In 1785, the French physicist Charles Coulomb experimentally established the basic law of electrostatics - the law of the interaction of two motionless point charged bodies or particles.

The law of interaction of motionless electric charges - Coulomb's law - is the main (fundamental) physical law and can only be established empirically. It does not follow from any other laws of nature.

If we designate charge modules as | 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– coefficient of proportionality, 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 /Cl 2, where ε 0 is an electrical constant equal to 8.85 10 -12 C 2 /Nm 2 .

The wording of the law:

the force of interaction of two point motionless charged bodies in vacuum is directly proportional to the product of 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, as experience shows, does not significantly affect the interaction between them. In this case, the bodies can be considered as point ones.

It is easy to find that two charged balls suspended on strings either attract each other or repel each other. It follows from this that the forces of interaction of two motionless point charged bodies are directed along the straight line connecting these bodies. Such forces are called central. If through \(~\vec F_(1,2)\) we denote the force acting on the first charge from the second, and through \(~\vec F_(2,1)\) the force acting on the second charge from the first (Fig. 1), then, according to Newton's third law, \(~\vec F_(1,2) = -\vec F_(2,1)\) . 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 charge signs 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, it is possible to calculate the force of interaction of any charged bodies. To do this, the body must be mentally divided into such small elements that each of them can be considered a point. Adding geometrically the forces of interaction of all these elements with each other, it is possible to calculate the resulting force of interaction.

The discovery of Coulomb's law is the first concrete step in the study of 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 the Coulomb law. No deviations from the strict implementation of Coulomb's law have been found at present.

Coulomb experience

The need for Coulomb's experiments was caused by the fact that in the middle of the 18th century. accumulated a lot of qualitative data on electrical phenomena. There was a need to give them a quantitative interpretation. Since the forces of electrical interaction 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 from the elastic deformation of a metal wire is directly proportional to the angle of twist, the fourth power of the wire diameter 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 above mathematical expression, the proportionality coefficient k was found 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

The torsion balance (Fig. 3, a) consisted of a light glass beam 9 10.83 cm long, suspended from a silver wire 5 about 75 cm long, 0.22 cm in diameter. At one end of the rocker 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 instrument head 1 . There was also a pointer here. 2 , with the help of which the angle of twisting of the thread was counted on a circular scale 3 . The scale has been graduated. The whole 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 moving ball 8 charge was redistributed. However, due to the fact that the diameters of the balls were the same, the charges on the balls were the same. 7 and 8 .

Due to the electrostatic repulsion of the balls (Fig. 3, b), the rocker 9 turned to some angle γ (on a scale 10 ). With head 1 this rocker returned to its original position. On a scale 3 pointer 2 allowed to determine the angle α thread twisting. Total twist angle φ = γ + α . The force of the interaction of the balls was proportional φ , i.e., the angle of twist can be used to judge the magnitude of this force.

At a constant distance between the balls (it was fixed on a scale 10 in degree measure) the dependence of the force of electrical interaction of point bodies on the magnitude of the charge on them was studied.

To determine the dependence of 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 investigated charge 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 electrical interaction force on the distance was discovered as follows. After the charge was communicated to the balls (they had the same charge), the rocker was deviated by a certain angle γ . Then turning the head 1 this angle is reduced to γ one . Total angle of twist φ 1 = α 1 + (γ - γ 1)(α 1 - head rotation angle). When the angular distance of the balls decreases to γ 2 total twist angle φ 2 = α 2 + (γ - γ 2). It was noticed that if γ 1 = 2γ 2 , THEN φ 2 = 4φ 1 , i.e., when the distance decreased by a factor of 2, the interaction force increased by a factor of 4. The moment of force increased by the same amount, since during torsion deformation the moment of force is directly proportional to the angle of twist, and hence the force (the arm of the force remained unchanged). From this follows the conclusion: The force between two charged spheres is inversely proportional to the square of the distance between them:

\(~F \sim \dfrac(1)(r^2)\) .

Literature

1. Myakishev G.Ya. Physics: Electrodynamics. 10-11 cells: textbook. for in-depth study of physics / G.Ya. Myakishev, A.Z. Sinyakov, B.A. Slobodskov. – M.: Bustard, 2005. – 476 p.
2. Volshtein S.L. et al. Methods of physical science at school: A guide for the teacher / S.L. Volshtein, S.V. Pozoisky, V.V. Usanov; Ed. S.L. Volshtein. - Mn.: Nar. asveta, 1988. - 144 p.

Charges and electricity are terms that are obligatory 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 away at a 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 a significant contribution to the theory of mechanisms. Coulomb is the author of works that studied the operation of windmills, the statistics of various structures, the twisting of threads under the influence of external forces. One of these works helped discover the Coulomb-Amonton law, which explains friction processes.

But Charles Coulomb made the main contribution to the study of static electricity. The experiments that this French scientist conducted led him to understand one of the most fundamental laws of physics. It is to him that we owe our 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 the distance increases, this force weakens. A century after Isaac Newton discovered his universal law of gravity, the French scientist C. 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 scheme of the device with which Charles Coulomb made his measurements is shown in the figure:

As you can see, in essence this design does not differ from the device that Cavendish once used 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 electric charge. Another metal ball is approached 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 the then-known Hooke's Law can 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 interaction force changes its value inversely with the square of the distance between the balls. The pendant managed 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 proportionally changed its value. 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 is the 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 the unit of measure. In the modern system, the magnitude of the electric charge is measured in coulombs, and the electrical constant, respectively, in newton × m 2 / coulomb 2.

