Page 56
COULLOMB'S LAW (10th grade study, pp. 354-362)
Basic law of electrostatics. The concept of a point charged body.
Measuring the force of interaction between charges using a torsion balance. Coulomb's experiments
Definition of a point charge
Coulomb's law. Formulation and formula
Coulomb force
Definition of charge unit
Coefficient in Coulomb's law
Comparison of electrostatic and gravitational forces in an atom
Equilibrium of static charges and its physical meaning (using the example of three charges)
The basic law of electrostatics is the law of interaction of two stationary point charged bodies.
Installed by Charles Augustin Coulon in 1785 and bears his name.
In nature, point-like charged bodies do not exist, 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 influence the interactions between them. In that case, these bodies can be considered as point bodies.
The strength of interaction between charged bodies depends on the properties of the medium between them. Experience shows that air has very little effect on the strength of this interaction and it turns out to be almost the same as in a vacuum.
Coulomb's experiment
The first results on measuring the force of interaction between charges were obtained in 1785 by the French scientist Charles Augustin Coulomb
A torsion balance was used to measure force.
A small, thin, uncharged golden sphere at one end of an insulating beam, suspended on an elastic silver thread, was balanced at the other end of the rocker by a paper disk.
By turning the rocker it was brought into contact with the same stationary charged sphere, as a result of which its charge was divided equally between the spheres.
The diameter of the spheres was chosen to be much smaller than the distance between them in order to exclude the influence of the size and shape of charged bodies on the measurement results.
A point charge is a charged body whose size is much smaller than the distance of its possible action on other bodies.
The spheres having the same charges began to repel each other, twisting the thread. The angle of rotation was proportional to the force acting on the moving sphere.
The distance between the spheres was measured using a special calibration scale.
By discharging sphere 1 after measuring the force and connecting it again with the stationary sphere, Coulomb reduced the charge on the interacting spheres by 2,4,8, etc. once,
Coulomb's Law:
The force of interaction between two stationary point charges located in a vacuum is directly proportional to the product of the charge moduli and inversely proportional to the square of the distance between them, and is directed along the straight line connecting the charges.
k – proportionality coefficient, depending on the choice of unit system.
I call the F12 force the Coulomb force
The Coulomb force is central, i.e. directed along the line connecting the charge centers.
In SI, the unit of charge is not fundamental, but derivative, and is determined using the Ampere, the basic SI unit.
A coulomb is an electric charge passing through the cross section of a conductor at a current of 1 A in 1 s.
In SI, the proportionality coefficient in Coulomb's law for vacuum is:
k = 9*109 Nm2/Cl2
The coefficient is often written as:
e0 = 8.85*10-12 C2/(Nm2) – electrical constant
Coulomb's law is written in the form:
If a point charge is placed in a medium with a relative permittivity e other than vacuum, the Coulomb force will decrease by a factor of e.
For any medium other than vacuum e > 1
According to Coulomb's law, two point charges of 1 C each, at a distance of 1 m in a vacuum, interact with a force
From this estimate it is clear that a charge of 1 Coulomb is a very large value.
In practice, they use submultiple units - µC (10-6), mC (10-3)
1 C contains 6*1018 charges of electrons.
Using the example of the interaction forces between an electron and a proton in the nucleus, it can be shown that the electrostatic force of interaction between particles is approximately 39 orders of magnitude greater than the gravitational force. However, the electrostatic forces of interaction of macroscopic bodies (generally electrically neutral) are determined only by very small excess charges located on them, and therefore are not large compared to gravitational forces, which depend on the mass of the bodies.
Is equilibrium of static charges possible?
Let's consider a system of two positive point charges q1 and q2.
We will find at what point the third charge should be placed so that it is in equilibrium, and we will also determine the magnitude and sign of this charge.
Static equilibrium occurs when the geometric (vector) sum of forces acting on the body is zero.
The point at which the forces acting on the third charge q3 can cancel each other is located on the straight line between the charges.
In this case, the charge q3 can be either positive or negative. In the first case, repulsive forces are compensated, in the second - attractive forces.
