Coulomb's law definition and formula. 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 Coulomb's law in quantum mechanics

Coulomb's law- this is the basis of electrostatics, knowledge of the formulation and basic formula describing this law is also necessary for studying the section “Electricity and Magnetism”.

Coulomb's law

The law that describes the forces of electrical interaction between charges was discovered in 1785 Charles Pendant, who conducted numerous experiments with metal balls. One of the modern formulations of Coulomb's law is as follows:

“The force of interaction between two point electric charges is directed along the straight line connecting these charges, is proportional to the product of their magnitudes and is inversely proportional to the square of the distance between them. If the charges are of different signs, then they attract, and if they are of the same sign, they repel.”

Formula illustrating this law:

*The second factor (in which the radius vector is present) is needed solely to determine the direction of the force.

F 12 – force that acts on the 2nd charge from the first;

q 1 and q 2 - charge values;

r 12 – distance between charges;

k– proportionality coefficient:

ε 0 is the electrical constant, sometimes called the dielectric constant of vacuum. Approximately equal to 8.85·10 -12 F/m or Cl 2 /(H m 2).

ε – dielectric constant of the medium (for vacuum equals 1).

Corollaries from Coulomb's law

• There are two types of charges - positive and negative
• like charges repel, and different charges attract
• charges can be transferred from one to another, since charge is not a constant and unchanging quantity. It may vary depending on the conditions (environment) in which the charge is located
• in order for the law to be true, it is necessary to take into account the behavior of charges in a vacuum and their immobility

A visual representation of Coulomb's law.

Law

Coulomb's Law

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).

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; - 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= c2·10−7 Gn/m = 8.9875517873681764 109 N m2/ Cl 2 (or F−1 m). 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 that describes the interaction forces 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 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 a 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:

1. 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;
2. their immobility. Otherwise, additional effects come into force: the magnetic field of a 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 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).

Coefficient k

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

In the International System of Units (SI), one of the basic units is the unit of electric current, the ampere, and the unit of charge, the coulomb, is a derivative of it. The ampere value is defined in such a way that k= c2·10-7 H/m = 8.9875517873681764·109 N·m2/Cl2 (or Ф−1·m). SI coefficient k is written as:

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

In a homogeneous isotropic substance, the relative dielectric constant 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 using the concept of force, as in classical mechanics, but using the concept of potential energy of the Coulomb interaction. In the case when the system considered in quantum mechanics contains electrically charged particles, terms are added to the Hamiltonian operator of the system, expressing the potential energy of the Coulomb interaction, as it is calculated in classical mechanics.

Thus, the Hamilton operator of an atom with a nuclear charge Z has the form:

Here m- electron mass, e is its charge, is the absolute value of the radius vector j th electron, . The first term expresses the kinetic energy of electrons, the second term expresses the potential energy of the Coulomb interaction of electrons with the nucleus, and the third term expresses 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 occurs over all pairs of electrons, with each pair occurring once.

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

According to quantum electrodynamics, the electromagnetic interaction of charged particles occurs through the exchange of virtual photons between particles. The uncertainty principle for time and energy allows for 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 it takes virtual photons to overcome this distance and, therefore, the greater the energy of virtual photons allowed by the uncertainty principle. At small distances between charges, the uncertainty principle allows the exchange of both long- and short-wave photons, and at large distances only long-wave photons participate in the exchange. Thus, using quantum electrodynamics, Coulomb's law can be derived.

Story

For the first time, G.V. Richman proposed to study experimentally the law of interaction of electrically charged bodies in 1752-1753. He intended to use the “pointer” electrometer he had designed for this purpose. 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 Richmann's chair after his death, first suggested that charges should interact in inverse proportion to the square of the distance. In 1760, a brief message appeared that D. Bernoulli in Basel had established the quadratic law using an electrometer he had designed. In 1767, Priestley noted in his History of Electricity that Franklin's discovery of the absence of an electric field inside a charged metal ball might mean that "electrical attraction follows exactly the same law as gravity, that is, the square of the distance". The Scottish physicist John Robison claimed (1822) to have discovered in 1769 that balls of equal electrical 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).

About 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). Cavendish's manuscripts were presented to D. C. Maxwell only in 1874 by one of Cavendish's descendants at the inauguration of the Cavendish Laboratory and published in 1879.

