The pendant's law states that. Coulomb's law. Point charge
It is known that every charged body has electric field... It can also be argued that if there is an electric field, then there is a charged body to which this field belongs. So, if there are two charged bodies with electric charges nearby, then we can say that each of them is in the electric field of a neighboring body. And in this case, the force will act on the first body
F 1 =q 1E 2,
where q 1- charge of the first body; E 2- the intensity of the field of the second body. Accordingly, the force will act on the second body
F 2 =q 2E 1,
where q 2- charge of the first body; E 1- the intensity of the field of the second body.
An electrically charged body interacts with the electric field of another charged body.
If these bodies are small (pointlike), then
E 1 =k. q 1 / r 2,
E 2 =k.q 2 /r 2,
The forces acting on each of the interacting charged bodies can be calculated, knowing only their charges and the distance between them.
Substitute the tension values and get
F 1 = k. q 1 q 2 / r 2 and F 2 = k. q 2 q 1 / r 2.
The value of each force is expressed only through the value of the charges of each body and the distance between them. Thus, it is possible to determine the forces acting on each body using only knowledge about the electric charges of bodies and the distance between them. On this basis, one of the fundamental laws of electrodynamics can be formulated - Coulomb's law.
Coulomb's law ... The force acting on a stationary point-point body with an electric charge in the field of another stationary point-like body with an electric charge is proportional to the product of the values of their charges and is inversely proportional to the square of the distance between them.
V general view the meaning of the force about which in question in the wording Coulomb's law, can be written like this:
F = k. q 1 q 2 / r 2,
In the formula for calculating the force of interaction, the values of the charges of both bodies are written. Therefore, we can conclude that both forces are equal in modulus. However, in direction - they are opposite. If the charges of the bodies are of the same name, the bodies repel (Fig. 4.48). If the charges of the bodies are different, then the bodies are attracted (Fig. 4.49). Finally, you can write:
F̅ 1 = -F̅ 2.
The written equality confirms the validity of the III law of Newton's dynamics for electrical interactions. Therefore, in one of the common formulations Coulomb's law it says that
the force of interaction of two charged point bodies is proportional to the product of their charge values and is inversely proportional to the square of the distance between them.
If charged bodies are in a dielectric, then the force of interaction will depend on the dielectric constant of this dielectric
F =k.q 1q 2 /ε r 2.
For the convenience of calculations based on Coulomb's law, the value of the coefficient k write differently:
k = 1/4πε 0 .
The magnitude ε 0 called electric constant... Its value is calculated in accordance with the definition:
9 . 10 9 N.m 2 / Cl 2 = 1 / 4π ε 0 ,
ε 0 = (1 / 4π). 9 . 10 9 N.m 2 / Cl 2 = 8.85. 10 -12 Cl 2 / Nm 2. Material from the site
In this way, Coulomb's law v general case can be expressed by the formula
F= (1 / 4π ε 0 ). q 1 q 2 / ε r 2 .
Coulomb's law is one of the fundamental laws of nature. All electrodynamics is based on it, and not a single case has been noted when Coulomb's law... There is only one limitation that applies to the action Coulomb law on the different distances... It is considered that Coulomb's law acts at distances of more than 10 -16 m and less than a few kilometers.
When solving problems, it is necessary to take into account that Coulomb's law concerns the forces of interaction of point stationary charged bodies. This reduces all problems to problems of the interaction of stationary charged bodies, in which two statics positions are applied:
- the resultant of all forces acting on the body is zero;
- the sum of the moments of forces is equal to zero.
In the vast majority of applications Coulomb's law it is enough to take into account only the first position.
On this page material on topics:
E-write the formula for the law of the pendant
Pendant's law abstract
Physics talk on Coulomb's law
-
Coulomb's Law Is a law that describes the forces of interaction between point electric charges.