Taking into account Coulomb's law, the static balance of charges will be in the case of:
The equilibrium of the charge q3 does not depend either on its magnitude or on the sign of the charge.
When the charge q3 changes, both the attractive forces (q3 positive) and the repulsive forces (q3 negative) change equally.
By solving a quadratic equation for x, we can show that a charge of any sign and magnitude will be in equilibrium at a point at a distance x1 from charge q1:
Let's find out whether the position of the third charge will be stable or unstable.
(In stable equilibrium, a body removed from the equilibrium position returns to it; in unstable equilibrium, it moves away from it)
With a horizontal displacement, the repulsive forces F31, F32 change due to changes in the distances between the charges, returning the charge to the equilibrium position.
With a horizontal displacement, the charge q3 equilibrium is stable.
With a vertical displacement, the resultant F31, F32 pushes q3
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Charges and electricity are terms required for those cases when the interaction of charged bodies is observed. The forces of repulsion and attraction seem to emanate from charged bodies and spread simultaneously in all directions, gradually fading with distance. This force was once discovered by the famous French naturalist Charles Coulomb, and the rule that charged bodies obey has since been called Coulomb’s Law.
Charles Pendant
The French scientist was born in France, where he received an excellent education. He actively applied the acquired knowledge in engineering sciences and made significant contributions to the theory of mechanisms. Coulomb is the author of works that studied the operation of windmills, the statistics of various structures, and the torsion of threads under the influence of external forces. One of these works helped to discover the Coulomb-Amonton law, which explains friction processes.
But Charles Coulomb made his main contribution to the study of static electricity. The experiments carried out by this French scientist led him to understand one of the most fundamental laws of physics. It is to him that we owe knowledge of the nature of the interaction of charged bodies.
Background
The forces of attraction and repulsion with which electric charges act on each other are directed along the straight line connecting the charged bodies. As distance increases, this force weakens. A century after Isaac Newton discovered his universal law of gravitation, the French scientist Charles Coulomb experimentally investigated the principle of interaction between charged bodies and proved that the nature of such a force is similar to the forces of gravity. Moreover, as it turned out, interacting bodies in an electric field behave in the same way as any bodies with mass in a gravitational field.
Coulomb device
The diagram of the device with which Charles Coulomb made his measurements is shown in the figure:
As you can see, this design is essentially no different from the device that Cavendish used in his time to measure the value of the gravitational constant. An insulating rod suspended on a thin thread ends with a metal ball, which is given a certain electrical charge. Another metal ball is brought closer to the ball, and then, as it approaches, the interaction force is measured by the degree of twisting of the thread.
Coulomb experiment
Coulomb suggested that Hooke's Law, already known at that time, could be applied to the force with which the thread is twisted. The scientist compared the change in force at different distances of one ball from another and found that the force of interaction changes its value in inverse proportion to the square of the distance between the balls. The pendant was able to change the values of the charged ball from q to q/2, q/4, q/8 and so on. With each change in charge, the interaction force changed its value proportionally. So, gradually, a rule was formulated, which was later called “Coulomb’s Law”.
Definition
Experimentally, the French scientist proved that the forces with which two charged bodies interact are proportional to the product of their charges and inversely proportional to the square of the distance between the charges. This statement is Coulomb's law. In mathematical form it can be expressed as follows:
In this expression:
- q - amount of charge;
- d is the distance between charged bodies;
- k is the electrical constant.
The value of the electrical constant largely depends on the choice of unit of measurement. In the modern system, the magnitude of the electric charge is measured in coulombs, and the electrical constant, accordingly, in newton×m 2 / coulomb 2.
Recent measurements have shown that this coefficient must take into account the dielectric constant of the medium in which the experiment is carried out. Now the value is shown in the form of the ratio k=k 1 /e, where k 1 is the electrical constant already familiar to us, and is not an indicator of dielectric constant. Under vacuum conditions this value is equal to unity.