Recent measurements have shown that this coefficient should take into account the dielectric constant of the medium in which the experiment is carried out. Now the value is shown as the ratio k=k 1 /e, where k 1 is the electrical constant already familiar to us, and is not an indicator of the permittivity. Under vacuum conditions, this value is equal to unity.

Conclusions from Coulomb's law

The scientist experimented with different charges, testing the interaction between bodies with different charges. Of course, he could not measure the electric charge in any units - he lacked neither knowledge nor appropriate instruments. Charles Coulomb was able to separate the projectile by touching the charged ball uncharged. So he received fractional values ​​of the initial charge. A number of experiments have shown that the electric charge is conserved, the exchange takes place without an increase or decrease in the amount of charge. This fundamental principle formed the basis of the law of conservation of electric charge. At present, it has been proved that this law is observed both in the microcosm of elementary particles and in the macrocosm of stars and galaxies.

Conditions necessary for the fulfillment of Coulomb's law

In order for the law to be fulfilled with greater accuracy, the following conditions must be met:

• Charges must be point. In other words, the distance between the observed charged bodies must be much larger than their sizes. If charged bodies are spherical, then we can assume that all the charge is at a point that is the center of the sphere.
• The bodies to be measured must be stationary. Otherwise, the moving charge will be influenced by numerous third-party factors, for example, the Lorentz force, which gives the charged body additional acceleration. As well as 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 results of observations.

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 supported by the uncertainty principle. According to this principle, a virtual photon can exist between the moments of emission of such a particle and its absorption. The smaller the distance between the bodies, the less time the photon spends on the passage of the path, therefore, the greater the energy of the emitted photons. At a small distance between the observed charges, the uncertainty principle allows 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 fully 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 charged bodies and the characteristics of the medium in which the observation is made. For example, some researchers have observed that a body that carries a small charge and is forcibly brought 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 to the end, which science will be able to explain a little later.

The basic law of interaction of electric charges was found by Charles Coulomb in 1785 experimentally. 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 in vector form:
,

where -charge side ,

is the radius vector connecting the charge with charge ;

is the modulus of the radius vector.

Force acting on a charge from the side is equal to
,
.

Coulomb's law in this form

fair only for the interaction of point electric charges, that is, such charged bodies, the linear dimensions of which can be neglected in comparison with the distance between them.

expresses the strength of the interaction between fixed electric charges, that is, this is the electrostatic law.

Formulation of Coulomb's Law:

The strength of the 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 measure for the quantities included in the formula.

So can be represented by the relation
,

where -coefficient depending only on the choice of system of units;

- a dimensionless quantity characterizing the electrical properties of the medium is called relative permittivity of the medium . It does not depend on the choice of the system of units and is equal to one in vacuum.

Then Coulomb's law takes the form:
,

for vacuum
,

then
-the relative permittivity of a medium shows how many times in a given medium the force of interaction between two point electric charges and , located at a distance from each other , less than in vacuum.

In the SI system coefficient
, and

Coulomb's law has the form:
.

This is rationalized notation of the law K oolon.

- electrical constant,
.

In the GSSE system
,
.

In vector form, Coulomb's law takes the form

where -the vector of the force acting on the charge charge side ,

is the radius vector connecting the charge with charge

r is the modulus of the radius vector .

Any charged body consists of many point electric charges, so 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 from each point charge of the first body.

1.3 Electric field. Tension.

Space, in which there is an electric charge, has certain physical properties.

For everyone another the charge introduced into this space is acted upon by electrostatic Coulomb forces.

If a force acts at every point in space, then we say that there is a force field in this space.

The field, along with matter, is a form of matter.

If the field is stationary, that is, does not change in time, and is created by stationary electric charges, then such a field is called electrostatic.

Electrostatics studies only electrostatic fields and interactions of fixed charges.

To characterize the electric field, the concept of intensity is introduced . tensionu 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.

trial charge, which is introduced into the field, is assumed to be a point and is often called a test charge.

- He does not participate in the creation of the field, which is measured with it.

It is assumed that this charge does not distort the field under study, that is, it is small enough and does not cause a redistribution of the charges that create the field.

If for a test point charge the field acts as a force , then the tension
.

Tension units:

SI:

SGSE:

In the SI system expression for point charge fields:

.

In vector form:

Here is the radius vector drawn from the charge q, which creates a field, to a given point.

T
how, electric field strength vectors of a point chargeq at all points the fields are directed radially(fig.1.3)

- from the charge, if it is positive, "source"

- and to the charge if it is negative"stock"

For graphical interpretation electric field is injected the concept of a line of force ortension lines . This is

curve , the tangent at each point to which coincides with the intensity vector.

The tension line starts on a positive charge and ends on a negative one.

The tension lines do not intersect, since at each point of the field the tension vector has only one direction.

Law

Coulomb's law

The module of the interaction force of two point charges in vacuum is directly proportional to the product of the modules 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 modules 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).

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.

where is the force with which charge 1 acts on charge 2; - the magnitude of the charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in modulus, to the distance between charges - ); - coefficient of proportionality. Thus, the law indicates that charges of the same name repel (and opposite charges attract).

AT SGSE unit charge is chosen in such a way that the coefficient k is equal to one.

AT International System of Units (SI) one of the basic units is the unit electric current strength ampere, and the unit of charge is pendant is its derivative. The ampere is defined in such a way that k= c2 10−7 gn/m = 8.9875517873681764 109 H m2/ Cl 2 (or Ф−1 m). In SI coefficient k is written as:

where ≈ 8.854187817 10−12 F/m - electrical constant.

