Electric constant: Difference between revisions
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The '''electric constant''' (also: ''vacuum permittivity''), designated ε<sub>0</sub>, 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: | The '''electric constant''' (also: ''vacuum permittivity'' or ''permittivity of free space''), designated ε<sub>0</sub>, is a [[physical constant]], an electromagnetic property of [[classical vacuum]], appearing in equations relating [[electrical charge]] to mechanical quantities in the [[International System of Units|SI system of units]], for example in [[Coulomb's law]]. In scalar form, Coulomb's law can be given as: | ||
:<math> F = \frac{1}{4 \pi \varepsilon_0} \ \frac{| | :<math> F = \frac{1}{4 \pi \varepsilon_0} \ \frac{\left |q_1 q_2 \right|}{r^2} </math>, | ||
where ''F'' is the magnitude of the force between two point charges ''q'' and '' | where ''F'' is the magnitude of the force between two point charges ''q<sub>1</sub>'' and ''q<sub>2</sub>'', separated by a distance ''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 (electromagnetism)|free space]]. | ||
Its value is given by | Its value is given by | ||
:<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> | :<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> | ||
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. | ||
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== | ||
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==Footnotes== | ==Footnotes== | ||
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Latest revision as of 19:28, 14 October 2021
The electric constant (also: vacuum permittivity or permittivity of free space), designated ε0, 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 q1 and q2, separated by a distance 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 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:
- ;[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 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.