Coulomb himself studied the torsion of threads and invented the torsion balance. He discovered his law by using them to measure the interaction forces of charged balls.

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

Coulomb's law and the principle of superposition for electric fields are completely equivalent to Maxwell's equations for electrostatics and. That is, Coulomb's law and the superposition principle for electric fields are satisfied if and only if Maxwell's equations for electrostatics are satisfied and, conversely, Maxwell's equations for electrostatics are satisfied if and only if Coulomb's 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 increasingly accurate experiments. One direction of such experiments is to test whether the exponent differs r in the law from 2. To find this difference, we use the fact that if the power 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 carried out in 1971 in the USA by E. R. Williams, D. E. Voller and G. A. Hill showed that the exponent in Coulomb's law is equal to 2 to within .

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

The coefficient in Coulomb's law remains constant with an accuracy of 15·10−6.

Amendments to Coulomb's law in quantum electrodynamics

At short distances (on the order of the Compton electron wavelength, ≈3.86·10−13 m, where is the electron mass, is Planck’s constant, is the speed of light), the nonlinear effects of quantum electrodynamics become significant: the exchange of virtual photons is superimposed on the generation of virtual electron-positron (and also muon-antimuon and taon-antitaon) pairs, and the influence of screening is reduced (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 Coulomb’s law. For example, the expression for the potential of a point charge in the SGS system, taking into account first-order radiation corrections, takes the form:

where is the Compton wavelength of the electron, is the fine structure constant and. 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, constituting a noticeable fraction of the vacuum breakdown field (of the order of ~1018 V/m or ~109 Tesla, such fields are observed, for example, near some types of neutron stars, namely magnetars), Coulomb’s law is also violated due to Delbrück scattering of exchange photons on external field photons and other, more complex nonlinear effects. This phenomenon reduces the Coulomb force not only on a micro but also on a macro scale; in particular, in a strong magnetic field, the Coulomb potential does not fall in inverse proportion to distance, but exponentially.

Coulomb's law and vacuum polarization

The phenomenon of vacuum polarization in quantum electrodynamics consists in the formation of virtual electron-positron pairs. A cloud of electron-positron pairs screens the electrical charge of the electron. Screening increases with increasing distance from the electron; as a result, the effective electric charge of the electron is a decreasing function of 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..

Juhling effect

The phenomenon of deviation of the electrostatic potential of point charges in a vacuum from the value of Coulomb's law is known as the Juhling effect, which was the first to calculate deviations from Coulomb's law for the hydrogen atom. The Uehling effect provides a correction to the Lamb shift of 27 MHz.

Coulomb's law and superheavy nuclei

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

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

Coulomb's law is the first open quantitative law for electromagnetic phenomena formulated in mathematical language. 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 of measurement)
• Superposition principle
• Maxwell's equations

