# Coulomb's law

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## Coulomb's law

(ko͞o`lŏmz), in physics, law stating that the electrostatic force between two charged bodies is proportional to the product of the amount of charge on the bodies divided by the square of the distance between them. If the bodies are oppositely charged, one positive and one negative, they are attracted toward one another; if the bodies are similarly charged, both positive or both negative, the force between them is repulsive (see charge**charge,**

property of matter that gives rise to all electrical phenomena (see electricity). The basic unit of charge, usually denoted by

*e,*is that on the proton or the electron; that on the proton is designated as positive (+

*e*

**.....**Click the link for more information. ). Coulomb's law applies exactly only when the charged bodies are much smaller than the distance separating them and therefore can be treated approximately as point charges. When combined with principles of quantum physics, Coulomb's law helps describe the forces that bind electrons to an atomic nucleus, that bind atoms together into molecules, and that hold together solids and liquids. The law was deduced in 1785 by C. A. de Coulomb

**Coulomb, Charles Augustin de**

, 1736–1806, French physicist. In 1789 he retired from his posts as military engineer and as superintendent of waters and fountains and devoted himself to continuing his scientific research.

**.....**Click the link for more information. from experimental measures of the forces between charged bodies; the experiments were made using his torsion balance.

## Coulomb's law

For electrostatics, Coulomb's law states that the direct force *F* of point charge *q*_{1} on point charge *q*_{2}, when the charges are separated by a distance *r*, is given by *F* = *k*_{0}*q*_{1}*q*_{2}/*r*^{2}, where *k*_{0} is a constant of proportionality whose value depends on the units used for measuring *F*, *q*, and *r*. It is the basic quantitative law of electrostatics. In the rationalized meter-kilogram-second (mks) system of units, *k*_{0} = 1/(4 πε_{0}), where ε_{0} is called the permittivity of empty space and has the value 8.85 × 10^{-12} farad/m. Thus, Coulomb's law in the rationalized mks system is as in the equation below,

*q*

_{1}and

*q*

_{2}are expressed in coulombs,

*r*is expressed in meters, and

*F*is given in newtons.

*See*Electrical units and standards

The direction of *F* is along the line of centers of the point charges *q*_{1} and *q*_{2}, and is one of attraction if the charges are opposite in sign and one of repulsion if the charges have the same sign. For a statement of Coulomb's law as applied to point magnet poles.

Experiments have shown that the exponent of *r* in the equation is very accurately the number 2. Lord Rutherford's experiments, in which he scattered alpha particles by atomic nuclei, showed that the equation is valid for charged particles of nuclear dimensions down to separations of about 10^{-12} cm. Nuclear experiments have shown that the forces between charged particles do not obey the equation for separations smaller than this. *See* Electrostatics

## Coulomb's Law

one of the fundamental laws of electrostatics; determines the force of interaction between two point electric charges at rest—that is, between two electrically charged bodies whose dimensions are small compared with the distance between them. It was established experimentally in 1785 by C. Coulomb using the torsion balance, which he invented.

According to Coulomb's law, two point charges interact with each other in a vacuum with a force *F* whose magnitude is proportional to the product of the charges *e*_{1} and *e*_{2} and inversely proportional to the square of the distance *r* between them:

Here *k* is a proportionality factor that depends on the system of units chosen: in the absolute (Gaussian) system of units (the cgs system), *k =* 1; in the International System of Units (SI), *k =* l/47T€o, where eo is the electric constant. The force *F* is directed along a straight line connecting the charges and is attractive for unlike charges *(F* < 0) and repulsive for like charges *(F* > 0).

If the interacting charges are situated in a homogeneous di-electric with dielectric constant €, the force of interaction is then reduced by a factor of ∊:

Coulomb's law is one of the experimental foundations of classical electrodynamics; its generalization leads, among other things, to Gauss' theorem.

The law that defines the force of interaction between two magnetic poles is also called Coulomb's law:

Here *f* is a proportionality factor (in the general case it does not coincide with *k* in the absolute system of units *f* = 1), m^{1} and *m*_{2} are magnetic charges, and JLI is the magnetic permeability of the medium that surrounds the interacting poles. In a vacuum *F = fm _{1}m_{2}/r^{2}.*

### REFERENCE

Tamm, I. E.*Osnovy teorii elektrichestva,*7th ed. Moscow, 1957. Chapter

1, sec. 21; ch. 2, sec. 23.

G. V. VOSKRESENSKII