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. How are the forces directed?

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.”

A 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.

In electrostatics, one of the fundamental ones is Coulomb's law. It is used in physics to determine the force of interaction between two stationary point charges or the distance between them. This is a fundamental law of nature that does not depend on any other laws. Then the shape of the real body does not affect the magnitude of the forces. In this article we will tell in simple language Coulomb's law and its application in practice.

History of discovery

Sh.O. Coulomb in 1785 was the first to experimentally prove the interactions described by the law. In his experiments he used special torsion balances. However, back in 1773, Cavendish proved, using the example of a spherical capacitor, that there is no electric field inside the sphere. This indicated that electrostatic forces vary depending on the distance between the bodies. To be more precise - the square of the distance. His research was not published then. Historically, this discovery was named after Coulomb, and the quantity in which charge is measured has a similar name.

Formulation

The definition of Coulomb's law states: In a vacuumF interaction of two charged bodies is directly proportional to the product of their moduli and inversely proportional to the square of the distance between them.

It sounds short, but may not be clear to everyone. In simple words: The more charge the bodies have and the closer they are to each other, the greater the force.

And vice versa: If you increase the distance between the charges, the force will become less.

The formula for Coulomb's rule looks like this:

Designation of letters: q - charge value, r - distance between them, k - coefficient, depends on the chosen system of units.

The charge value q can be conditionally positive or conditionally negative. This division is very arbitrary. When bodies come into contact, it can be transmitted from one to another. It follows from this that the same body can have a charge of different magnitude and sign. A point charge is a charge or body whose dimensions are much smaller than the distance of possible interaction.

It is worth considering that the environment in which the charges are located affects the F interaction. Since it is almost equal in air and vacuum, Coulomb’s discovery is applicable only for these media; this is one of the conditions for the use of this type of formula. As already mentioned, in the SI system the unit of measurement of charge is Coulomb, abbreviated Cl. It characterizes the amount of electricity per unit time. It is derived from the SI base units.

1 C = 1 A*1 s

It is worth noting that the dimension of 1 C is redundant. Due to the fact that carriers repel each other, it is difficult to contain them in a small body, although the 1A current itself is small if it flows in a conductor. For example, in the same 100 W incandescent lamp a current of 0.5 A flows, and in an electric heater it flows more than 10 A. Such a force (1 C) is approximately equal to the 1 ton mass acting on a body from the side of the globe.

You may have noticed that the formula is almost the same as in gravitational interaction, only if masses appear in Newtonian mechanics, then charges appear in electrostatics.

Coulomb formula for a dielectric medium

The coefficient, taking into account the SI system values, is determined in N 2 * m 2 / Cl 2. It is equal to:

In many textbooks, this coefficient can be found in the form of a fraction:

Here E 0 = 8.85*10-12 C2/N*m2 is the electrical constant. For a dielectric, E is added - the dielectric constant of the medium, then Coulomb's law can be used to calculate the forces of interaction of charges for vacuum and medium.

Taking into account the influence of the dielectric, it has the form:

From this we see that the introduction of a dielectric between the bodies reduces the force F.

How are the forces directed?

Charges interact with each other depending on their polarity - like charges repel, and unlike (opposite) charges attract.

By the way, this is the main difference from a similar law of gravitational interaction, where bodies always attract. The forces are directed along a line drawn between them, called the radius vector. In physics it is denoted as r 12 and as the radius vector from the first to the second charge and vice versa. The forces are directed from the center of the charge to the opposite charge along this line, if the charges are opposite, and in reverse side, if they are of the same name (two positive or two negative). In vector form:

The force applied to the first charge by the second is denoted as F 12. Then, in vector form, Coulomb’s law looks like this:

To determine the force applied to the second charge, the designations F 21 and R 21 are used.

If the body has a complex shape and is large enough that at a given distance it cannot be considered a point charge, then it is divided into small sections and each section is considered a point charge. After geometrically adding all the resulting vectors, the resulting force is obtained. Atoms and molecules interact with each other according to the same law.

Application in practice

Coulomb's work is very important in electrostatics; in practice, it is used in a number of inventions and devices. A striking example is a lightning rod. With its help, they protect buildings and electrical installations from thunderstorms, thereby preventing fire and equipment failure. When it rains with a thunderstorm, an induced charge of large magnitude appears on the ground, they are attracted towards the cloud. It turns out that a large electric field appears on the surface of the earth. Near the tip of the lightning rod it is larger, as a result of which a corona discharge is ignited from the tip (from the ground, through the lightning rod to the cloud). The charge from the ground is attracted to the opposite charge of the cloud, according to Coulomb's law. The air is ionized, and the electric field strength decreases near the end of the lightning rod. Thus, charges do not accumulate on the building, in which case the likelihood of a lightning strike is low. If a strike does occur on the building, then all the energy will go into the ground through the lightning rod.

