What Is Coulomb's Law?

Coulomb's law is the law of the interaction forces of charges at rest points. In 1785, French scientist C, -A.de Coulomb experimentally obtained that the interaction force between two stationary point charges in a vacuum is proportional to the product of their charge amounts and inversely proportional to the square of their distance. , The direction of the force is on their line, the charges of the same name repel, and the charges of different names attract. ^[1]

Chinese name: Coulomb's law
Foreign name: Coulomb's law
expression: F = kQ1.Q2 / r² (k = 1 / 40)
Presenter: coulomb
Presentation time: 1785

Applied discipline: Physics, electricity
Scope of application: Physics, electricity, electrostatics
Main research works: "Law of Electricity"
Outstanding Contributors: Cavendish, Mitchell, Priestley
Earliest research time: 1760
Theory maturity time: 1785

Coulomb's law definition

Illustration of Coulomb's law (4 photos)

A common expression of Coulomb's law: the product of the interaction force between two stationary point charges in a vacuum and their charge amount (

) Is proportional to the square of the distance from them (

) Are inversely proportional, the direction of the force is on their line, the charges of the same name are repelled, and the charges of the other name are attracted. ^[2-3]

Mathematical expression of Coulomb's law:

. Where r is the distance between the two;

Is the sagittal direction from q ₁ to q ₂ ; k is the Coulomb constant (static force constant). When the physical quantities are in SI units,

. When calculating with this formula, do not substitute the positive and negative signs of the charge into the formula. The calculation process can be calculated using the absolute value. The direction of the force can be judged based on the repulsion of the charges of the same name and the attraction of the charges of the same name.

Differential form of Coulomb's law:

. Where D is the electric displacement vector, in a vacuum,

, E is the electric field strength,

Is the charge density,

Is the dielectric constant in vacuum, and its size is measured experimentally

. This formula is described as the divergence of the electric displacement vector at a point in space equal to the charge density there. Coulomb's theorem in differential form, also known as Gauss's law of electric fields, is part of Maxwell's equations. ^[4]

Scope of Coulomb's Law

Conditions for Coulomb's law

In common expressions of Coulomb's law, there are usually vacuum and stillness , because the experimental basis of Coulomb's law, the torsion scale experiment, is done in a sub-vacuum in order to exclude other factors. In addition, generally speaking, the phenomenon of static electricity usually starts from the condition of vacuum, so Coulomb's law has the term "vacuum". In fact, Coulomb's law applies not only to vacuum, but also to homogeneous media, and also between stationary point charges. ^[5]

Coulomb's law also applies to homogeneous media. Coulomb force in vacuum

(d refers to the distance between two charges), k is a universal constant, often introduced

Is the dielectric constant in vacuum, and its size is measured experimentally

. ^[6] According to Gauss' theorem, in a uniform infinite medium (dielectric constant

), The interaction force between two point charges is in a vacuum

Times, ie

, The form is exactly the same as the vacuum. Therefore, Coulomb's law applies not only to vacuum, but also to media.

Coulomb's law applies to the case where the field source charge is stationary and the force charge moves, but it is not applicable to the action of the moving charge on the static charge. Since the spatial distribution of the electric field generated by the stationary field source charge does not change with time, the electric field force applied by the stationary field source charge received by the moving charge is subject to Coulomb's law; The electric field force generated by the excited electric field does not follow Coulomb's law, because the moving charge excites the magnetic field in addition to the electric field. ^[7] At this time, the Coulomb force needs to be corrected to electromagnetic force. But practice has shown that as long as the relative speed of the charge's relative motion is far less than the speed of light c, the results given by Coulomb's law are very close to the actual situation.

Coulomb's law applies only between point charges. The distance between charged bodies is much larger than their own size, so that the influence of the shape, size, and charge distribution on the interaction force can be ignored. When studying their interaction, people abstract them into an ideal physics Model-point charge, Coulomb's law applies only to the force between point charges. ^[8]

Limitations of Coulomb's Law

Coulomb's law does not address how the forces of interaction between charges are transferred. Even according to the content of Coulomb's law, Coulomb's force does not need to contact any medium or time, but acts directly from one charged body to another. That is, the interaction between charges is a kind of "overrange action", but another group of physicists think that this kind of force is a "close action", and electricity is transmitted through an elastic medium filled with space-ether.

The British scientist Faraday first put forward the point of view of the electric field. He believes that charges will excite an electric field in the surrounding space, and other charges in the electric field will be subjected to forces, that is, the interaction between the charges and the charges is achieved through the field existing between them.