Conclusions from Coulomb's law
The scientist experimented with different amounts of charges, testing the interaction between bodies with different amounts of charge. Of course, he could not measure the electric charge in any units - he lacked both knowledge and appropriate instruments. Charles Coulomb was able to separate a projectile by touching a charged ball with an uncharged one. This is how he obtained fractional values of the initial charge. A number of experiments have shown that the electric charge is conserved and an exchange occurs without increasing or decreasing the amount of charge. This fundamental principle forms the basis of the law of conservation of electric charge. It has now been proven that this law is observed both in the microworld of elementary particles and in the macroworld of stars and galaxies.
Conditions necessary for the fulfillment of Coulomb's law
In order for the law to be implemented with greater accuracy, the following conditions must be met:
- The charges must be point charges. In other words, the distance between the observed charged bodies should be much greater than their sizes. If charged bodies have a spherical shape, then we can assume that the entire charge is located at a point that is the center of the sphere.
- The measured bodies must be motionless. Otherwise, the moving charge will be influenced by numerous external factors, for example, the Lorentz force, which gives the charged body additional acceleration. And also the magnetic field of a moving charged body.
- The observed bodies must be in a vacuum to avoid the influence of air mass flows on the observation results.
Coulomb's law and quantum electrodynamics
From the point of view of quantum electrodynamics, the interaction of charged bodies occurs through the exchange of virtual photons. The existence of such unobservable particles and zero mass, but not zero charge, is indirectly confirmed by the uncertainty principle. According to this principle, a virtual photon can exist between the instants of emission of such a particle and its absorption. The smaller the distance between the bodies, the less time it takes the photon to travel the path, therefore, the greater the energy of the emitted photons. At a small distance between the observed charges, the uncertainty principle allows for the exchange of both short-wave and long-wave particles, and at large distances, short-wave photons do not participate in the exchange.
Are there limits to the application of Coulomb's law?
Coulomb's law completely explains the behavior of two point charges in a vacuum. But when it comes to real bodies, one should take into account the volumetric dimensions of the charged bodies and the characteristics of the environment in which the observation is carried out. For example, some researchers have observed that a body carrying a small charge and forced into the electric field of another object with a large charge begins to be attracted to this charge. In this case, the statement that similarly charged bodies repel each other fails, and another explanation for the observed phenomenon should be sought. Most likely, we are not talking about a violation of Coulomb's law or the principle of conservation of electric charge - it is possible that we are observing phenomena that have not been fully studied, which science will be able to explain a little later.
In this lesson, the topic of which is “Coulomb’s Law,” we will talk about Coulomb’s law itself, what point charges are, and to consolidate the material, we will solve several problems on this topic.
Lesson topic: “Coulomb’s Law.” Coulomb's law quantitatively describes the interaction of stationary point charges - that is, charges that are in a static position relative to each other. This interaction is called electrostatic or electrical and is part of the electromagnetic interaction.
Electromagnetic interaction
Of course, if the charges are in motion, they also interact. This interaction is called magnetic and is described in the section of physics called “Magnetism”.
It is worth understanding that “electrostatics” and “magnetism” are physical models, and together they describe the interaction of both mobile and stationary charges relative to each other. And all together this is called electromagnetic interaction.
Electromagnetic interaction is one of the four fundamental interactions that exist in nature.
Electric charge
What is an electric charge? Definitions in textbooks and the Internet tell us that charge is a scalar quantity that characterizes the intensity of the electromagnetic interaction of bodies. That is, electromagnetic interaction is the interaction of charges, and charge is a quantity that characterizes electromagnetic interaction. It sounds confusing - the two concepts are defined through each other. Let's figure it out!
The existence of electromagnetic interaction is a natural fact, something like an axiom in mathematics. People noticed it and learned to describe it. To do this, they introduced convenient quantities that characterize this phenomenon (including electric charge) and built mathematical models (formulas, laws, etc.) that describe this interaction.
Coulomb's law
Coulomb's law looks like this:
The force of interaction between two stationary point electric charges in a vacuum is directly proportional to the product of their moduli and inversely proportional to the square of the distance between them. It is directed along the straight line connecting the charges, and is an attractive force if the charges are opposite, and a repulsive force if the charges are like.
