Coulomb constant


Value of Units
N·m2/C2
14.3996eV·Å·e−2
10−7c2

The Coulomb constant, the electric force constant, or the electrostatic constant is a proportionality constant in electrostatics equations. In SI units it is equal to. It was named after the French physicist Charles-Augustin de Coulomb who introduced Coulomb's law.

Value of the constant

The Coulomb constant is the constant of proportionality in Coulomb's law,
where is a unit vector in the -direction. In SI:
where is the vacuum permittivity. This formula can be derived from Gauss' law,
Taking this integral for a sphere, radius, centred 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,
In some modern systems of units, the Coulomb constant has an exact numeric value; in Gaussian units, in Lorentz–Heaviside units . This was previously true in SI when the vacuum permeability was defined as. Together with the speed of light in vacuum, defined as, the vacuum permittivity can be written as, which gave an exact value of
Since the redefinition of SI base units, the Coulomb constant is no longer exactly defined and is subject to the measurement error in the fine structure constant, 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:
Electric potential energy:
Electric field: