# Electric constant

The electric constant (also: vacuum permittivity), designated ε0, is a physical constant appearing in equations relating electrical charge to mechanical quantities, for example in Coulomb's law. In scalar form, Coulomb's law can be given as:

$F = \frac{1}{4 \pi \varepsilon_0} \ \frac{|q| |Q|}{r^2}$,

where F is the magnitude of the force between two point charges q and Q, separated by a distance r.

Its value is given by

$\varepsilon_0 = \frac{1}{\mu_0 c^2}$,

where c is the speed of light in vacuum and μ0 is the magnetic constant. In the SI system of units, c is defined and μ0 is a consequence of the definition of the ampere: μ0 = 4π × 10−7 N/A2. Consequently, ε0 is exact and expressed up to ten digits by:

$\varepsilon_0 = \frac{10^7}{4\pi\,c^2} = 8.854\;187\;817... 10^{-12}$ F / m;[1]
$\frac{1}{4 \pi \varepsilon_0} = 8.987\ 551\ 787... 10^9$ N m²/C².

## Terminology

Historically, the physical constant ε0 has had different names. One of these was dielectric constant of vacuum.[2] Although still in use,[3] "dielectric constant" is now deemed obsolete.[4][5] In the 1987 IUPAP Red book this constant was called permittivity of vacuum.[6] Currently the nomenclature is electric constant.[1][7] The vacuum permittivity ε = εr ε0 is equal to the electric constant ε0.

## Footnotes

1. 1.0 1.1 CODATA. Electric constant. 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
2. King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover, p. 139.
3. for example in this random patent
4. IEEE Standards Board (1997). IEEE Standard Definitions of Terms for Radio Wave Propagation p. 6.
5. Braslavsky, S.E. (2007), "Glossary of terms used in photochemistry (IUPAC recommendations 2006)", Pure and Applied Chemistry 79: p. 324.
6. SUNAMCO Commission (1987), Recommended values of the fundamental physical constants, Symbols, Units, Nomenclature and Fundamental Constants in Physics, at p.54; (the IUPAP "Red book").
7. National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.