It was discovered by Charles Coulomb in 1785. a large number of experiments with metal balls, Charles Coulomb gave the following formulation of the law:
The modulus of the force of interaction of two point charges in a vacuum is directly proportional to the product of the moduli of these charges and is 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 are directed along a 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:
- the point nature of charges - that is, the distance between charged bodies is much larger than their size - however, it can be proved that the interaction force of two volumetric distributed charges with spherically symmetric disjoint spatial distributions is equal to the interaction force of two equivalent point charges located at the 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 S. Coulomb, the law is written as follows:
where is the force with which charge 1 acts on charge 2; - the magnitude of the charges; - radius vector (vector directed from charge 1 to charge 2, and equal, in modulus, to the distance between charges -); - coefficient of proportionality. Thus, the law indicates that like charges repel (and unlike charges attract).
Coefficient k
In the CGSE, the unit for measuring the charge is chosen in such a way that the coefficient k is equal to one.
V The international system units (SI) one of the basic units is the unit of force electric current ampere, and the unit of charge - the coulomb - is a derivative of it. The ampere is defined in such a way that k= c2 10-7 H / m = 8.9875517873681764 109 N m2 / Cl2 (or F − 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
V quantum mechanics Coulomb's law is not formulated using the concept of force, as in classical mechanics, but using the concept of the potential energy of the Coulomb interaction. In the case when the system considered in quantum mechanics contains electrically charged particles, the terms expressing the potential energy of the Coulomb interaction are added to the Hamiltonian operator of the system, as it is calculated in classical mechanics.
Thus, the Hamilton operator of an atom with a nuclear charge Z looks like:
j) \ frac (e ^ 2) (r_ (ij)) "src =" http://upload.wikimedia.org/math/d/0/8/d081b99fac096b0e0c5b4290a9573794.png ">.
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 - the potential energy of the Coulomb interaction of electrons with the nucleus, and the third term - the potential Coulomb energy of mutual repulsion of electrons. The summation in the first and second terms is carried out over all N electrons. In the third term, the summation is over all pairs of electrons, and each pair occurs once.
Coulomb's law in terms 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 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 for virtual photons to overcome this distance and, therefore, the greater the energy of virtual photons is allowed by the uncertainty principle. At small distances between charges, the uncertainty principle allows the exchange of both long-wave and short-wave photons, and at large distances, only long-wave photons participate in the exchange. Thus, using quantum electrodynamics, you can derive Coulomb's law.
Story
For the first time to study experimentally the law of interaction of electrically charged bodies was proposed by GV Rikhman in 1752-1753. He intended to use an electrometer-"pointer" designed by him for this. The implementation of this plan was prevented by the tragic death of Richman.
In 1759, professor of physics at the St. Petersburg Academy of Sciences F. Epinus, who took over the department of Richmann after his death, first suggested that charges should interact inversely with the square of the distance. In 1760, a brief report appeared that D. Bernoulli in Basel established a quadratic law with the help of an electrometer constructed by him. In 1767, Priestley, in his History of Electricity, noted that the experience of Franklin, who discovered the absence of electric field inside a charged metal ball may mean that "Electric attraction follows exactly the same law as gravity, that is, the square of the distance"... Scottish physicist John Robison claimed (1822) that in 1769 he discovered that balls with the same electric charge repel with a force inversely proportional to the square of the distance between them, and thus anticipated the discovery of Coulomb's law (1785).
Approximately 11 years before Coulomb, in 1771, the law of interaction of charges was experimentally discovered by G. Cavendish, but the result was not published and for a long time(over 100 years) remained unknown. The Cavendish manuscripts were presented to D.C. Maxwell only in 1874 by one of the Cavendish descendants at the grand opening of the Cavendish Laboratory and published in 1879.
Coulomb himself studied the twisting of threads and invented the torsion balance. He discovered his law by measuring with the help of them the forces of interaction 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 principle of superposition for electric fields are fulfilled if and only if Maxwell's equations for electrostatics are fulfilled and, conversely, Maxwell's equations for electrostatics are fulfilled if and only if Coulomb's law and the principle of superposition for electric fields are fulfilled.
Accuracy Degree of Coulomb's Law
Coulomb's law is an experimentally established fact. Its validity has been repeatedly confirmed by more and more precise experiments. One of the directions of such experiments is to check whether the exponent differs r in the law of 2. To search for this difference, the fact is used that if the degree is exactly 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 up to.
