Coulomb's constant
Coulomb's constant, the electric force constant, or the electrostatic constant (denoted ke ) is a proportionality constant in equations relating electric variables and is exactly equal to ke = 8.9875517873681764×109 N·m2/C2 (i.e. m/F). It was named after the French physicist Charles-Augustin de Coulomb (1736–1806) who first used it in Coulomb's law.
Value of the constant
Coulomb's constant can be empirically derived as the constant of proportionality in Coulomb's law,
where êr is a unit vector in the r direction. However, its theoretical value 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,
This exact value of Coulomb's constant ke comes from three of the fundamental, invariant quantities that define free space in the SI system: the speed of light c0 , magnetic permeability μ0 , and electric permittivity ε0 , related by Maxwell as:
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