The Coulomb constant, the electric force constant, or the electrostatic constant (denoted , or ) is a
proportionality constant in
electrostatics equations. In SI base units it is equal to .
[Derived from ''k''e = 1/(4''πε''0) – ] It was named after the French physicist
Charles-Augustin de Coulomb
Charles-Augustin de Coulomb (; ; 14 June 1736 – 23 August 1806) was a French officer, engineer, and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attra ...
(1736–1806) who introduced
Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
.
Value of the constant
The Coulomb constant is the constant of proportionality in
Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
,
:
where is a unit vector in the -direction.
In
SI:
:
where
is the
vacuum permittivity. This formula can be derived from
Gauss' law
In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...
,
:
Taking this integral for a sphere, radius , centered on a point charge, the electric field points radially outwards and is normal to a differential
surface element on the sphere with constant magnitude for all points on the sphere.
:
Noting that for some test charge ,
:
Coulomb's law is an
inverse-square law, and thereby similar to many other scientific laws ranging from gravitational pull to light attenuation. This law states that a specified physical quantity is inversely proportional to the square of the distance.
In some modern systems of units, the Coulomb constant has an exact numeric value; in
Gaussian units
Gaussian units constitute a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs uni ...
, in
Heaviside–Lorentz units
Heaviside–Lorentz units (or Lorentz–Heaviside units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that th ...
(also called ''rationalized'') . This was previously true in
SI when the
vacuum permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
was defined as . Together with the
speed of light in vacuum
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit f ...
, defined as , the
vacuum permittivity can be written as , which gave an exact value of
:
Since the
redefinition of
SI base units,
[ The day is the 144th anniversary of the ]Metre Convention
The Metre Convention (french: link=no, Convention du Mètre), also known as the Treaty of the Metre, is an international treaty that was signed in Paris on 20 May 1875 by representatives of 17 nations (Argentina, Austria-Hungary, Belgium, Brazi ...
. the Coulomb constant is no longer exactly defined and is subject to the measurement error in the
fine structure constant
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by (the Greek letter ''alpha''), is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between ele ...
, as calculated from
CODATA 2018 recommended values being
:
Use
The Coulomb constant is used in many electric equations, although it is sometimes expressed as the following product of the
vacuum permittivity constant:
:
The Coulomb constant appears in many expressions including the following:
;
Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
:
;
Electric potential energy
:
;
Electric field
:
See also
*
Gravitational constant
*
Vacuum permittivity
*
Vacuum permeability
The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...
*
Inverse-square law
References
{{Scientists whose names are used in physical constants
Electricity
Electromagnetism
Physical constants