Coulomb Constant

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## Value of the constant

## Use

## See also

## References

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

Coulomb Constant

The **Coulomb constant**, the **electric force constant**, or the **electrostatic constant** (denoted *k*_{e}, *k* or *K*) is a proportionality constant in electrostatics equations. In SI units it is equal to .^{[1]} It was named after the French physicist Charles-Augustin de Coulomb (1736-1806) who introduced Coulomb's law.

The Coulomb constant is the constant of proportionality in Coulomb's law,

where **ê**_{r} is a unit vector in the **r**-direction.^{[2]} In SI:

where is the vacuum permittivity. This formula can be derived from Gauss' law,

Taking this integral for a sphere, radius **r**, centered on a point charge, the electric field points radially outwards and is normal to a differential surface element on the sphere with constant magnitude for all points on the sphere.

Noting that **E** = for some test charge *q*,

Also note that this is an Inverse Square Law, and thereby similar to many other scientific laws ranging from gravitational pull to light attenuation. This law states that a specified physical quantity is inversely proportional to the square of the distance.

In some modern systems of units, the Coulomb constant *k*_{e} has an exact numeric value; in Gaussian units *k*_{e} = 1, in Lorentz-Heaviside units (also called *rationalized*) *k*_{e} = . This was previously true in SI when the vacuum permeability was defined as *?*_{0} = H?m^{-1}. Together with the speed of light in vacuum *c*, defined as , the vacuum permittivity *?*_{0} can be written as , which gave an exact value of^{[3]}

Since the redefinition of SI base units,^{[4]}^{[5]} the Coulomb constant is no longer exactly defined and is subject to the measurement error in the fine structure constant, as calculated from CODATA 2018 recommended values being^{[1]}

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:

- ^
^{a}^{b}Derived from*k*_{e}= 1/(4_{0}) - "2018 CODATA Value: vacuum electric permittivity".*The NIST Reference on Constants, Units, and Uncertainty*. NIST. 20 May 2019. Retrieved . Cite has empty unknown parameter:`|month=`

(help) **^**Tomilin, K. (1999). "Fine-structure constant and dimension analysis".*European Journal of Physics*.**20**(5): L39-L40. Bibcode:1999EJPh...20L..39T. doi:10.1088/0143-0807/20/5/404.**^**Coulomb's constant, HyperPhysics**^***BIPM statement: Information for users about the proposed revision of the SI*(PDF)**^**"Decision CIPM/105-13 (October 2016)". The day is the 144th anniversary of the Metre Convention.

This article uses material from the Wikipedia page available here. It is released under the Creative Commons Attribution-Share-Alike License 3.0.

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