Modern science has confirmed that the interaction is not "overrange", but the ether assumed by the "close" view does not exist. The interaction force between the charges is transmitted through the electric field, and the interaction between the charges is transferred. Speed is the speed of light. ^[9]

Coulomb's Law Experiment

Cavendish's concentric sphere charge distribution experiment was more accurate and several decades earlier than Coulomb's twist scale experiment, but Cavendish did not publish his own work. It was not until 1871 that Maxwell hosted the Cavendish Laboratory at Cambridge University that Cavendish's manuscripts were transferred to Maxwell. Maxwell himself repeated many of Cavendish's experiments. The manuscripts were compiled by Maxwell and published. Work is known to the world. ^[10]

In 1769, the British Scottish Robinson designed a lever device, he used the experimental results to formulae Expressed that the power F is inversely proportional to the nth power of the distance r . First assume that the exponent n is not exactly 2, but To get the exponential deviation .	Robinson's experimental setup
From 1784 to 1785, French physicist Charles Coulomb verified this law through torsion scale experiments. The structure of the torsion scale is shown in the right figure: a weighing rod is suspended under a thin metal wire, which has a small ball A at one end and a balance body P at the other end, and another fixed small device of the same size is placed beside A. Ball B. In order to study the force between the charged bodies, let A and B have a certain electric charge first. At this time, the weighing rod will be deflected by the force at the A end. Turn the suspension button on the upper end of the suspension wire to return the ball to its original position. At this time, the torsional moment of the suspension wire is equal to the moment of electric power applied to the small ball A. If the relationship between the torsion moment of the suspension wire and the torsion angle has been calibrated and calibrated in advance, the angle readings turned by the pointer on the knob and the known length of the weighing rod can be used to know the effect between A and B at this distance Force, and the angle of twisting through the suspension wire can compare the magnitude of the force.
In 1773, Cavendish experimented with two concentric metal spherical shells. As shown on the right, the outer spherical shell was assembled from two semicircles. The two hemispheres combined together just sealed the inner ball. The inner and outer balls are connected together by a wire. After the outer ball shell is dotted, remove the wire, open the shell, and test whether the electric ball is charged by the electric pulp tester. Charge. Based on this experiment, Cavendish determined the index deviation , More accurate than Robinson's 0.06 in 1769. ^[11] In 1873, Maxwell and McAllister improved this experiment by Cavendish. Maxwell personally designed the experimental device and method, and calculated the experimental processing formula. They represent F as Where q does not exceed . This experiment was so precise that no one surpassed them until 1936.	Cavendish's experimental setup ^[11]
In 1936, Plimpton and Lawton of Worcester Polytechnic Institute in the United States verified Coulomb's law on a new basis. They used new measuring methods to improve Cavendish and Maxwell's zero value method, eliminating and avoiding experiments Several main errors have greatly improved the measurement accuracy. The test circuit and device are shown in the figure on the right. They conducted many experiments with this device. Different experimenters have confirmed that the galvanometer has no vibration except for the 1 microvolt indicator caused by thermal motion. They calculated it using Maxwell's formula and got	Plimpton and Lawton's experimental setup
Edwin R. Wesleyan University, USA, 1971 Williams, James E. Faller and Henry A. Hill used modern testing methods to extend the exponential deviation of the inverse square law by several orders of magnitude. Prior to this, there have been several experimental results, and the record has been continuously set. Williams and others used high-frequency high-voltage signals, lock-in amplifiers, and optical fiber transmission to ensure experimental conditions, but the basic methods and design ideas are in the same vein as Cavendish and Maxwell. The picture on the right is a simple diagram. They used five concentric metal shells instead of two, and adopted a dodecahedron shape instead of a spherical shape. A 4 MHz high-frequency high-voltage signal with a peak value of 10 kV was applied to the two outermost metal shells. The detector was connected to the two innermost layers to check whether the signal was received. ^[11] ^[12] According to Maxwell's formula, they get the exponential deviation of the inverse square law.	Modern experimental device

Coulomb's Law Evaluation

Coulomb's law was proposed by the French physicist Coulomb in a paper entitled "The Law of Electricity" in 1785. Coulomb's law is the first quantitative law in the history of the development of electricity. It is one of the basic laws of electromagnetics and electromagnetic field theory.

Coulomb's law is not only the basic law of electromagnetics, but also one of the basic laws of physics. Coulomb's law clarifies the law of the interaction of charged bodies, determines the nature of the electrostatic field, and lays the foundation for the entire electromagnetics. The impact of Coulomb's work on French physicists can also be confirmed from a brief outline of Laplacian physics later. The basic starting point of this brief outline of physics is to reduce all physical phenomena to the phenomenon of attraction and repulsion between particles. Electric or magnetic motion is generated by the attraction and repulsion between charged particles or magnetic particles. effect. This simplification facilitates the application of analytical mathematical methods to physics. ^[13]

The unit of electricity is named after him in honor of Coulomb. ^[14] (symbol is Q, unit coulomb, symbol C)