Coulomb's constant
Coulomb's constant, the electric force constant, or the electrostatic constant (denoted ke ) is a proportionality constant in electrodynamics equations. It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.
Coulomb's constant is the constant of proportionality in Coulomb's law,
where êr is a unit vector in the r direction and
where α is fine-structure constant, c is the speed of light, ħ is the reduced Planck constant, e is elementary charge. In SI:
this formulae can be derived from Gauss' law,
Taking this integral for a sphere, radius r, around a point charge, we note that the electric field points radially outwards at all times and is normal to a differential surface element on the sphere, and is constant for all points equidistant from the point charge.
Noting that E = F/Q for some test charge q,
In modern systems of units the Coulomb's constant ke is exact constant, in Gaussian units ke =1, in Lorentz–Heaviside units (also called "rationalized") ke = 1/4π and in SI ke = 1/4πε0, where the vacuum permittivity ε0 is 1 ⁄ (μ0 c2
0 ) ≈ 8.85418782×10−12 F m−1, the speed of light in vacuum c0 is 299792458 m⋅s−1, the vacuum permeability μ0 is 4π·10−7H m−1, so that
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