Serious scientific research uses the greatest device of the 21st century - the particle accelerator. In it, the electric field does work to increase the energy of the particle. Considering these processes from the point of view of the influence of a group of charges on a point charge, then all the relations of the law turn out to be valid.

Useful

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 a large number of experiments with metal balls, Charles Coulomb gave the following formulation of the law:

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:

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 come into force: the magnetic field of a moving charge and the corresponding additional Lorentz force acting on another moving charge;
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 it appeared short message that D. Bernoulli in Basel established the quadratic law using the electrometer he 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 for a long time(over 100 years) remained unknown. 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.

Notes

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
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
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
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
L. B. Okun... z Elementary introduction to the physics of elementary particles, M., Nauka, 1985, Library “Kvant”, vol. 45, p. “Virtual particles”, p. 57.
Novi Comm. Acad. Sc. Imp. Petropolitanae, v. IV, 1758, p. 301.
Epinus F.T.U. Theory of electricity and magnetism. - L.: USSR Academy of Sciences, 1951. - 564 p. - (Classics of science). - 3000 copies.
Abel Socin (1760) Acta Helvetica, vol. 4, pages 224-225.
J. Priestley. The History and present state of Electricity with original experiments. London, 1767, p. 732.
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.
S. R. Filonovich “Cavendish, Coulomb and Electrostatics”, M., “Knowledge”, 1988, BBK 22.33 F53, ch. "The Fate of the Law", p. 48
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;
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;
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);
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.
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;
CODATA (the Committee on Data for Science and Technology)
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
Neda Sadooghi Modified Coulomb potential of QED in a strong magnetic field (English).
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;
“Physics of the microworld”, ch. ed. D. V. Shirkov, M., “ Soviet encyclopedia", 1980, 528 p., ill., 530.1(03), F50, art. "Effective charge", author. Art. D. V. Shirkov, p. 496;
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;
Uehling E.A., Phys. Rev., 48, 55, (1935)
“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
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Literature

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 between 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:

The accuracy of charges - between charged bodies - may be much greater depending on the size of the body.
Unbreakable charges. In a protracted episode, it is necessary to add a magnetic field to the charge that is collapsing.
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 (SI)

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 understood in terms of which the law is formulated (the concept of force is nya), 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.: Radyanska 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

A b Coulomb's law can be closely applied to dry charges, since their fluidity is much lower than that of light
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.
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 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's immediately note two interesting moments 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 general description 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 within the framework of the theory of relativity. In this way we can trace how the most abstract and universal theories modern science developed step by step, absorbing previously obtained results, starting with simple conclusions drawn on the basis of desktop physical experiments.
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Coulomb's law quantitatively describes the interaction of charged bodies. It is a fundamental law, that is, it was established through experiment and does not follow from any other law of nature. It is formulated for stationary point charges in a vacuum. In reality, point charges do not exist, but charges whose sizes are significantly smaller than the distance between them can be considered such. The force of interaction in air is almost no different from the force of interaction in vacuum (it is weaker by less than one thousandth).

Electric charge- This physical quantity, characterizing the property of particles or bodies to enter into electromagnetic force interactions.

The law of interaction of stationary charges was first discovered by the French physicist C. Coulomb in 1785. In Coulomb's experiments, the interaction between balls whose dimensions were much smaller than the distance between them was measured. Such charged bodies are usually called point charges.

Based on numerous experiments, Coulomb established the following law:

The force of interaction between two stationary point electric charges in a vacuum is directly proportional to the product of their moduli and inversely proportional to the square of the distance between them. It is directed along the straight line connecting the charges, and is an attractive force if the charges are opposite, and a repulsive force if the charges are like.

