Electric constant: Difference between revisions
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:<math>\varepsilon_0 = \frac{1}{\mu_0 c^2}</math>, | :<math>\varepsilon_0 = \frac{1}{\mu_0 c^2}</math>, | ||
where ''c'' is the [[speed of light|speed of light in vacuum]] and ''μ''<sub>0</sub> is the [[magnetic constant]]. In the [[SI]] system of units, ''c'' is defined and ''μ''<sub>0</sub> is a consequence of the definition of the [[ampere]]: μ<sub>0</sub> = 4π × 10<sup>−7</sup> N/A<sup>2</sup>. | where ''c'' is the [[speed of light|speed of light in vacuum]] and ''μ''<sub>0</sub> is the [[magnetic constant]]. In the [[SI]] system of units, ''c'' is defined and ''μ''<sub>0</sub> is a consequence of the definition of the [[ampere]]: μ<sub>0</sub> = 4π × 10<sup>−7</sup> N/A<sup>2</sup>. | ||
Consequently, ε<sub>0</sub> | Consequently, ε<sub>0</sub> has an exact value and to ten digits is expressed by: | ||
:<math>\varepsilon_0 = \frac{10^7}{4\pi\,c^2} = 8.854\;187\;817... 10^{-12}</math> [[farad|F]] / [[metre|m]];<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}{4\pi\,c^2} = 8.854\;187\;817... 10^{-12}</math> [[farad|F]] / [[metre|m]];<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>\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. | ||
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== | ==Terminology== | ||
Revision as of 16:47, 8 March 2011
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:
- ,
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
- ,
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 has an exact value and to ten digits is expressed by:
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 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
- ↑ 1.0 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.