To check the accuracy of Coulomb's law at intra-atomic distances, W. Yu. Lamb and R. Rutherford in 1947 used measurements of the relative arrangement of the energy levels of hydrogen. It was found that even at distances of the order of atomic 10−8 cm, the exponent in the 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.
Corrections to Coulomb's Law in Quantum Electrodynamics
At small distances (of the order of the Compton wavelength of an electron, ≈3.86 10−13 m, where is the electron mass, is the Planck constant, is the speed of light), nonlinear effects of quantum electrodynamics become significant: the generation of virtual electron-positron (a also muon-anti-muon and taon-anti-tyon) pairs, and the effect of screening also decreases (see renormalization). Both effects lead to the appearance of exponentially decreasing order terms in the expression for the potential energy of interaction of charges and, as a result, to an increase in the interaction force in comparison with that calculated according to the Coulomb law. For example, the expression for the potential of a point charge in the CGS system, taking into account the first-order radiative 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, which make up a noticeable fraction of the vacuum breakdown field (of the order of ~ 1018 V / m or ~ 109 T, such fields are observed, for example, near some types of neutron stars, namely magnetars), the Coulomb law is also violated due to the Delbrück scattering of exchange photons on photons of an external field and other more complex nonlinear effects. This phenomenon decreases the Coulomb force not only on microscales but also on macroscales, in particular, in a strong magnetic field, the Coulomb potential decreases not inversely with the 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. The cloud of electron-positron pairs screens the electric charge of the electron. The shielding increases with the distance from the electron; as a result, the effective electric charge of the electron is a decreasing function of the distance. The effective potential created by an electron with an electric charge can be described by a dependence of the form. The effective charge depends on the distance according to the logarithmic law:
- so-called. fine structure constant ≈7.3 · 10−3;
- so-called. the classical radius of an electron is ≈2.8 × 10−13 cm.
Youhling effect
The phenomenon of the deviation of the electrostatic potential of point charges in vacuum from the value of the Coulomb's law is known as the Yuling effect, who was the first to calculate the deviations from the Coulomb's law for the hydrogen atom. The Youhling effect gives a correction for the Lamb shift of 27 MHz.
Coulomb's law and superheavy nuclei
In a strong electromagnetic field near superheavy nuclei with a charge of 170 "src =" http://upload.wikimedia.org/math/0/d/7/0d7b5476a5437d2a99326cf04b131458.png "> the vacuum is rearranged similar to the usual phase transition. This leads to corrections to Coulomb's law.
The value of Coulomb's law in the history of science
Coulomb's law is the first open quantitative and formulated in mathematical language law for electromagnetic phenomena. With the discovery of Coulomb's law began modern science about electromagnetism.
Page 56
THE LAW OF PENDANT (section 10, pp. 354-362)
The basic law of electrostatics. The concept of a point charged body.
Measurement of the force of interaction of charges using a torsion balance. Pendant's Experiments
Determination of a point charge
Coulomb's law. Formulation and formula
Pendant Strength
Determination of the unit of charge
Coefficient in Coulomb's law
Comparison of electrostatic and gravitational forces in an atom
Equilibrium of static charges and its physical meaning(for example, three charges)
The basic law of electrostatics is the law of interaction of two stationary point charged bodies.
Installed by Charles Augustin Coulomb in 1785 and bears his name.
In nature, point charged bodies do not exist, but if the distance between bodies is many times greater than their dimensions, then neither the shape nor the dimensions of the charged bodies significantly affect the interactions between them. In the current case, these bodies can be considered as point ones.
The force of interaction of charged bodies depends on the properties of the medium between them. Experience shows that air has very little effect on the strength of this interaction and it turns out to be almost the same as in a vacuum.
Pendant's Experience
The first results on measuring the force of interaction of charges were obtained in 1785 by the French scientist Charles Augustin Coulomb
A torsion balance was used to measure the force.
A small, thin, uncharged gold sphere at one end of an insulating rocker suspended by an elastic silver thread was balanced at the other end of the rocker by a paper disc.