If we denote the charge modules by | q 1 | and | q 2 |, then Coulomb’s law can be written in the following form:

\[ F = k \cdot \dfrac(\left|q_1 \right| \cdot \left|q_2 \right|)(r^2) \]

The proportionality coefficient k in Coulomb's law depends on the choice of system of units.

\[ k=\frac(1)(4\pi \varepsilon _0) \]

The full formula of Coulomb's law:

\[ F = \dfrac(\left|q_1 \right|\left|q_2 \right|)(4 \pi \varepsilon_0 \varepsilon r^2) \]

\(F\) - Coulomb Force

\(q_1 q_2 \) - Electric charge of the body

\(r\) - Distance between charges

\(\varepsilon_0 = 8.85*10^(-12)\)- Electrical constant

\(\varepsilon \) - Dielectric constant of the medium

\(k = 9*10^9 \) - Proportionality coefficient in Coulomb’s law

Interaction forces obey Newton's third law: \(\vec(F)_(12)=\vec(F)_(21) \). They are repulsive forces with the same signs of charges and attractive forces with different signs.

Electric charge is usually denoted by the letters q or Q.

The totality of all known experimental facts allows us to draw the following conclusions:

There are two types of electric charges, conventionally called positive and negative.

Charges can be transferred (for example, by direct contact) from one body to another. Unlike body mass, electric charge is not an integral characteristic of a given body. The same body under different conditions can have a different charge.

Like charges repel, unlike charges attract. This also reveals the fundamental difference between electromagnetic forces and gravitational ones. Gravitational forces are always attractive forces.

The interaction of stationary electric charges is called electrostatic or Coulomb interaction. The branch of electrodynamics that studies the Coulomb interaction is called electrostatics.

Coulomb's law is valid for point charged bodies. In practice, Coulomb's law is well satisfied if the sizes of charged bodies are much smaller than the distance between them.

Note that for Coulomb’s law to be satisfied, 3 conditions are necessary:

Accuracy of charges- that is, the distance between charged bodies is much greater than their sizes.
Immobility of charges. Otherwise, additional effects come into force: the magnetic field of a moving charge and the corresponding additional Lorentz force acting on another moving charge.
Interaction of charges in vacuum.

In the International SI system, the unit of charge is the coulomb (C).

A coulomb is a charge passing through the cross section of a conductor in 1 s at a current of 1 A. The SI unit of current (Ampere) is, along with units of length, time and mass, the basic unit of measurement.

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Example 1

Task

A charged ball is brought into contact with exactly the same uncharged ball. Being at a distance of \(r = 15\) cm, the balls repel with a force of \(F = 1\) mN. What was the initial charge of the charged ball?

Solution

Upon contact, the charge will be divided exactly in half (the balls are identical). Based on this interaction force, we can determine the charges of the balls after contact (let’s not forget that all quantities must be presented in SI units - \(F = 10^(-3) \) N, \( r = 0.15\) m):

\(F = \dfrac(k\cdot q^2)(r^2) , q^2 = \dfrac(F\cdot r^2)(k) \)

\(k=\dfrac(1)(4\cdot \pi \cdot \varepsilon _0) = 9\cdot 10^9 \)

\(q=\sqrt(\dfrac(f\cdot r^2)(k) ) = \sqrt(\dfrac(10^(-3)\cdot (0.15)^2 )(9\cdot 10^9) ) = 5\cdot 10^8\)

Then, before contact, the charge of the charged ball was twice as large: \(q_1=2\cdot 5\cdot 10^(-8)=10^(-7)\)

Answer

\(q_1=10^(-7)=10\cdot 10^(-6) \) C, or 10 µC.

Example 2

Task

Two identical small balls weighing 0.1 g each are suspended on non-conducting threads of length \(\displaystyle(\ell = 1\,(\text(m))) \) to one point. After the balls were given identical charges \(\displaystyle(q)\) , they diverged to a distance \(\displaystyle(r=9\,(\text(cm))) \). Dielectric constant of air \(\displaystyle(\varepsilon=1)\). Determine the charges of the balls.

Data

\(\displaystyle(m=0.1\,(\text(g))=10^(-4)\,(\text(kg))) \)

\(\displaystyle(\ell=1\,(\text(m))) \)

\(\displaystyle(r=9\,(\text(cm))=9\cdot 10^(-2)\,(\text(m))) \)

\(\displaystyle(\varepsilon = 1)\)

\(\displaystyle(q) - ? \)

Solution

Since the balls are identical, the same forces act on each ball: the force of gravity \(\displaystyle(m \vec g)\), the tension force of the thread \(\displaystyle(\vec T) \) and the force of Coulomb interaction (repulsion) \( \displaystyle(\vec F)\). The figure shows the forces acting on one of the balls. Since the ball is in equilibrium, the sum of all forces acting on it is 0. In addition, the sum of the projections of the forces on the \(\displaystyle(OX)\) and \(\displaystyle(OY)\) axes is 0:

