# Difference between revisions of "Electric constant"

Mark Widmer (Talk | contribs) (Added description as "permittivity of free space." Adjusted defining equation to include units properly.) |
Mark Widmer (Talk | contribs) (Added explanation of why constant is given in terms of 1/(4*pi*epsilon-naught)) |
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:<math>\varepsilon_0 = \frac{10^7\mbox{ A}^2 \mbox{/N}}{4\pi\,c^2} = 8.854\;187\;817... 10^{-12} \mbox{ F/m}</math> ;<ref name="NIST">{{cite web |url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0 |title=Electric constant |accessdate=2007-08-08 |author=[[CODATA]] |work=2006 CODATA recommended values |publisher=[[NIST]] }}</ref> | :<math>\varepsilon_0 = \frac{10^7\mbox{ A}^2 \mbox{/N}}{4\pi\,c^2} = 8.854\;187\;817... 10^{-12} \mbox{ F/m}</math> ;<ref name="NIST">{{cite web |url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0 |title=Electric constant |accessdate=2007-08-08 |author=[[CODATA]] |work=2006 CODATA recommended values |publisher=[[NIST]] }}</ref> | ||

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+ | Alternatively, the electric constant is sometimes given in the form of the constant factor that appears in Coulomb's law, | ||

:<math>\frac{1}{4 \pi \varepsilon_0} = 8.987\ 551\ 787... 10^9 </math> [[newton|N]] [[meter|m]]²/[[coulomb|C]]². | :<math>\frac{1}{4 \pi \varepsilon_0} = 8.987\ 551\ 787... 10^9 </math> [[newton|N]] [[meter|m]]²/[[coulomb|C]]². |

## Latest revision as of 00:28, 15 October 2021

The **electric constant** (also: *vacuum permittivity* or *permittivity of free space*), designated ε_{0}, is a physical constant, an electromagnetic property of classical vacuum, appearing in equations relating electrical charge to mechanical quantities in the SI system of units, for example in Coulomb's law. In scalar form, Coulomb's law can be given as:

- ,

where *F* is the magnitude of the force between two point charges *q _{1}* and

*q*, separated by a distance

_{2}*r*and located in an idealized medium sometimes called simply "vacuum" (although it is not intended to imply that this ideal medium is in fact physically realizable as some real "vacuum") and sometimes called free space.

Its value is given by

- ,

where *c* is the speed of light in vacuum and *μ*_{0} is the magnetic constant. In the SI system of units, *c* is defined and *μ*_{0} is a consequence of the definition of the ampere: μ_{0} = 4π × 10^{−7} N/A^{2}.
Consequently, ε_{0} has an exact value and to ten digits is expressed by:

- ;
^{[1]}

Alternatively, the electric constant is sometimes given in the form of the constant factor that appears in Coulomb's law,

The uncertainty denoted by dots after the last digits is not related to some experimental uncertainty, but is a consequence of the impossibility of expressing an irrational number with a finite number of decimal figures. Despite the sometimes used name of "vacuum permittivity", this *defined* value cannot be interpreted as a *measured property* of any real medium that one might refer to as a "vacuum".

## Terminology

Historically, the physical constant ε_{0} 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 = ε_{r} ε_{0} is equal to the electric constant ε_{0}.

## Footnotes

- ↑
^{1.0}^{1.1}CODATA. Electric constant.*2006 CODATA recommended values*. NIST. Retrieved on 2007-08-08. - ↑ King, Ronold W. P. (1963).
*Fundamental Electromagnetic Theory*. New York: Dover, p. 139. - ↑ for example in this random patent
- ↑ IEEE Standards Board (1997). IEEE Standard Definitions of Terms for Radio Wave Propagation p. 6.
- ↑ Braslavsky, S.E. (2007), "Glossary of terms used in photochemistry (IUPAC recommendations 2006)",
*Pure and Applied Chemistry***79**: p. 324. - ↑ 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"). - ↑ National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.