By turning the rocker, it was brought into contact with the same stationary charged sphere, as a result of which its charge was divided equally between the spheres.
The diameter of the spheres was chosen much less than the distance between them in order to exclude the influence of the size and shape of the charged bodies on the measurement results.
Point charge- a charged body, the size of which is much less than the distance of its possible action on other bodies.
The spheres with the same charges began to repel, twisting the thread. The angle of rotation was proportional to the force acting on the moving sphere.
The distance between the spheres was measured using a special calibration scale.
By discharging sphere 1 after measuring the force and connecting it again with the stationary sphere, Coulomb reduced the charge on the interacting spheres by 2,4,8, etc. once,
Coulomb's law:
The force of interaction between two stationary point charges in a vacuum is directly proportional to the product of the moduli of the charges and is inversely proportional to the square of the distance between them, and is directed along a straight line connecting the charges.
k - coefficient of proportionality, depending on the choice of the system of units.
I call the F12 force the Coulomb force.
The Coulomb force is central, i.e. directed along the line connecting the centers of charges.
In SI, the unit of charge is not the basic, but the derivative, and is determined using the Ampere - the basic unit of the SI.
Pendant - an electric charge passing through the cross-section of a conductor at a current of 1 A for 1 s
In SI proportionality coefficient in Coulomb's law for vacuum:
k = 9 * 109 Nm2 / Cl2
The coefficient is often written as:
e0 = 8.85 * 10-12 Cl2 / (Nm2) - electrical constant
Coulomb's law is written in the form:
If a point charge is placed in a medium with a relative permittivity e, different from vacuum, the Coulomb force will decrease by a factor of e.
Any medium except vacuum has e> 1
According to Coulomb's law, two point charges of 1 C each, at a distance of 1 m in vacuum, interact with the force
It can be seen from this estimate that a charge of 1 Coulomb is a very large value.
In practice, fractional units are used - μC (10-6), mC (10-3)
1 Cl contains 6 * 1018 electron charges.
Using the example of the forces of interaction of an electron and a proton in the nucleus, it can be shown that the electrostatic force of interaction of particles is greater than the gravitational force by about 39 orders of magnitude. However, the electrostatic forces of interaction of macroscopic bodies (generally electrically neutral) are determined only by very small excess charges located on them, and therefore are not large in comparison with gravitational forces, which depend on the mass of the bodies.
Is the balance of static charges possible?
Consider a system of two positive point charges q1 and q2.
We will find where the third charge should be placed so that it is in equilibrium, as well as determine the magnitude and sign of this charge.
Static equilibrium occurs when the geometric (vector) sum of the forces acting on the body is zero.
The point at which the forces acting on the third charge q3 can compensate each other is on the straight line between the charges.
In this case, the charge q3 can be either positive or negative. In the first case, the repulsive forces are compensated, in the second, the forces of attraction.
Taking into account Coulomb's law, the static balance of charges will be in the case:
The balance of the charge q3 does not depend on either its magnitude or the sign of the charge.
When the charge q3 changes, both the attractive forces (q3 positive) and the repulsive forces (q3 negative) change equally
By solving the quadratic equation for x, we can show that a charge of any sign and magnitude will be in equilibrium at a point at a distance x1 from the charge q1:
Let us find out whether the position of the third charge will be stable or unstable.
(In case of stable equilibrium, the body, taken out of the equilibrium position, returns to it; in case of unstable balance, it moves away from it)
With a horizontal displacement, the repulsive forces F31, F32 change due to a change in the distances between the charges, returning the charge to the equilibrium position.
With a horizontal displacement, the balance of the charge q3 is stable.
With vertical displacement, the resultant of F31, F32 pushes q3
Go to page:
In electrostatics, one of the fundamental 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 explain simple language Coulomb's law and its application in practice.
Discovery history
Sh.O. Pendant in 1785 for the first time experimentally proved the interactions described by the law. In his experiments, he used a special torsion balance. However, back in 1773 it was proved by Cavendish, using the example of a spherical capacitor, that there is no electric field inside the sphere. This indicated that the electrostatic forces change depending on the distance between the bodies. More precisely, the square of the distance. Then his research was not published. Historically, this discovery was named after Coulomb, the same name is also given to the value in which the charge is measured.