Links

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

Notes

1. Landau L. D., Lifshits E. M. Theoretical physics: Textbook. manual: For universities. In 10 volumes. T. 2 Field theory. - 8th ed., stereot. - M.: FIZMATLIT, 2001. - 536 p. - ISBN 5-9221-0056-4 (Vol. 2), Ch. 5 Constant electromagnetic field, paragraph 38 Field of a uniformly moving charge, p. 132
2. Landau L. D., Lifshits E. M. Theoretical physics: Textbook. manual: For universities. In 10 volumes. T. 3. Quantum mechanics (non-relativistic theory). - 5th ed., stereot. - 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 atomic structure, Ch. 1 Schrödinger equation and approximate methods for its solution, p. eleven
4. R. E. Peierls Laws of nature. lane from English edited by prof. I. M. Khalatnikova, State Publishing House of Physical and Mathematical Literature, M., 1959, tier. 20,000 copies, 339 pp., Ch. 9 “Electrons at high speeds”, paragraph “Forces at high speeds. Other difficulties", p. 263
5. L. B. Okun... z Elementary introduction to the physics of elementary particles, M., Nauka, 1985, Library “Kvant”, vol. 45, p. “Virtual particles”, p. 57.
6. Novi Comm. Acad. Sc. Imp. Petropolitanae, v. IV, 1758, p. 301.
7. Epinus F.T.U. Theory of electricity and magnetism. - L.: USSR Academy of Sciences, 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 like charge, and also describes the history of research in this field, noting the names of Apinus, Cavendish and Coulomb. On page 73 the author writes that force changes as x−2,06.
11. S. R. Filonovich “Cavendish, Coulomb and Electrostatics”, M., “Knowledge”, 1988, BBK 22.33 F53, ch. "The Fate of the Law", p. 48
12. R. Feynman, R. Layton, M. Sands, Feynman Lectures on 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”, paragraph 1 “Statics”, p. 70-71;
13. R. Feynman, R. Layton, M. Sands, Feynman Lectures on 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 “Application of Gauss’s Law”, paragraph 10 “Field inside the conductor cavity”, 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. - P. 241-243.
16. 1 2 R. Feynman, R. Layton, M. Sands, Feynman Lectures on 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 “Application of Gauss’s Law”, paragraph 8 “Is Coulomb’s Law Accurate?”, p. 103;
17. CODATA (the Committee on Data for Science and Technology)
18. Berestetsky, V. B., Lifshits, E. M., Pitaevsky, L. P. Quantum electrodynamics. - 3rd edition, revised. - M.: Nauka, 1989. - P. 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, BBK 22.382 22.315 22.3o, ch. 2 “Gravity. Electrodynamics", "Vacuum Polarization", p. 26-27;
21. “Physics of the microworld”, ch. ed. D. V. Shirkov, M., “Soviet Encyclopedia”, 1980, 528 pp., ill., 530.1(03), F50, art. "Effective charge", author. 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 rev., M.: Onyx Publishing House LLC, Mir and Education Publishing House LLC, 2006, 1056 pp.: ill., ISBN 5-488-00330-4 (Onyx Publishing House LLC), ISBN 5-94666 -260-0 (Publishing House Mir and Education LLC), ISBN 985-13-5975-0 (Harvest LLC), UDC 530 (035) BBK 22.3, Ya22, “Applications”, “Fundamental physical constants”, with . 1008;
23. Uehling E. A., Phys. Rev., 48, 55, (1935)
24. “Mesons and fields” S. Schweber, G. Bethe, F. Hoffmann volume 1 Fields ch. 5 Properties of the Dirac equation p. 2. States with negative energy c. 56, ch. 21 Renormalization, paragraph 5 Vacuum polarization from 336
25. A. B. Migdal “Vacuum polarization in strong fields and pion condensation”, “Advances in Physical Sciences”, v. 123, v. 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 pp., ISBN 5-02-014087-2 (Kvant Library, issue 79), ref. 70500 copies

Categories:

• Physical laws
• Electrostatics

Coulomb's law

Torsion Teresis of Coulomb

Coulomb's law- one of the basic laws of electrostatics, which determines the magnitude and direct force of interaction between two indestructible point charges. The law was first established experimentally with satisfactory accuracy by Henry Cavendish in 1773. He developed the spherical capacitor method without publishing his results. In 1785, the law was established by Charles Coulomb with the help of special torsional clamps.

Viznachennya

The electrostatic force of interaction F 12 of two point immovable charges q 1 and q 2 in a vacuum is directly proportional to the addition of the absolute value of the charges and is proportional 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 interaction is directed in the same direction as the charges, whereby similar charges attract each other and opposite ones attract. The forces that are determined by Coulomb’s law are additive.

For the law to be formulated, it is necessary for the following minds to be consecrated:

1. The accuracy of charges - between charged bodies - may be much greater depending on the size of the body.
2. Unbreakable charges. In a protracted episode, it is necessary to add a magnetic field to the charge that is collapsing.
3. The law is formulated for charges in vacuum.

Became electrostatic

Proportionality coefficient k This is called electrostatic steel. Vіn to lie in the selection of units of extinction. Thus, the International System has units (CI)

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

de ε 0 (\displaystyle \varepsilon _(0)) - became electric. Coulomb's law looks like this:

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)) .

For the past three years, the main system of some modifications has been the GHS system. A lot of classical physical literature has been written on the basis of one of the varieties of the GHS system - the Gaussian system of units. Her unit of charge is arranged in such a manner that k=1, and Coulomb’s law takes on the form:

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 form of Coulomb’s law may exist in the atomic system, which is used in atomic physics for quantum chemical reactions.

Coulomb's law in the middle

In the medium, the force of interaction between charges changes as a result of polarization. For a homogeneous isotropic medium, there is a change in the proportional value characteristic of this medium, which is called dielectric steel or dielectric penetration and is also called ε (\displaystyle \varepsilon). The Coulomb force in the CI system looks like

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)) .