Coefficient k in Coulomb's law is numerically equal to:
Analogy with gravitational interaction
The law of universal gravitation states: all bodies with mass are attracted to each other. This interaction is called gravitational. For example, the force of gravity with which we are attracted to the Earth is a special case of gravitational interaction. After all, both we and the Earth have mass. The force of gravitational interaction is directly proportional to the product of the masses of interacting bodies and inversely proportional to the square of the distance between them.
The coefficient γ is called the gravitational constant.
Numerically it is equal to: 
.
As you can see, the type of expressions that quantitatively describe gravitational and electrostatic interactions are very similar.
The numerators of both expressions are the product of units characterizing this type of interaction. For gravitational - these are masses, for electromagnetic - charges. The denominator of both expressions is the square of the distance between the objects of interaction.
The inverse relationship with the square of the distance is often found in many physical laws. This allows us to speak about a general pattern connecting the magnitude of the effect with the square of the distance between the objects of interaction.
This proportionality is valid for gravitational, electrical, magnetic interactions, sound force, light, radiation, etc.
This is explained by the fact that the surface area of the sphere of distribution of the effect increases in proportion to the square of the radius (see Fig. 1).
Rice. 1. Increasing the surface area of the spheres
This will look natural if you remember that the area of a sphere is proportional to the square of the radius:
Physically, this means that the force of interaction between two stationary point charges of 1 C, located at a distance of 1 m from each other in a vacuum, will be equal to 9·10 9 N (see Fig. 2).
Rice. 2. The force of interaction between two point charges in 1 C
It would seem that this power is enormous. But it is worth understanding that its order is associated with another characteristic - the amount of charge 1 C. In practice, the charged bodies with which we interact in everyday life have a charge on the order of micro- or even nanocoulombs.
Coefficientand electrical constant
Sometimes, instead of a coefficient, another constant is used that characterizes the electrostatic interaction, which is called the “electric constant”. It is designated . It is related to the coefficient as follows:
By performing simple mathematical transformations, you can express and calculate it:
Both constants, of course, are present in the problem book tables. Coulomb's law will then take the following form:
Let's pay attention to a few subtle points.
It is important to understand that we are talking about interaction. That is, if we take two charges, then each of them will act on the other with a force equal in magnitude. These forces will be directed in opposite directions along a straight line connecting the point charges.
Charges will repel if they have the same sign (both positive or both negative (see Fig. 3)), and attract if they have different signs (one negative, the other positive (see Fig. 4)).
Rice. 3. Interaction of like charges
Rice. 4. Interaction of unlike charges
Point charge
The formulation of Coulomb's law contains the term "point charge". What does this mean? Let's remember the mechanics. When studying, for example, the movement of a train between cities, we neglected its size. After all, the size of the train is hundreds or thousands of times smaller than the distance between cities (see Fig. 5). In this problem we considered the train “material point” - a body whose dimensions we can neglect within the framework of solving a certain problem.
Rice. 5. In this case, we neglect the dimensions of the train
So, point charges are material points that have a charge. In practice, using Coulomb's law, we neglect the sizes of charged bodies in comparison with the distances between them. If the sizes of charged bodies are comparable to the distance between them, then due to the redistribution of charge within the bodies, the electrostatic interaction will be more complex.
At the vertices of a regular hexagon with a side, charges are placed one after another. Find the force acting on the charge located in the center of the hexagon (see Fig. 6).
Rice. 6. Drawing for the conditions of task 1
Let's think: the charge located in the center of the hexagon will interact with each of the charges located at the vertices of the hexagon. Depending on the signs, this will be an attractive force or a repulsive force. With charges 1, 2 and 3 being positive, the charge in the center will experience electrostatic repulsion (see Figure 7).
Rice. 7. Electrostatic repulsion
And with charges 4, 5 and 6 (negative), the charge at the center will have an electrostatic attraction (see Fig. 8).
