the balls were the same, the charges on the balls were also the same 7 And 8 .
Due to the electrostatic repulsion of the balls (Fig. 3, b), the rocker 9 turned by some angle γ (on a scale 10 ). Using the head 1 this rocker returned to its original position. On a scale 3 pointer 2 allowed to determine the angle α twisting the thread. Total twist angle φ = γ + α . The force of interaction between the balls was proportional φ , i.e., by the angle of twist one can judge the magnitude of this force.
With a constant distance between the balls (it was recorded on a scale 10 in degree measure) the dependence of the force of electrical interaction of point bodies on the amount of charge on them was studied.
To determine the dependence of the force on the charge of the balls, Coulomb found a simple and ingenious way to change the charge of one of the balls. To do this, he connected a charged ball (balls 7 or 8 ) with the same size uncharged (ball 12 on the insulating handle). In this case, the charge was distributed equally between the balls, which reduced the charge under study by 2, 4, etc. times. The new value of the force at the new value of the charge was again determined experimentally. At the same time, it turned out that the force is directly proportional to the product of the charges of the balls:
\(~F \sim q_1 \cdot q_2\) .
The dependence of the strength of electrical interaction on distance was discovered as follows. After imparting a charge to the balls (they had the same charge), the rocker deviated at a certain angle γ . Then turn the head 1 this angle decreased to γ 1 . Total twist angle φ 1 = α 1 + (γ - γ 1)(α 1 – head rotation angle). When the angular distance of the balls is reduced to γ 2 total twist angle φ 2 = α 2 + (γ - γ 2) . It was noticed that if γ 1 = 2γ 2, TO φ 2 = 4φ 1, i.e., when the distance decreases by a factor of 2, the interaction force increases by a factor of 4. The moment of force increased by the same amount, since during torsional deformation the moment of force is directly proportional to the angle of twist, and therefore the force (the arm of the force remained unchanged). This leads to the following conclusion: The force of interaction between two charged balls is inversely proportional to the square of the distance between them:
\(~F \sim \dfrac(1)(r^2)\) .
Literature
- Myakishev G.Ya. Physics: Electrodynamics. 10-11 grades: textbook. for in-depth study of physics / G.Ya. Myakishev, A.Z. Sinyakov, B.A. Slobodskov. – M.: Bustard, 2005. – 476 p.
- Volshtein S.L. et al. Methods of physical science at school: A manual for teachers / S.L. Volshtein, S.V. Pozoisky, V.V. Usanov; Ed. S.L. Wolshtein. – Mn.: Nar. Asveta, 1988. – 144 p.