The wording
The definition of Coulomb's law reads: 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 it may not be clear to everyone. In simple words: The more charge 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 the Coulomb rule looks like this:
Designation of letters: q is the amount of charge, r is the distance between them, k is the coefficient, depends on the selected system of units.
The value of the charge 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. Hence it follows that one and the same body can have a charge different in magnitude and sign. A point charge is a charge or a body whose dimensions are much smaller than the distance of possible interaction.
It should be borne in mind that the environment in which the charges are located affects the F interactions. Since it is almost equal in air and in vacuum, Coulomb's discovery is applicable only for these media, this is one of the conditions for the application of this type of formula. As already mentioned, in the SI system, the unit of measure for charge is Coulomb, abbreviated Cl. It characterizes the amount of electricity per unit of time. Derived from base SI units.
1 Cl = 1 A * 1 s
It should be noted that the dimension of 1 C is redundant. Due to the fact that the carriers repel each other, it is difficult to keep them in a small body, although the current of 1A itself is small if it flows in the conductor. For example, in the same 100 W incandescent lamp, a current of 0.5 A flows, and in an electric heater even 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 practically the same as in the gravitational interaction, only if in Newtonian mechanics masses appear, then in electrostatics - charges.
Coulomb's formula for a dielectric medium
The coefficient, taking into account the values of the SI system, is determined in H 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 Cl2 / N * m2 is an 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 a vacuum and a medium.
Taking into account the influence of the dielectric, it has the form:
From here we see that the introduction of a dielectric between the bodies reduces the force F.
How the forces are directed
The charges interact with each other depending on their polarity - the same ones repel, and the opposite (opposite) ones attract.
By the way, this is the main difference from a similar law of gravitational interaction, where bodies are always attracted. The forces are directed along the line drawn between them, called the radius vector. In physics, denoted as r 12 and as a 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 from the side of 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 complex shape and it 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 as a point charge. After geometric addition of 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 works are very important in electrostatics; in practice, they are used in a number of inventions and devices. A striking example is a lightning rod. With its help, buildings and electrical installations are protected 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 has a large value, 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 earth 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, the charges do not accumulate on the building, in which case the probability of a lightning strike is small. If a blow to the building occurs, then through the lightning rod all the energy will go into the ground.
In serious scientific research use the greatest structure of the 21st century - a particle accelerator. In it, the electric field does the work to increase the energy of the particle. Considering these processes from the point of view of the effect on a point charge by a group of charges, then all the relations of the law turn out to be true.
Useful
Charges and electricity are terms that are mandatory for those cases when the interaction of charged bodies is observed. The forces of repulsion and attraction seem to emanate from charged bodies and spread simultaneously in all directions, gradually fading away at a distance. This force was once discovered by the famous French naturalist Charles Coulomb, and the rule that charged bodies obey has since then been called Coulomb's Law.
Charles Pendant
The French scientist was born in France, where he received an excellent education. He actively applied the acquired knowledge in engineering sciences and made significant contributions to the theory of mechanisms. Pendant is the author of works in which the work of windmills, statistics of various structures, twisting of threads under the influence of external forces... One of these works helped to discover the Coulomb-Amonton law, which explains the processes of friction.
But Charles Coulomb made the main contribution to the study of static electricity. The experiments carried out by this French scientist led him to understand one of the most fundamental laws of physics. It is to him that we owe our knowledge of the nature of the interaction of charged bodies.
Background
The forces of attraction and repulsion with which electric charges act on each other are directed along a straight line connecting charged bodies. With increasing distance, this force weakens. A century after Isaac Newton discovered his universal law of gravitation, the French scientist C. Coulomb experimentally investigated the principle of interaction between charged bodies and proved that the nature of such a force is analogous to the forces of gravity. Moreover, as it turned out, interacting bodies in an electric field behave in the same way as any bodies with mass in a gravitational field.