Dielectricity has become very close to one, so in this case the formula for vacuum can be determined with sufficient accuracy.

Discovery history

Conjectures about the fact that the interactions between electrified bodies are subject to the same law of proportionality to the square of the area that is heavy were repeatedly determined by the descendants in the middle of the 18th century. At the beginning of the 1770s, Henry Cavendish discovered experimentally, but did not publish his results, and they became known only at the end of the 19th century. after the publication of my archives. Charles Coulomb published the law of 1785 in two memoirs presented to the French Academy of Sciences. In 1835, Karl Gaus published Gaus’s theorem, derived on the basis of Coulomb’s law. According to Gaus's theorem, Coulomb's law is included in the basic principles of electrodynamics.

Reversing the law

For macroscopic examinations in experiments in terrestrial minds, which were carried out using the Cavendish method, an indicator of the degree of r In Coulomb's law, it is impossible to subdivide 2 more than 6·10−16. From experiments with the scattering of alpha particles, it appears that Coulomb’s law is not violated up to distances of 10−14 m. On the other hand, to describe the interaction of charged particles at such distances, it is necessary to understand how the law is formulated (the concept of force, position ), spend sense . This area of ​​vast scale has the laws of quantum mechanics.

Coulomb's law can be used as one of the inheritances of quantum electrodynamics, in the framework of which the interaction of charging frequencies involves the exchange of virtual photons. As a result, experiments from testing the principles of quantum electrodynamics can be followed by testing the Coulomb law. Thus, experiments with the annihilation of electrons and positrons indicate that the laws of quantum electrodynamics do not apply to distances of 10−18 m.

Div. also

• Gaus's 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. Electrics and magnetism // Zagalny course of physics. - K.: Tekhnika, 2006. - T. 2. - 456 p.
• Frish S. E., Timoreva A. V. Electrical and electromagnetic boxes // Course of global physics. - K.: Radyanskaya 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 closely applied to dry charges, since their fluidity is much lower than that of light
2. A b Y -- Coulomb (1785a) "Premier mémoire sur l'électricité et le magnétisme," , pages 569-577 -- The pendant is made of force for the insertion of identical 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 three conclusions it follows that the force between two electrified coils charged by electricity of the same nature follows the law of circumscribed proportionality up to the square of the distance..

   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 bodies with adjacent charges are attracted by force due to their proportional relationship.

3. The choice of such a clearly complex formula of reasoning is due to the fact that in the International System the basic unit is not the electric charge, but the unit of electric current ampere, and the main level of electrodynamics is written without the multiplier 4 π (\displaystyle 4\ pi).

Coulomb's law

Irina Ruderfer

Coulomb's law is a law about 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 between two point stationary charged bodies in a vacuum is directed along the straight line connecting the charges, is directly proportional to the product of the charge moduli and is 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 nature of charges - that is, the distance between charged bodies is much greater than their sizes.
2.their immobility. Otherwise, additional effects must be taken into account: the emerging magnetic field of a 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 C. 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 absolute value, to the distance between charges - r12); k - proportionality coefficient. Thus, the law indicates that like charges repel (and unlike charges attract).

Do not iron against the grain!

Knowing about the existence of electricity for thousands of years, people began to study it scientifically only in the 18th century. (It is interesting that the scientists of that era who took up this problem identified electricity as a separate science 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 conducted 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 came closer. When they came close enough, the balls began to be attracted to each other (with opposite polarities of electric charges) or repelled (in the case of unipolar charges). As a result, the threads deviated from the vertical at a sufficiently large angle at which the forces of electrostatic attraction or repulsion were balanced by the forces of gravity. Having measured the angle of deflection 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 electrostatic charges, D is the distance between them, and k is the experimentally determined Coulomb constant.