Rice. 8. Electrostatic attraction
The total force acting on the charge located in the center of the hexagon will be the resultant of the forces ,,,, and, the modulus of each of which can be found using Coulomb’s law. Let's start solving the problem.
Solution
The strength of interaction between the charge located in the center and each of the charges at the vertices depends on the modules of the charges themselves and the distance between them. The distance from the vertices to the center of the regular hexagon is the same, the modules of the interacting charges in our case are also equal (see Fig. 9).
Rice. 9. The distances from the vertices to the center in a regular hexagon are equal
This means that all forces of interaction between the charge in the center of the hexagon and the charges at the vertices will be equal in magnitude. Using Coulomb's law, we can find this module:
The distance from the center to the vertex in a regular hexagon is equal to the length of the side of the regular hexagon, which we know from the condition, therefore:
Now we need to find the vector sum - for this we choose a coordinate system: the axis is along the force, and the axis is perpendicular (see Fig. 10).
Rice. 10. Axes selection
Let's find the total projections on the axis - let's simply denote the module of each of them.
Since the forces are both co-directed with the axis and are at an angle to the axis (see Fig. 11).
Let's do the same for the axis:
The “-” sign is because the forces are directed in the opposite direction of the axis. That is, the projection of the total force on the axis that we have chosen will be equal to 0. It turns out that the total force will act only along the axis; all that remains is to substitute here only the expressions for the modulus of the interaction forces and get the answer. The total force will be equal to:
The problem is solved.
Another subtle point is this: Coulomb’s law says that charges are in a vacuum (see Fig. 12).
Rice. 12. Interaction of charges in vacuum
This is a really important note. Because in an environment other than vacuum, the force of electrostatic interaction will be weakened (see Fig. 13).
Rice. 13. Interaction of charges in a medium other than vacuum
To take this factor into account, a special value was introduced into the electrostatics model, which allows one to make a “correction for the environment.” It is called the dielectric constant of the medium. It is denoted, like the electrical constant, by the Greek letter “epsilon”, but without an index.
The physical meaning of this quantity is as follows.
The force of electrostatic interaction between two stationary point charges in a medium other than vacuum will be ε times less than the force of interaction of the same charges at the same distance in vacuum.
Thus, in a medium other than vacuum, the force of electrostatic interaction between two stationary point charges will be equal to:
The values of the dielectric constant of various substances have long been found and collected in special tables (see Fig. 14).
Rice. 14. Dielectric constant of some substances
We can freely use tabulated values of the dielectric constant of the substances we need when solving problems.
It is important to understand that when solving problems, the force of electrostatic interaction is considered and described in the equations of dynamics as an ordinary force. Let's solve the problem.
Two identical charged balls are suspended in a medium with a dielectric constant on threads of the same length fixed at one point. Determine the charge modulus of the balls if the threads are at right angles to each other (see Fig. 15). The sizes of the balls are negligible compared to the distance between them. The masses of the balls are equal.
Rice. 15. Drawing for problem 2
Let's think: three forces will act on each of the balls - gravity; the force of electrostatic interaction and the tension force of the thread (see Fig. 16).
Rice. 16. Forces acting on the balls
By condition, the balls are identical, that is, their charges are equal both in magnitude and sign, which means that the force of electrostatic interaction in this case will be a repulsive force (in Fig. 16, the forces of electrostatic interaction are directed in different directions). Since the system is in equilibrium, we will use Newton's first law:
Since the condition says that the balls are suspended in a medium with dielectric constant , and the sizes of the balls are negligible compared to the distance between them, then, in accordance with Coulomb’s law, the force with which the balls will repel will be equal to:
Solution
Let's write Newton's first law in projections on the coordinate axes. Let's direct the axis horizontally and the axis vertically (see Fig. 17).
Coulomb's Law is a law that describes the interaction forces between point electric charges.
The modulus of the force of interaction between two point charges in a vacuum is directly proportional to the product of the moduli of these charges and inversely proportional to the square of the distance between them.
