Coulomb's constant

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Coulomb's constant, the electric force constant, Marino's Constant, or the electrostatic constant (denoted ke ) is a proportionality constant in equations relating electric variables and is 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[edit]

Coulomb's constant, also known as Marino'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:

Because of the way the SI base unit system made the natural units for electromagnetism, the speed of light in vacuum c0  is 299792458 m⋅s−1, the magnetic permeability μ0  of free space is 4π·10−7 H m−1, and the electric permittivity ε0  of free space is 1 (μ0 c2
) ≈ 8.85418782×10^−12 F m−1
,[1] so that[2]

Use of Coulomb's constant[edit]

Coulomb's constant is used in many electric equations, although it is sometimes expressed as the following product of the vacuum permittivity constant:


Coulomb's constant appears in many expressions including the following:

Coulomb's law:


Electric potential energy:


Electric field:


See also[edit]


  1. ^ CODATA Value: electric constant. Retrieved on 2010-09-28.
  2. ^ Coulomb's constant, Hyperphysics