Let us 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 is every reason for this similarity. According to modern quantum field theory, both electric and gravitational fields arise when physical bodies exchange among themselves elementary energy-carrying particles 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 note concerns the Coulomb constant. When Scottish theoretical physicist James Clerk Maxwell derived Maxwell's system of equations for a general description of electromagnetic fields, it turned out that Coulomb's constant is directly related to the speed of light c. Finally, Albert Einstein showed that c plays the role of a fundamental world constant within the framework of the theory of relativity. In this way, one can trace how the most abstract and universal theories of modern science gradually developed, absorbing previously obtained results, starting with simple conclusions drawn 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

The forces of electrostatic interaction depend on the shape and size of the electrified bodies, as well as on the nature of the charge distribution on these bodies. In some cases, we can neglect the shape and size of charged bodies and assume that each charge is concentrated at one point. Point charge is an electric charge when the size of the body on which this charge is concentrated is much less than the distance between the charged bodies. Approximately point charges can be obtained experimentally by charging, for example, fairly small balls.

The interaction of two point charges at rest determines the basic law of electrostatics - Coulomb's law. This law was experimentally established in 1785 by a French physicist Charles Augustin Pendant(1736 – 1806). The formulation of Coulomb's law is as follows:

The power of interaction two point stationary charged bodies in a vacuum is directly proportional to the product of the charge modules and inversely proportional to the square of the distance between them.

This interaction force is called Coulomb force, And Coulomb's law formula will be the following:

F = k (|q 1 | |q 2 |) / r 2

Where |q1|, |q2| – charge modules, r – distances between charges, k – proportionality coefficient.

The coefficient k in SI is usually written in the form:

K = 1 / (4πε 0 ε)

Where ε 0 = 8.85 * 10 -12 C/N*m 2 is the electrical constant, ε is the dielectric constant of the medium.

For vacuum ε = 1, k = 9 * 10 9 N*m/Cl 2.

The force of interaction between stationary point charges in a vacuum:

F = · [(|q 1 | · |q 2 |) / r 2 ]

If two point charges are placed in a dielectric and the distance from these charges to the boundaries of the dielectric is significantly greater than the distance between the charges, then the force of interaction between them is equal to:

F = · [(|q 1 | · |q 2 |) / r 2 ] = k · (1 /π) · [(|q 1 | · |q 2 |) / r 2 ]

Dielectric constant of the medium is always greater than unity (π > 1), therefore the force with which charges interact in a dielectric is less than the force of their interaction at the same distance in vacuum.

The forces of interaction between two stationary point charged bodies are directed along the straight line connecting these bodies (Fig. 1.8).

Rice. 1.8. Forces of interaction between two stationary point charged bodies.

Coulomb forces, like gravitational forces, obey Newton's third law:

F 1.2 = -F 2.1

The Coulomb force is a central force. As experience shows, like charged bodies repel, oppositely charged bodies attract.

The force vector F 2.1 acting from the second charge on the first is directed towards the second charge if the charges are of different signs, and in the opposite direction if the charges are of the same sign (Fig. 1.9).

Rice. 1.9. Interaction of unlike and like electric charges.

Electrostatic repulsive forces is considered to be positive gravity– negative. The signs of the interaction forces correspond to Coulomb's law: the product of like charges is a positive number, and the repulsive force has a positive sign. The product of opposite charges is a negative number, which corresponds to the sign of the force of attraction.

In Coulomb's experiments, the interaction forces of charged balls were measured, for which they used torsion scales(Fig. 1.10). A light glass rod is suspended from a thin silver thread. With, at one end of which a metal ball is attached A, and on the other there is a counterweight d. The upper end of the thread is fixed to the rotating head of the device e, the angle of rotation of which can be accurately measured. Inside the device there is a metal ball of the same size b, fixedly mounted on the lid of the scale. All parts of the device are placed in a glass cylinder, on the surface of which there is a scale that allows you to determine the distance between the balls a And b at their various positions.

Rice. 1.10. Coulomb experiment (torsion balance).

When the balls are charged with the same charges, they repel each other. In this case, the elastic thread is twisted at a certain angle to hold the balls at a fixed distance. The angle of twist of the thread determines the force of interaction between the balls depending on the distance between them. The dependence of the interaction force on the magnitude of the charges can be established as follows: give each of the balls a certain charge, place them at a certain distance and measure the angle of twist of the thread. Then you need to touch one of the balls with a charged ball of the same size, changing its charge, since when bodies of equal size come into contact, the charge is distributed equally between them. To maintain the same distance between the balls, it is necessary to change the angle of twist of the thread, and therefore, determine a new value of the interaction force with a new charge.

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 the bodies does not change: these charges are only redistributed between the 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 than 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).

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.