Otherwise: Two point charges in vacuum act on each other with forces that are proportional to the product of the moduli of these charges, inversely proportional to the square of the distance between them and directed along the straight line connecting these charges. These forces are called electrostatic (Coulomb).
It is important to note that in order for the law to be true, it is necessary:
point-like charges - that is, the distance between charged bodies is much larger than their sizes - however, it can be proven that the force of interaction of two volumetrically distributed charges with spherically symmetrical non-intersecting spatial distributions is equal to the force of interaction of two equivalent point charges located at centers of spherical symmetry;
their immobility. Otherwise, additional effects take effect: a magnetic field moving charge and the corresponding additional Lorentz force, acting on another moving charge;
interaction in vacuum.
However, with some adjustments, the law is also valid for interactions of charges in a medium and for moving charges.
In vector form in the formulation of C. Coulomb, the law is written as follows:
where is the force with which charge 1 acts on charge 2; - magnitude of charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in absolute value, to the distance between charges - ); - proportionality coefficient. Thus, the law indicates that like charges repel (and unlike charges attract).
IN SSSE unit charge is chosen in such a way that the coefficient k equal to one.
IN International System of Units (SI) one of the basic units is the unit electric current strength ampere, and the unit of charge is pendant- a derivative of it. The ampere value is defined in such a way that k= c 2 10 −7 Gn/m = 8.9875517873681764 10 9 N m 2 / Cl 2 (or Ф −1 m). SI coefficient k is written as:
where ≈ 8.854187817·10 −12 F/m - electrical constant.
Electricity concept. Electrification. Conductors, semiconductors and dielectrics. Elementary charge and its properties. Coulomb's law. Electric field strength. Superposition principle. Electric field as manifestations of interaction. Electric field of an elementary dipole.
The term electricity comes from the Greek word electron (amber).
Electrification is the process of transmitting electrical energy to the body.
charge. This term was introduced in the 16th century by the English scientist and physician Gilbert.
ELECTRIC CHARGE IS A PHYSICAL SCALAR QUANTITY THAT CHARACTERIZES THE PROPERTIES OF BODIES OR PARTICLES TO ENTER AND ELECTROMAGNETIC INTERACTIONS, AND DETERMINES THE STRENGTH AND ENERGY OF THESE INTERACTIONS.
Properties of electric charges:
1. In nature, there are two types of electric charges. Positive (occurs on glass rubbed against leather) and negative (occurs on ebonite rubbed against fur).
2. Like charges repel, unlike charges attract.
3. Electric charge DOES NOT EXIST WITHOUT CHARGE CARRIER PARTICLES (electron, proton, positron, etc.). For example, an electric charge cannot be removed from an electron and other elementary charged particles.
4. Electric charge is discrete, i.e. the charge of any body is an integer multiple of elementary electric charge e(e = 1.6 10 -19 C). Electron (i.e.= 9,11 10 -31 kg) and proton (t p = 1.67 10 -27 kg) are respectively carriers of elementary negative and positive charges. (Particles with a fractional electric charge are known: – 1/3 e and 2/3 e – This quarks and antiquarks , but they were not found in a free state).
5. Electric charge - magnitude relativistically invariant , those. does not depend on the reference frame, which means it does not depend on whether this charge is moving or at rest.
6. From a generalization of experimental data, it was established fundamental law of nature - charge conservation law: algebraic sum-
MA of electric charges of any closed system(a system that does not exchange charges with external bodies) remains unchanged no matter what processes occur within this system.
The law was experimentally confirmed in 1843 by an English physicist
M. Faraday ( 1791-1867) and others, confirmed by the birth and annihilation of particles and antiparticles.
Unit of electric charge (derived unit, since it is determined through the unit of current) - pendant (C): 1 C - electric charge,
passing through the cross section of a conductor at a current strength of 1 A for a time of 1 s.
All bodies in nature are capable of becoming electrified, i.e. acquire an electric charge. Electrification of bodies can be carried out in various ways: contact (friction), electrostatic induction
etc. Any charging process comes down to the separation of charges, in which an excess of positive charge appears on one of the bodies (or part of the body), and an excess of negative charge appears on the other (or other part of the body). The total number of charges of both signs contained in bodies does not change: these charges are only redistributed between bodies.