Coulomb's law is:

Coulomb's law For the law of dry friction, see Amonton-Coulomb law Magnetostatics Electrodynamics Electric circuit Covariant formulation Famous scientists

Coulomb's law is a law describing the forces of interaction between point electric charges.

It was discovered by Charles Coulomb in 1785. After conducting a large number of experiments with metal balls, Charles Coulomb gave the following formulation of the law:

The module of the interaction force of two point charges in a vacuum is directly proportional to the product of the modules 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 modules 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:

1. point charges - that is, the distance between charged bodies is much greater than their size - however, it can be proved that the force of interaction of two volumetrically distributed charges with spherically symmetric non-intersecting spatial distributions is equal to the force of interaction of two equivalent point charges located at the centers of spherical symmetry;
2. their immobility. Otherwise, additional effects come into force: the magnetic field of the moving charge and the corresponding additional Lorentz force acting on another moving charge;
3. interaction in a 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 S. Coulomb, the law is written as follows:

where is the force with which charge 1 acts on charge 2; - the magnitude of the charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in absolute value, to the distance between charges -); - coefficient of proportionality. Thus, the law indicates that charges of the same name repel (and opposite charges attract).

Coefficient k

In the CGSE, the unit of charge is chosen in such a way that the coefficient k is equal to one.

In the International System of Units (SI), one of the basic units is the unit of electric current strength, the ampere, and the unit of charge, the coulomb, is a derivative of it. The ampere is defined in such a way that k= c2 10-7 H/m = 8.9875517873681764 109 N m2/C2 (or F−1 m). In SI coefficient k is written as:

where ≈ 8.854187817 10−12 F/m is the electrical constant.

In a homogeneous isotropic substance, the relative permittivity of the medium ε is added to the denominator of the formula.

Coulomb's law in quantum mechanics

In quantum mechanics, Coulomb's law is formulated not with the help of the concept of force, as in classical mechanics, but with the help of the concept of the potential energy of the Coulomb interaction. In the case when the system considered in quantum mechanics contains electrically charged particles, the terms expressing the potential energy of the Coulomb interaction are added to the Hamiltonian operator of the system, as it is calculated in classical mechanics.

Thus, the Hamilton operator of an atom with a nuclear charge Z looks like:

Here m is the mass of the electron, e- its charge, - the absolute value of the radius vector j th electron, . The first term expresses the kinetic energy of electrons, the second term - the potential energy of the Coulomb interaction of electrons with the nucleus and the third term - the potential Coulomb energy of mutual repulsion of electrons. The summation in the first and second terms is carried out over all N electrons. In the third term, the summation goes over all pairs of electrons, and each pair occurs once.

Coulomb's law from the point of view of quantum electrodynamics

According to quantum electrodynamics, the electromagnetic interaction of charged particles is carried out by the exchange of virtual photons between particles. The uncertainty principle for time and energy allows the existence of virtual photons for the time between the moments of their emission and absorption. The smaller the distance between charged particles, the less time virtual photons need to overcome this distance and, consequently, the greater the energy of virtual photons is allowed by the uncertainty principle. At small distances between charges, the uncertainty principle allows the exchange of both long-wavelength and short-wavelength photons, and at large distances, only long-wavelength photons participate in the exchange. Thus, with the help of quantum electrodynamics, one can derive Coulomb's law.

Story

For the first time to investigate experimentally the law of interaction of electrically charged bodies was proposed by G. V. Richman in 1752-1753. He intended to use for this purpose the "indicator" electrometer designed by him. The implementation of this plan was prevented by the tragic death of Richman.

In 1759 F. Epinus, a professor of physics at the St. Petersburg Academy of Sciences, who took over the chair of Richmann after his death, suggested for the first time that charges should interact inversely with the square of the distance. In 1760, a brief report appeared that D. Bernoulli in Basel established a quadratic law using an electrometer designed by him. In 1767, Priestley noted in his History of Electricity that Franklin's experience of finding the absence of an electric field inside a charged metal sphere could mean that "electrical attraction follows exactly the same law as gravitation, that is, the square of distance". The Scottish physicist John Robison claimed (1822) to have discovered in 1769 that balls with the same electric charge repel with a force inversely proportional to the square of the distance between them, and thus anticipated the discovery of Coulomb's law (1785).

Approximately 11 years before Coulomb, in 1771, the law of interaction of charges was experimentally discovered by G. Cavendish, but the result was not published and remained unknown for a long time (over 100 years). The Cavendish manuscripts were handed over to D.K. Maxwell only in 1874 by one of Cavendish's descendants at the grand opening of the Cavendish Laboratory and published in 1879.

Coulomb himself was engaged in the study of the torsion of threads and invented the torsion balance. He discovered his law, using them to measure the forces of interaction of charged balls.

Coulomb's law, superposition principle and Maxwell's equations

Coulomb's law and the superposition principle for electric fields are completely equivalent to Maxwell's equations for electrostatics and. That is, the Coulomb law and the superposition principle for electric fields are satisfied if and only if the Maxwell equations for electrostatics are satisfied and, conversely, the Maxwell equations for electrostatics are satisfied if and only if the Coulomb law and the superposition principle for electric fields are satisfied.

Degree of accuracy of Coulomb's law

Coulomb's law is an experimentally established fact. Its validity has been repeatedly confirmed by more and more precise experiments. One of the directions of such experiments is to check whether the exponent differs r in the law of 2. To find this difference, one uses the fact that if the degree is exactly equal to two, then there is no field inside the cavity in the conductor, whatever the shape of the cavity or conductor.

Experiments conducted in 1971 in the United States by E. R. Williams, D. E. Voller, and G. A. Hill showed that the exponent in Coulomb's law is 2 to within .

