Value of k | Units |
---|---|
8.9875517923(14)×10^{9} | N·m^{2}/C^{2} |
14.3996 | eV·Å·e^{−2} |
10^{−7} | (N·s^{2}/C^{2})c^{2} |
The Coulomb constant, the electric force constant, or the electrostatic constant (denoted k_{e}, k or K) is a proportionality constant in electrostatics equations. In SI base units it is equal to 8.9875517923(14)×10^{9} kg⋅m^{3}⋅s^{−4}⋅A^{−2}.^{[1]} It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.^{[2]}^{[3]}
The Coulomb constant is the constant of proportionality in Coulomb's law,
where ê_{r} is a unit vector in the r-direction.^{[4]} In SI:
where is the vacuum permittivity. This formula can be derived from Gauss' law,
Taking this integral for a sphere, radius r, 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 E = F/q for some test charge q,
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.
Since the redefinition of SI base units,^{[6]}^{[7]} 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^{[1]}
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:
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