Pendant device
The diagram of the device with which Charles Coulomb made his measurements is shown in the figure:
As you can see, in essence, this design does not differ from the device with which at one time Cavendish measured the value of the gravitational constant. An insulating rod, suspended by a thin thread, ends with a metal ball, which is imparted with a certain electric charge. Another metal ball is brought closer to the ball, and then, as it approaches, the force of interaction is measured by the degree of twisting of the thread.
Coulomb experiment
Coulomb suggested that the then known Hooke's Law can be applied to the force with which the thread is twisted. The scientist compared the change in force at different distances of one ball from another and found that the force of interaction changes its value in inverse proportion to the square of the distance between the balls. The pendant was able to change the values of the charged ball from q to q / 2, q / 4, q / 8 and so on. With each change in the charge, the force of interaction proportionally changed its value. So, gradually, a rule was formulated, which was later named "Coulomb's Law".
Definition
Experimentally, the French scientist proved that the forces with which two charged bodies interact are proportional to the product of their charges and inversely proportional to the square of the distance between the charges. This statement is Coulomb's law. In mathematical form, it can be expressed as follows:
In this expression:
- q is the amount of charge;
- d is the distance between charged bodies;
- k is the electric constant.
The value of the electrical constant largely depends on the choice of the unit of measurement. V modern system the magnitude of the electric charge is measured in coulombs, and the electric constant, respectively, in newtons × m 2 / coulomb 2.
Recent measurements have shown that this coefficient should take into account the dielectric constant of the environment in which the experiment is carried out. Now the value is shown in the form of the ratio k = k 1 / e, where k 1 is the electrical constant already familiar to us, and is not an indicator of the dielectric constant. Under vacuum conditions, this value is equal to unity.
Conclusions from Coulomb's law
The scientist experimented with different amounts of charges, checking the interaction between bodies with different amounts of charge. Of course, he could not measure the electric charge in any units - he lacked neither the knowledge nor the appropriate instruments. Charles Coulomb was able to split the projectile by touching a charged ball unloaded. So he received fractional values of the original charge. A number of experiments have shown that the electric charge is conserved, exchange takes place without increasing or decreasing the amount of charge. This fundamental principle formed the basis of the law of conservation of electric charge. It has now been proven that this law is observed in the microcosm of elementary particles and in the macrocosm of stars and galaxies.
Conditions required for the implementation of Coulomb's law
In order for the law to be fulfilled with greater accuracy, the following conditions must be met:
- The charges must be point-like. In other words, the distance between the observed charged bodies should be much greater than their size. If charged bodies have a spherical shape, then we can assume that the entire charge is located at a point that is the center of the sphere.
- The measured body must be motionless. Otherwise, the moving charge will be influenced by numerous external factors, for example, the Lorentz force, which gives the charged body additional acceleration. And also the magnetic field of a moving charged body.
- Observed bodies must be in a vacuum to avoid exposure to currents air masses on the results of observations.
Coulomb's Law and Quantum Electrodynamics
From the point of view of quantum electrodynamics, the interaction of charged bodies occurs through the exchange of virtual photons. The existence of such unobservable particles and zero mass, but not zero charge, is indirectly confirmed by the uncertainty principle. According to this principle, a virtual photon can exist between the moments of emission of such a particle and its absorption. The smaller the distance between the bodies, the less time a photon spends to travel the path, therefore, the greater the energy of the emitted photons. At a small distance between the observed charges, the uncertainty principle allows exchange of both short-wave and long-wave particles, and at large distances, short-wave photons do not participate in the exchange.
Are there limits to the application of Coulomb's law
Coulomb's law fully explains the behavior of two point charges in a vacuum. But when it comes to real bodies, one should take into account the volumetric dimensions of charged bodies and the characteristics of the medium in which the observation is carried out. For example, some researchers have observed that a body carrying a small charge and forcibly introduced into the electric field of another object with a large charge begins to be attracted to this charge. In this case, the assertion that similarly charged bodies are repelled fails, and another explanation for the observed phenomenon should be sought. Most likely, here we are not talking about a violation of Coulomb's law or the principle of conservation of electric charge - it is possible that we are observing phenomena that have not been fully studied, which science will be able to explain a little later.
Search
We can notify you about new articles,