To test the accuracy of Coulomb's law at intraatomic distances, W. Yu. Lamb and R. Rutherford in 1947 used measurements of the relative arrangement of hydrogen energy levels. It was found that even at distances of the order of atomic 10−8 cm, the exponent in the Coulomb law differs from 2 by no more than 10−9.

The coefficient in Coulomb's law remains constant up to 15·10−6.

Corrections to Coulomb's law in quantum electrodynamics

At short distances (on the order of the Compton wavelength of an electron, ≈3.86 10−13 m, where is the mass of the electron, is the Planck constant, is the speed of light), the nonlinear effects of quantum electrodynamics become significant: the exchange of virtual photons is superimposed by the generation of virtual electron-positron (and also muon-antimuon and taon-antitaon) pairs, and the effect of screening also decreases (see renormalization). Both effects lead to the appearance of exponentially decreasing order terms in the expression for the potential energy of interaction of charges and, as a result, to an increase in the interaction force compared to that calculated by the Coulomb law. For example, the expression for the potential of a point charge in the CGS system, taking into account the radiative corrections of the first order, takes the form:

where is the Compton wavelength of the electron, is the fine structure constant u. At distances of the order of ~ 10−18 m, where is the mass of the W-boson, electroweak effects come into play.

In strong external electromagnetic fields, which make up a significant fraction of the vacuum breakdown field (on the order of ~1018 V/m or ~109 T, such fields are observed, for example, near certain types of neutron stars, namely magnetars), the Coulomb law is also violated due to the Delbrück scattering of exchange photons on photons of the external field and other, more complex nonlinear effects. This phenomenon reduces the Coulomb force not only on the microscale but also on the macroscale; in particular, in a strong magnetic field the Coulomb potential decreases exponentially rather than inversely with the distance.

Coulomb's law and vacuum polarization

The phenomenon of vacuum polarization in quantum electrodynamics is the formation of virtual electron-positron pairs. A cloud of electron-positron pairs shields the electric charge of an electron. The screening increases with increasing distance from the electron, as a result, the effective electric charge of the electron is a decreasing function of the distance. The effective potential created by an electron with an electric charge can be described by a dependence of the form. The effective charge depends on the distance according to the logarithmic law:

T. n. fine structure constant ≈7.3 10−3;

T. n. classical electron radius ≈2.8 10−13 cm..

Yuling effect

The phenomenon of the deviation of the electrostatic potential of point charges in vacuum from the value of the Coulomb's law is known as the Yuling effect, which first calculated the deviations from the Coulomb's law for the hydrogen atom. The Yuling effect corrects for the Lamb shift by 27 MHz.

Coulomb's law and superheavy nuclei

In a strong electromagnetic field near superheavy nuclei with a charge, a rearrangement of the vacuum occurs, similar to an ordinary phase transition. This leads to amendments to Coulomb's law

The meaning of Coulomb's law in the history of science

Coulomb's law is the first open quantitative and mathematically formulated law for electromagnetic phenomena. The modern science of electromagnetism began with the discovery of Coulomb's law.

see also

• Electric field
• long range
• Biot-Savart-Laplace law
• law of attraction
• Pendant, Charles Augustin de
• Pendant (unit)
• Superposition principle
• Maxwell's equations

Links

• Coulomb's law (video lesson, 10th grade program)

