Coulomb's constant, the electric force constant, or the electrostatic constant (denoted Template:SubSup) is a proportionality constant in equations relating electric variables and is exactly equal to Template:SubSup = Template:GapsTemplate:E N·m2/C2 (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 Template:SubSup comes from three of the fundamental, invariant quantities that define free space in the SI system: the speed of light Template:SubSup, magnetic permeability Template:SubSup, and electric permittivity Template:SubSup, related by Maxwell as:
Because of the way the SI base unit system made the natural units for electromagnetism, the speed of light in vacuum Template:SubSup is Template:Gaps, the magnetic permeability Template:SubSup of free space is 4π·10−7 H m−1, and the electric permittivity Template:SubSup of free space is 1 Template:Frac (Template:SubSupTemplate:SubSup) ≈ Template:Gaps, so that
Use of Coulomb's constant
Coulomb's constant is used in many electric equations, although it is sometimes expressed as the following product of the vacuum permittivity constant:
Some examples of use of Coulomb's constant are the following: