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 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,

\oiint

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.

\oiint

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 ms−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
0
 
) 8.85418782×10^−12 F m−1
,[1] so that[2]

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:

.

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

Coulomb's law:

.

Electric potential energy:

.

Electric field:

.

See also

References

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