Notes

1. Landau L. D., Lifshits E. M. Theoretical Physics: Proc. allowance: For universities. In 10 vols. T. 2 Field Theory. - 8th ed., stereo. - M.: FIZMATLIT, 2001. - 536 p. - ISBN 5-9221-0056-4 (vol. 2), Chap. 5 Constant electromagnetic field, p. 38 Field of a uniformly moving charge, p. 132
2. Landau L. D., Lifshits E. M. Theoretical Physics: Proc. allowance: For universities. In 10 vols. Vol. 3. Quantum mechanics (non-relativistic theory). - 5th ed., stereo. - M.: Fizmatlit, 2002. - 808 p. - ISBN 5-9221-0057-2 (vol. 3), ch. 3 Schrödinger equation, p. 17 Schrödinger equation, p. 74
3. G. Bethe Quantum mechanics. - per. from English, ed. V. L. Bonch-Bruevich, "Mir", M., 1965, Part 1 Theory of the structure of the atom, Ch. 1 The Schrödinger equation and approximate methods for its solution, p. eleven
4. R. E. Peierls Laws of nature. per. from English. ed. prof. I. M. Khalatnikova, State publishing house of physical and mathematical literature, M., 1959, shooting gallery. 20,000 copies, 339 pp., Ch. 9 “Electrons at high speeds”, p. “Forces at high speeds. Other Difficulties, p. 263
5. L. B. Okun ... z Elementary introduction to elementary particle physics, M., Nauka, 1985, Kvant Library, vol. 45, p. "Virtual particles", p. 57.
6. novi comm. Acad. Sc. Imp. Petropolitanae, v. IV, 1758, p. 301.
7. Aepinus F.T.W. Theory of electricity and magnetism. - L.: AN SSSR, 1951. - 564 p. - (Classics of science). - 3000 copies.
8. Abel Socin (1760) Acta Helvetica, vol. 4, pages 224-225.
9. J. Priestley. The History and present state of Electricity with original experiments. London, 1767, p. 732.
10. john Robison, A System of Mechanical Philosophy(London, England: John Murray, 1822), vol. 4. On page 68, Robison states that in 1769 he published his measurements of the force acting between spheres of the same charge, and also describes the history of research in this area, noting the names of Aepinus, Cavendish and Coulomb. On page 73, the author writes that the force changes as x−2,06.
11. S. R. Filonovich "Cavendish, Coulomb and electrostatics", M., "Knowledge", 1988, LBC 22.33 F53, ch. "The Fate of the Law", p. 48
12. R. Feynman, R. Layton, M. Sands, The Feynman Lectures in Physics, vol. 5, Electricity and Magnetism, trans. from English, ed. Ya. A. Smorodinsky, ed. 3, M., Editorial URSS, 2004, ISBN 5-354-00703-8 (Electricity and Magnetism), ISBN 5-354-00698-8 (Complete work), ch. 4 "Electrostatics", p. 1 "Statics", p. 70-71;
13. R. Feynman, R. Layton, M. Sands, The Feynman Lectures in Physics, vol. 5, Electricity and Magnetism, trans. from English, ed. Ya. A. Smorodinsky, ed. 3, M., Editorial URSS, 2004, ISBN 5-354-00703-8 (Electricity and Magnetism), ISBN 5-354-00698-8 (Complete work), ch. 5 "Applications of the Gauss law", p. 10 "Field inside the cavity of the conductor", p. 106-108;
14. E. R. Williams, J. E. Faller, H. A. Hill "New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass", Phys. Rev. Lett. 26, 721-724 (1971);
15. W. E. Lamb, R. C. Retherford Fine Structure of the Hydrogen Atom by a Microwave Method (English) // Physical Review. - T. 72. - No. 3. - S. 241-243.
16. 1 2 R. Feynman, R. Layton, M. Sands, The Feynman Lectures in Physics, vol. 5, Electricity and Magnetism, trans. from English, ed. Ya. A. Smorodinsky, ed. 3, M., Editorial URSS, 2004, ISBN 5-354-00703-8 (Electricity and Magnetism), ISBN 5-354-00698-8 (Complete work), ch. 5 "Applications of Gauss' Law", p. 8 "Is Coulomb's Law Accurate?", p. 103;
17. CODATA (the Committee on Data for Science and Technology)
18. Berestetsky, V. B., Lifshitz, E. M., Pitaevsky, L. P. Quantum electrodynamics. - 3rd edition, corrected. - M.: Nauka, 1989. - S. 565-567. - 720 s. - (“Theoretical Physics”, Volume IV). - ISBN 5-02-014422-3
19. Neda Sadooghi Modified Coulomb potential of QED in a strong magnetic field (English).
20. Okun L. B. "Physics of elementary particles", ed. 3rd, M., "Editorial URSS", 2005, ISBN 5-354-01085-3, BBC 22.382 22.315 22.3o, ch. 2 “Gravity. Electrodynamics”, “Vacuum Polarization”, p. 26-27;
21. "Physics of the microcosm", ch. ed. D. V. Shirkov, M., "Soviet Encyclopedia", 1980, 528 p., ill., 530.1 (03), F50, art. "Effective charge", ed. Art. D. V. Shirkov, p. 496;
22. Yavorsky B. M. "Handbook of physics for engineers and university students" / B. M. Yavorsky, A. A. Detlaf, A. K. Lebedev, 8th ed., revised. and corrected, M .: Publishing House Onyx LLC, Publishing House Mir and Education LLC, 2006, 1056 pages: illustrations, ISBN 5-488-00330-4 (OOO Publishing House Onyx), ISBN 5-94666 -260-0 (World and Education Publishing House LLC), ISBN 985-13-5975-0 (Harvest LLC), UDC 530(035) BBK 22.3, Ya22, "Appendices", "Fundamental physical constants", p. . 1008;
23. Uehling E.A., Phys. Rev. 48, 55 (1935)
24. "Mesons and fields" S. Schweber, G. Bethe, F. Hoffman volume 1 Fields ch. 5 Properties of the Dirac equation p. 2. States with negative energy p. 56, ch. 21 Renormalization, Sec. 5 Vacuum polarization s 336
25. A. B. Migdal “Vacuum polarization in strong fields and pion condensation”, “Uspekhi fizicheskikh nauk”, vol. 123, c. 3, 1977, November, p. 369-403;
26. Spiridonov O. P. "Universal physical constants", M., "Enlightenment", 1984, p. 52-53;

Literature

1. Filonovich S. R. The fate of the classical law. - M., Nauka, 1990. - 240 p., ISBN 5-02-014087-2 (Quantum Library, issue 79), circ. 70500 copies

Categories:

• physical laws
• Electrostatics

Coulomb's law

Torsion bars of Coulomb

Coulomb's law- one of the main laws of electrostatics, which determines the magnitude of the force directly between two non-violent point charges. Experimentally, with sufficient accuracy, the law was first established by Henry Cavendish in 1773. He defeated the method of a spherical capacitor, but did not publish his results. In 1785, the law was introduced by Charles Coulomb for the help of special torsion terms.

Appointment

The electrostatic force of interaction F 12 of two point non-violent charges q 1 and q 2 in vacuum is directly proportional to the absolute value of the charges and is wrapped in proportion to the square of the distance r 12 between them. F 12 = k ⋅ q 1 ⋅ q 2 r 12 2 (\displaystyle F_(12)=k\cdot (\frac (q_(1)\cdot q_(2))(r_(12)^(2))) ) ,

for vector form:

F 12 = k ⋅ q 1 ⋅ q 2 r 12 3 r 12 (\displaystyle \mathbf (F_(12)) =k\cdot (\frac (q_(1)\cdot q_(2))(r_(12) ^(3)))\mathbf (r_(12)) ) ,

The force of mutual modality is directed in a straight line, which is equal to one charge, and the same charges are mixed, but differently attracted. Forces that are determined by Coulomb's law are additive.

For vikonannya formulated law is necessary, so that they vikonuyutsya so mind:

1. The point of charges - between the charged bodies can be loaded with more water.
2. Indestructibility of charges. In the opposite direction, it is necessary to restore the magnetic field to the charge that is collapsing.
3. The law is formulated for charges in vacuum.

Has become electrostatic

Proportionality coefficient k I can name electrostatic steel. Vіn to fall in vіd choice alone vimіryuvannya. So, the International system has one (СІ)

K = 1 4 π ε 0 ≈ (\displaystyle k=(\frac (1)(4\pi \varepsilon _(0)))\approx ) 8.987742438 109 N m2 C-2,

de ε 0 (\displaystyle \varepsilon _(0)) - became electric. Coulomb's law can be seen:

F 12 = 1 4 π ε 0 q 1 q 2 r 12 3 r 12 (\displaystyle \mathbf (F) _(12)=(\frac (1)(4\pi \varepsilon _(0)))(\ frac (q_(1)q_(2))(r_(12)^(3)))\mathbf (r) _(12)) .

Updating the last hour, the main system of alone vimiryuvannya was the SGS system. A lot of classical physical literature has been written using different sources of one of the different CGS systems - the Gaussian system of units. Her single charge was taken away in such a rank that k=1, and Coulomb's law looks like:

F 12 = q 1 q 2 r 12 3 r 12 (\displaystyle \mathbf (F) _(12)=(\frac (q_(1)q_(2))((r)_(12)^(3) ))\mathbf (r) _(12)) .

A similar view of Coulomb's law can be unique in atomic systems, which is victorious for atomic physics for quantum chemical research.

Coulomb's law in the middle

At the middle, the force of interrelation between charges changes, causing a polarization to appear. For a homogeneous isotropic medium, a change in a proportional value characteristic of this medium is called dielectric steel, or dielectric penetration and sound means ε ( \ displaystyle \ varepsilon ) . Coulomb force in the system СІ may look

F 12 = 1 4 π ε ε 0 q 1 q 2 r 12 3 r 12 (\displaystyle \mathbf (F) _(12)=(\frac (1)(4\pi \varepsilon \varepsilon _(0)) )(\frac (q_(1)q_(2))(r_(12)^(3)))\mathbf (r) _(12)) .

The dielectric became more and more close to unity, so in the future it is possible to win the formula for vacuum with sufficient accuracy.

History

Conjectures about those that the interplay between electrified bodies is subject to the same law of proportionality to the square of the distance, which is heavy, were repeatedly discussed by the survivors in the middle of the 18th century. On the cob of the 1770s, Henry Cavendish experimentally discovered, but did not publish his results, and only became aware of them in the 19th century. after the event and publication of yogo archives. Charles Coulomb published the law of 1785 in two memoirs, presented to the French Academy of Sciences. In 1835, Karl Gaus published the Gaus theorem based on Coulomb's law. In view of the Gauss theorem, Coulomb's law is included before the main equalities of electrodynamics.

Rechecking the law

For macroscopic views during experiments in earthly minds, which were carried out using the Cavendish method, the indicator of the degree r in Coulomb's law, it is impossible to change in 2 larger lower by 6 10−16. From experiments with the expansion of alpha particles, it appears that Coulomb's law does not break down to 10−14 m. . In this region of spacious scales, the laws of quantum mechanics are developed.

Coulomb's law can be considered as one of the last examples of quantum electrodynamics, in the framework of which the interaction of charging frequencies is based on the exchange of virtual photons. In consequence of this, experiments on the re-verification of quantum electrodynamics can be taken as evidence of the re-verification of Coulomb's law. So, experiments on annihilation of electrons and positrons show that the laws of quantum electrodynamics cannot be modified until the distance of 10−18 m.

Div. also

• Gaus' theorem
• Lorentz force

Dzherela

• Goncharenko S. U. Physics: Basic laws and formulas. - K. : Libid, 1996. - 47 p.
• Kucheruk I. M., Gorbachuk I. T., Lutsik P. P. Electricity and magnetism // Zagalny course of physics. - K. : Tehnika, 2006. - T. 2. - 456 p.
• Frish S. E., Timoreva A. V. Electrical and electromagnetic phenomena // Course of global physics. - K .: Radianska school, 1953. - T. 2. - 496 p.
• Physical Encyclopedia / Ed. A. M. Prokhorova. - M.: Soviet Encyclopedia, 1990. - T. 2. - 703 p.
• Sivukhin D.V. Electricity // General course of physics. - M. : Fizmatlit, 2009. - T. 3. - 656 p.

Notes

1. a b Coulomb's law can be approximated for ruhomy charges, because their lightness is richer than the lightness of the light
2. a b Y -- Coulomb (1785a) "Premier mémoire sur l'électricité et le magnétisme," , pages 569-577 -- Pendant wielding the power of one-shot charges:
   

   Page 574: Il résulte donc de ces trois essais, que l "action répulsive que les deux balles électrifées de la même nature d" électricité exercent l "une sur l" autre, suit la raison inverse du carré des distances.

   translation: Also, from these triokh doslіdіv sluduє, that the power of vіdshtovhuvannya between two electrified coils, charged with electricity of the same nature, follows the law of proportionality turned to the square of the vіdstani ..

   Y -- Coulomb (1785b) "Second mémoire sur l'électricité et le magnétisme," Histoire de l'Académie Royale des Sciences, pages 578-611. - The pendant showed that the bodies from the opposite charges are attracted by the force of the fiery-proportional force.

3. Choose such a reasonably collapsible formula of minds, that in the International System the basic unit is not the electric charge, but the unit of the power of the electric current ampere, but the main equalization of electrodynamics is written without the multiplier 4 π ( \ displaystyle 4 \ pi ) .

Coulomb's law

Irina Ruderfer

Coulomb's law is the law of the interaction of point electric charges.

It was discovered by Coulomb in 1785. After conducting a large number of experiments with metal balls, Charles Coulomb gave the following formulation of the law:

The force of interaction of two point motionless charged bodies in vacuum is directed along the straight line connecting the charges, is directly proportional to the product of charge modules and inversely proportional to the square of the distance between them.
It is important to note that in order for the law to be true, it is necessary:
1. point charges - that is, the distance between charged bodies is much larger than their size.
2. their immobility. Otherwise, additional effects must be taken into account: the emerging magnetic field of the moving charge and the corresponding additional Lorentz force acting on another moving charge.
3. interaction in a vacuum.
However, with some adjustments, the law is also valid for the interactions of charges in a medium and for moving charges.

In vector form, in the formulation of S. Coulomb, the law is written as follows:

Where F1,2 is the force with which charge 1 acts on charge 2; q1,q2 - magnitude of charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in modulus, to the distance between charges - r12); k - coefficient of proportionality. Thus, the law indicates that like charges repel (and unlike charges attract).

Do not iron against wool!

Knowing about the existence of electricity for thousands of years, man began to study it scientifically only in the 18th century. (It is interesting that the scientists of that era, who took up this problem, singled out electricity as a science separate from physics, and called themselves "electricians".) One of the leading pioneers of electricity was Charles Augustin de Coulomb. Having carefully studied the forces of interaction between bodies carrying various electrostatic charges, he formulated the law that now bears his name. Basically, he carried out his experiments as follows: various electrostatic charges were transferred to two small balls suspended on the thinnest threads, after which the suspensions with the balls approached. With sufficient approach, the balls began to attract each other (with opposite polarity of electric charges) or repel (in the case of unipolar charges). As a result, the filaments deviated from the vertical by a sufficiently large angle at which the forces of electrostatic attraction or repulsion were balanced by the forces of the earth's gravity. Having measured the deflection angle and knowing the mass of the balls and the length of the suspensions, Coulomb calculated the forces of electrostatic interaction at different distances of the balls from each other and, based on these data, derived an empirical formula:

Where Q and q are the magnitudes of the electrostatic charges, D is the distance between them, and k is the experimentally determined Coulomb's constant.

We immediately note two interesting points in Coulomb's law. Firstly, in its mathematical form, it repeats Newton's law of universal gravitation, if in the latter we replace masses with charges, and Newton's constant with Coulomb's constant. And there are good reasons for this similarity. According to modern quantum field theory, both electric and gravitational fields arise when physical bodies exchange elementary particles-energy carriers, devoid of rest mass - photons or gravitons, respectively. Thus, despite the apparent difference in the nature of gravity and electricity, these two forces have much in common.

The second important remark concerns the Coulomb constant. When the Scottish theoretical physicist James Clark Maxwell developed Maxwell's system of equations for a general description of electromagnetic fields, it turned out that the Coulomb constant is directly related to the speed of light c. Finally, Albert Einstein showed that c plays the role of a fundamental world constant in the framework of the theory of relativity. In this way, one can trace how the most abstract and universal theories of modern science have gradually developed, absorbing the previously obtained results, starting with simple conclusions made on the basis of desktop physical experiments.
http://elementy.ru/trefil/coulomb_law
http://www.fieldphysics.ru/coulombs_law/
http://www.vnz.ru/spravki/zakon-Kulona.html

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Subtitles

Wording

The force of interaction of two point charges in vacuum is directed along the straight line connecting these charges, is proportional to their magnitudes and is inversely proportional to the square of the distance between them. It is an attractive force if the signs of the charges are different, and a repulsive force if these signs are the same.

It is important to note that in order for the law to be true, it is necessary:

1. Point charges, that is, the distance between charged bodies must be much larger than their size. However, it can be proved that the force of interaction of two volumetrically distributed charges with spherically symmetric non-intersecting spatial distributions is equal to the force of interaction of two equivalent point charges located at the centers of spherical symmetry;
2. Their immobility. Otherwise, additional effects come into force: the magnetic field of the moving charge and the corresponding additional force Lorentz acting on another moving charge;
3. Arrangement of charges 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 S. Coulomb, the law is written as follows:

F → 12 = k ⋅ q 1 ⋅ q 2 r 12 2 ⋅ r → 12 r 12 , (\displaystyle (\vec (F))_(12)=k\cdot (\frac (q_(1)\cdot q_ (2))(r_(12)^(2)))\cdot (\frac ((\vec (r))_(12))(r_(12))),)

where F → 12 (\displaystyle (\vec (F))_(12)) is the force with which charge 1 acts on charge 2; q 1 , q 2 (\displaystyle q_(1),q_(2))- the magnitude of the charges; r → 12 (\displaystyle (\vec (r))_(12))- radius vector (vector directed from charge 1 to charge 2, and equal, in absolute value, to the distance between charges - r 12 (\displaystyle r_(12))); k (\displaystyle k)- coefficient of proportionality.

Coefficient k

k = 1 ε . (\displaystyle k=(\frac (1)(\varepsilon )).) k = 1 4 π ε ε 0 . (\displaystyle k=(\frac (1)(4\pi \varepsilon \varepsilon _(0))).)

Coulomb's law in quantum mechanics

Coulomb's law from the point of view of quantum electrodynamics

Story

For the first time to investigate experimentally the law of interaction of electrically charged bodies was suggested by G. V. Richmann in 1752-1753. He intended to use for this purpose the "indicator" electrometer designed by him. The implementation of this plan was prevented by the tragic death of Richman.

Approximately 11 years before Coulomb, in 1771, the law of interaction of charges was experimentally discovered by G. Cavendish, but the result was not published and remained unknown for a long time (over 100 years). The Cavendish manuscripts were handed over to D.C. Maxwell only in 1874 by one of Cavendish's descendants at the grand opening of the Cavendish Laboratory and published in 1879.

Coulomb himself was engaged in the study of the torsion of threads and invented the torsion balance. He discovered his law, using them to measure the forces of interaction of charged balls.

Coulomb's law, superposition principle and Maxwell's equations

Degree of accuracy of Coulomb's law

Coulomb's law is an experimentally established fact. Its validity has been repeatedly confirmed by more and more precise experiments. One of the directions of such experiments is to check whether the exponent differs r in the law of 2. To find this difference, the fact is used that if the degree is exactly equal to two, then there is no field inside the cavity in the conductor, whatever the shape of the cavity or conductor.

Such experiments were first carried out by Cavendish and repeated by Maxwell in an improved form, obtaining for the maximum difference of the exponent in a power of two the value 1 21600 (\displaystyle (\frac (1)(21600)))

Experiments conducted in 1971 in the United States by E. R. Williams, D. E. Voller and G. A. Hill showed that the exponent in Coulomb's law is 2 to within (3 , 1 ± 2 , 7) × 10 − 16 (\displaystyle (3,1\pm 2,7)\times 10^(-16)) .

To test the accuracy of Coulomb's law at intraatomic distances, W. Yu. Lamb and R. Rutherford in 1947 used measurements of the relative arrangement of hydrogen energy levels. It was found that even at distances of the order of atomic 10 −8 cm, the exponent in the Coulomb law differs from 2 by no more than 10 −9 .

Coefficient k (\displaystyle k) in Coulomb's law remains constant up to 15⋅10 −6 .

Corrections to Coulomb's law in quantum electrodynamics

At short distances (of the order of the Compton length electron wave , λ e = ℏ m e c (\displaystyle \lambda _(e)=(\tfrac (\hbar )(m_(e)c)))≈3.86⋅10 −13 m , where m e (\displaystyle m_(e)) is the mass of the electron, ℏ (\displaystyle \hbar )- Planck's constant, c (\displaystyle c)- the speed of light) nonlinear effects of quantum electrodynamics become significant: the generation of virtual electron-positron (as well as muon-antimuon and taon-antitaon) pairs is superimposed on the exchange of virtual photons, and the effect of screening also decreases (see renormalization). Both effects lead to the appearance of exponentially decreasing order terms e − 2 r / λ e (\displaystyle e^(-2r/\lambda _(e))) in the expression for the potential energy of the interaction of charges and, as a result, to an increase in the interaction force compared to that calculated by the Coulomb law.

Φ (r) = Q r ⋅ (1 + α 4 π e − 2 r / λ e (r / λ e) 3 / 2) , (\displaystyle \Phi (r)=(\frac (Q)(r) )\cdot \left(1+(\frac (\alpha )(4(\sqrt (\pi ))))(\frac (e^(-2r/\lambda _(e)))((r/\ lambda _(e))^(3/2)))\right),)

where λ e (\displaystyle \lambda _(e))- Compton wavelength electron, α = e 2 ℏ c (\displaystyle \alpha =(\tfrac (e^(2))(\hbar c)))- constant fine structure and r ≫ λ e (\displaystyle r\gg \lambda _(e)).

At distances of the order λ W = ℏ m w c (\displaystyle \lambda _(W)=(\tfrac (\hbar )(m_(w)c)))~ 10 −18 m, where m w (\displaystyle m_(w)) is the mass of the W-boson, electroweak effects come into play.

In strong external electromagnetic fields, which make up a significant fraction of the breakdown field vacuum (on the order of m e c 2 e λ e (\displaystyle (\tfrac (m_(e)c^(2))(e\lambda _(e))))~10 18 V/m or m e c e λ e (\displaystyle (\tfrac (m_(e)c)(e\lambda _(e))))~10 9 T, such fields are observed, for example, near some types of neutron stars, namely magnetars), the Coulomb law is also violated due to the Delbrück scattering of exchange photons on photons of the external field and other, more complex nonlinear effects. This phenomenon reduces the Coulomb force not only in micro but also in macro scales, in particular, in a strong magnetic field, the Coulomb potential does not fall inversely proportional to the distance, but exponentially.

Coulomb's law and polarization vacuum

Coulomb's law and superheavy nuclei

The meaning of Coulomb's law in the history of science

Coulomb's law is the first open quantitative and mathematically formulated fundamental law for electromagnetic phenomena. With the discovery of Coulomb's law, the modern science of electromagnetism began.

see also

Links

• Coulomb's law (video lesson, 10th grade program)

Notes

1. Sivukhin D. V. General course of physics. - M.: Fizmatlit; MIPT Publishing House, 2004. - Vol. III. Electricity. - S. 17. - 656 p. - ISBN 5-9221-0227-3.
2. Landau L.D., Lifshitz E.M. Theoretical Physics: Textbook. allowance: For universities. V 10 t. T. 2 Field Theory. - 8th ed., stereo. - M.: FIZMATLIT, 2001. - 536 p. -