\(\begin(equation) ((\mbox(to axis )) (OX) : \atop ( \mbox( to axis )) (OY) : )\quad \left\(\begin(array)(ll) F-T \sin(\alpha) & =0 \\ T\cos(\alpha)-mg & =0 \end(array)\right. \quad(\text(or))\quad \left\(\begin(array )(ll) T\sin(\alpha) & =F \\ T\cos(\alpha) & = mg \end(array)\right \end(equation) \)

Let's solve these equations together. Dividing the first equality term by term by the second, we get:

\(\begin(equation) (\mbox(tg)\,)= (F\over mg)\,. \end(equation) \)

Since the angle \(\displaystyle(\alpha)\) is small, then

\(\begin(equation) (\mbox(tg)\,)\approx\sin(\alpha)=(r\over 2\ell)\,. \end(equation) \)

Then the expression will take the form:

\(\begin(equation) (r\over 2\ell)=(F\over mg)\,. \end(equation) \)

The force \(\displaystyle(F) \)according to Coulomb's law is equal to: \(\displaystyle(F=k(q^2\over\varepsilon r^2)) \). Let's substitute the value \(\displaystyle(F) \) into expression (52):

\(\begin(equation) (r\over 2\ell)=(kq^2\over\varepsilon r^2 mg)\, \end(equation) \)

from where we express it in general view required charge:

\(\begin(equation) q=r\sqrt(r\varepsilon mg\over 2k\ell)\,. \end(equation) \)

After substituting numerical values we will have:

\(\begin(equation) q= 9\cdot 10^(-2)\sqrt(9\cdot 10^(-2)\cdot 1 \cdot 10^(-4)\cdot 9.8\over 2\ cdot 9\cdot 10^9\cdot 1)\, ((\text(Cl)))=6.36\cdot 10^(-9)\, ((\text(Cl)))\end(equation ) \)

It is suggested that you check the dimension for the calculation formula yourself.

Answer: \(\displaystyle(q=6.36\cdot 10^(-9)\,(\text(Kl))\,.) \)

Answer

\(\displaystyle(q=6.36\cdot 10^(-9)\,(\text(Kl))\,.) \)

Example 3

Task

How much work must be done to transfer a point charge \(\displaystyle(q=6\,(\text(nC))) \) from infinity to a point located at a distance \(\displaystyle(\ell = 10\,(\ text(cm))) \) from the surface of a metal ball, the potential of which is \(\displaystyle(\varphi_(\text(w))=200\,(\text(V))) \), and the radius \(\displaystyle (R = 2\,(\text(cm)))\)? The ball is in the air (count \(\displaystyle(\varepsilon=1) \)).

Data

\(\displaystyle(q=6\,(\text(nKl))=6\cdot 10^(-9)\,(\text(Kl))) \)\(\displaystyle(\ell=10\, (\text(cm))) \)\(\displaystyle(\varphi_(\text(w))=200\,(\text(H))) \)\(\displaystyle(R=2\,(\ text(cm))) \) \(\displaystyle(\varepsilon = 1) \) \(\displaystyle(A) \) - ?

Solution

The work that must be done to transfer a charge from a point with potential \(\displaystyle(\varphi_1)\) to a point with potential \(\displaystyle(\varphi_2)\) is equal to the change in potential energy of a point charge, taken with the opposite sign:

\(\begin(equation) A=-\Delta W_n\,. \end(equation) \)

It is known that \(\displaystyle(A=-q(\varphi_2-\varphi_1) ) \) or

\(\begin(equation) A=q(\varphi_1-\varphi_2) \,. \end(equation) \)

Since the point charge is initially at infinity, the potential at this point in the field is 0: \(\displaystyle(\varphi_1=0)\) .

Let's define the potential at the end point, that is, \(\displaystyle(\varphi_2)\) .

Let \(\displaystyle(Q_(\text(w))) \) be the charge of the ball. According to the conditions of the problem, the potential of the ball is known (\(\displaystyle(\varphi_(\text(w))=200\,(\text(V)))\)), then.

Coulomb's Law is a law that describes the interaction forces between point electric charges.

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:

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.

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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. How are the forces directed?

Coulomb's law

Corollaries from Coulomb's law

History of discovery

Formulation

Coulomb formula for a dielectric medium

How are the forces directed?

Application in practice

Law