Electrification of bodies is possible because bodies consist of charged particles. In the process of electrification of bodies, electrons and ions that are in a free state can move. Protons remain in the nuclei.
Depending on the concentration of free charges, bodies are divided into conductors, dielectrics and semiconductors.
Conductors- bodies in which an electric charge can mix throughout its entire volume. Conductors are divided into two groups:
1) conductors of the first kind (metals) - transfer to
their charges (free electrons) are not accompanied by chemical
transformations;
2) conductors of the second kind (for example, molten salts, ra-
solutions of acids) - transfer of charges (positive and negative) into them
ions) leads to chemical changes.
Dielectrics(for example, glass, plastics) - bodies in which there are practically no free charges.
Semiconductors (for example, germanium, silicon) occupy
intermediate position between conductors and dielectrics. This division of bodies is very conditional, however, the large difference in the concentrations of free charges in them causes huge qualitative differences in their behavior and therefore justifies the division of bodies into conductors, dielectrics and semiconductors.
ELECTROSTATICS- science of stationary charges
Coulomb's law.
Law of interaction fixed point electric charges
Experimentally installed in 1785 by Sh. Coulomb using torsion balances.
similar to those used by G. Cavendish to determine the gravitational constant (previously this law was discovered by G. Cavendish, but his work remained unknown for more than 100 years).
Point charge, called a charged body or particle, the dimensions of which can be neglected in comparison with the distance to them.
Coulomb's law: the force of interaction between two stationary point charges located in a vacuum proportional to charges q 1 And q2, and is inversely proportional to the square of the distance r between them :
k - proportionality factor depending on system choice
In SI 
Magnitude ε 0 called electrical constant; it refers to
number fundamental physical constants and is equal to:
ε 0 = 8.85 ∙10 -12 Cl 2 /N∙m 2
In vector form, Coulomb's law in vacuum has the form:
where is the radius vector connecting the second charge to the first, F 12 is the force acting from the second charge on the first.
Accuracy of Coulomb's law at large distances, up to
10 7 m, established during the study of the magnetic field using satellites
in near-Earth space. The accuracy of its implementation at short distances, up to 10 -17 m, verified by experiments on the interaction of elementary particles.
Coulomb's law in the environment
In all media, the force of the Coulomb interaction is less compared to the force of interaction in vacuum or air. A physical quantity that shows how many times the force of electrostatic interaction in a vacuum is greater than in a given medium is called the dielectric constant of the medium and is denoted by the letter ε.
ε = F in vacuum / F in medium
Coulomb's law in general form in SI:
Properties of Coulomb forces.
1. Coulomb forces are forces of the central type, because directed along the straight line connecting the charges
The Coulomb force is an attractive force if the signs of the charges are different and a repulsive force if the signs of the charges are the same
3. Newton's 3rd law is valid for Coulomb forces
4. Coulomb forces obey the principle of independence or superposition, because the force of interaction between two point charges will not change when other charges appear nearby. The resulting force of electrostatic interaction acting on a given charge is equal to the vector sum of the forces of interaction of a given charge with each charge of the system separately.
F= F 12 +F 13 +F 14 + ∙∙∙ +F 1 N
Interactions between charges are carried out through an electric field. An electric field is a special form of existence of matter through which the interaction of electric charges occurs. The electric field manifests itself in that it acts with force on any other charge introduced into this field. An electrostatic field is created by stationary electric charges and propagates in space with a finite speed c.
The strength characteristic of the electric field is called tension.
Tensions electric at a certain point is a physical quantity equal to the ratio of the force with which the field acts on a positive test charge placed at a given point to the modulus of this charge.
Field strength of a point charge q:
Superposition principle: the electric field strength created by a system of charges at a given point in space is equal to the vector sum of the electric field strengths created at this point by each charge separately (in the absence of other charges).
