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The Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrodynamics equations. In SI units, it is equal to approximately 8987551787.3681764 N·m2·C−2 or 8.99×109 N·m2·C−2. It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who introduced Coulomb's law.
Value of the constantEdit
The Coulomb constant is the constant of proportionality in Coulomb's law,
where êr is a unit vector in the r-direction and
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/ for some test charge q,
In modern systems of units, the Coulomb constant ke has an exact numeric value, in Gaussian units ke = 1, in Lorentz–Heaviside units (also called rationalized) ke = 1/ and in SI ke = 1/, where the vacuum permittivity ε0 = 1/ ≈ 8.85418782×10−12 F⋅m−1, the speed of light in vacuum c is 299792458 m/s, the vacuum permeability μ0 is 4π×10−7 H⋅m−1, so that
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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