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| {{about|the electric constant|the analogous magnetic constant|vacuum permeability|the ordinal number ε<sub>0</sub>|epsilon numbers (mathematics)}}
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| The [[physical constant]] ''ε''<sub>0</sub>, commonly called the '''vacuum permittivity''', '''permittivity of free space''' or '''electric constant''', is an ideal, (baseline) physical constant, which is the value of the absolute (''not'' relative) [[dielectric permittivity]] of [[classical vacuum]]. Its value is:
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| :ε<sub>0</sub> = 8.854 187 817... x 10<sup>−12</sup> <math> \left[\frac{F}{m}\right] </math> ([[farad]]s per [[meter]]).
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| This constant relates the units for [[electric charge]] to mechanical quantities such as length and force.<ref>{{Cite journal | contribution = electric constant | title = Electropedia: International Electrotechnical Vocabulary (IEC 60050) | publisher = International Electrotechnical Commission | location = Geneva | url = http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-03 | accessdate = 2010-04-02 | postscript = <!--None-->}}.</ref> For example, the force between two separated electric charges (in the [[Vacuum#Electromagnetism|vacuum of classical electromagnetism]]) is given by [[Coulomb's law]]:
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| :<math>\ F_C = \frac{1} {4 \pi \varepsilon_0} \frac{q_1 q_2} {r^2}</math>
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| where ''q''<sub>1</sub> and ''q''<sub>2</sub> are the charges, and ''r'' is the distance between them. Likewise, ''ε''<sub>0</sub> appears in [[Maxwell's equations]], which describe the properties of [[Electric field|electric]] and [[Magnetic field|magnetic]] fields and [[electromagnetic radiation]], and relate them to their sources.
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| ==Value==
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| The value of ''ε''<sub>0</sub> is currently ''defined'' by the formula<ref name=ep0>
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| The exact numerical value is found at:
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| {{cite web |title=Electric constant, ε<sub>0</sub> |work=NIST reference on constants, units, and uncertainty: Fundamental physical constants |url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0 |publisher=NIST |accessdate=2012-01-22}} This formula determining the exact value of ''ε''<sub>0</sub> is found in Table 1, p. 637 of {{cite journal |title=<u>Table 1: Some exact quantities relevant to the 2006 adjustment</u>'' in ''CODATA recommended values of the fundamental physical constants: 2006 |url=http://physics.nist.gov/cuu/Constants/RevModPhys_80_000633acc.pdf |journal =Rev Mod Phys |pages=633–729 |volume=80 |date=April–June 2008 |issue=2 |author=PJ Mohr, BN Taylor, DB Newell|bibcode = 2008RvMP...80..633M |doi = 10.1103/RevModPhys.80.633 |arxiv = 0801.0028 }}
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| </ref>
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| :<math> \varepsilon_0 =\frac {1}{\mu_0 c^2}</math>
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| where ''c'' is the defined value for the [[speed of light]] in [[classical vacuum]] in [[SI units]],<ref>
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| Quote from NIST: "The symbol ''c'' is the conventional symbol for the speed of light in vacuum. " See [http://physics.nist.gov/Pubs/SP330/sp330.pdf NIST ''Special Publication 330'', p. 18 ]
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| </ref> and ''μ''<sub>0</sub> is the parameter that international Standards Organizations call the "[[magnetic constant]]" (commonly called vacuum permeability). Since ''μ''<sub>0</sub> has the ''defined'' value 4π × 10<sup>−7</sup> H m<sup>−1</sup>,<ref>See the last sentence of the [http://physics.nist.gov/cuu/Units/ampere.html NIST definition of ampere].</ref> and ''c'' has the ''defined'' value {{gaps|299|792|458}} m·s<sup>−1</sup>,<ref>See the last sentence of the [http://physics.nist.gov/cuu/Units/meter.html NIST definition of meter].</ref> it follows that ''ε''<sub>0</sub> has a ''defined'' value given approximately by
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| :''ε''<sub>0</sub> ≈ {{gaps|8.854|187|817|620}}... × 10<sup>−12</sup> [[Farad|F]]·m<sup>−1</sup> (or [[Ampere|A]]<sup>2</sup>·[[second|s]]<sup>4</sup>·[[kilogram|kg]]<sup>−1</sup>·m<sup>−3</sup> in [[SI base unit]]s, or [[Coulomb|C]]<sup>2</sup>·[[Newton (unit)|N]]<sup>−1</sup>·m<sup>−2</sup> or [[Coulomb|C]]·[[Volt|V]]<sup>−1</sup>·m<sup>−1</sup> using other SI coherent units).<ref name="CODATA">{{CODATA2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0}}.</ref><ref>A summary of the definitions of ''c'', ''μ''<sub>0</sub> and ''ε''<sub>0</sub> is provided in the 2006 CODATA Report: [http://physics.nist.gov/cuu/Constants/codata.pdf CODATA report, pp. 6-7]</ref>
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| The historical origins of the electric constant ''ε''<sub>0</sub>, and its value, are explained in more detail below.
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| ===Redefinition of the SI units===
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| {{main|New SI definitions}}
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| Under the proposals to redefine the [[ampere]] as a fixed number of [[elementary charge]]s per second,<ref>
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| {{Cite journal |contribution = Resolution 1 of 24th meeting of the General Conference on Weights and Measures |title = On the possible future revision of the International System of Units, the SI | url = http://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf | publisher = International Bureau for Weights and Measures |location = Sèvres, France |date=21 Oct 2011}} It is not expected to be adopted until some prerequisite conditions are met, and in any case not before 2014. See {{cite journal |title=Possible changes to the international system of units |journal=IUPAC Wire |volume=34 |issue=1 |date=January–February 2012 |publisher=[[International Union of Pure and Applied Chemistry]] |url=http://www.iupac.org/publications/ci/2012/3401/iw4_si.html}}
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| </ref> the electric constant would no longer have an exact fixed value. The value of the electron charge would become a defined number, not measured, making μ<sub>0</sub> a measured quantity. Consequently, ε<sub>0</sub> also would not be exact. As before, it would be defined by the equation ε<sub>0</sub>= 1/(μ<sub>0</sub>c<sup>2</sup>), but now with a measurement error related to the error related to that in μ<sub>0</sub>, the [[magnetic constant]]. This measurement error can be related to that in the [[fine-structure constant]] α:
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| :<math> \varepsilon_0 = \frac {1}{\mu_0 c^2} = \frac {e^2}{2\alpha h c}\ ,</math>
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| with ''e'' the exact [[elementary charge]], ''h'' the exact [[Planck constant]], and ''c'' the exact [[speed of light]] in [[Vacuum#In electromagnetism|vacuum]]. Here use is made of the relation for the fine-structure constant:
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| :<math>\alpha=\frac {\mu_0 c e^2}{2 h } \ . </math>
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| The relative uncertainty in the value of ε<sub>0</sub> therefore would be the same as that for the fine-structure constant, currently 6.8{{e|−10}}.<ref name="CODATA"/>
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| ==Terminology==
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| Historically, the parameter ''ε''<sub>0</sub> has been known by many different names. The terms "vacuum permittivity" or its variants, such as "permittivity in/of vacuum",<ref name=Sze>
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| {{Cite book
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| |author=SM Sze & Ng KK
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| |title=Physics of semiconductor devices
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| |chapter=Appendix E
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| |page=788
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| |edition=Third
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| |year= 2007
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| |publisher=Wiley-Interscience
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| |location=New York
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| |isbn=0-471-14323-5
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| |url=http://worldcat.org/isbn/0-471-14323-5}}
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| </ref><ref name=Muller>
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| {{Cite book
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| |author=RS Muller, Kamins TI & Chan M
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| |title=Device electronics for integrated circuits
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| |page=Inside front cover
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| |edition=Third
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| |year= 2003
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| |publisher=Wiley
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| |location=New York
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| |isbn=0-471-59398-2
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| |url=http://worldcat.org/isbn/0-471-59398-2
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| |nopp=true}}
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| </ref> "permittivity of empty space",<ref name=Zemansky>{{Cite book
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| | author=FW Sears, Zemansky MW & Young HD
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| | title=College physics
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| |url=http://books.google.com/?id=AvVQAAAAMAAJ&q=zemansky+%22permittivity+of+empty+space%22&dq=zemansky+%22permittivity+of+empty+space%22 |publisher=Addison-Wesley |location=Reading, Mass.
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| |year=1985
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| |page=40
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| |isbn=0-201-07836-8}}</ref> or "permittivity of [[free space]]"<ref name="Saleh">B. E. A. Saleh and M. C. Teich, ''Fundamentals of Photonics'' (Wiley, 1991)</ref> are widespread. Standards Organizations worldwide now use "electric constant" as a uniform term for this quantity,<ref name="CODATA"/> and official standards documents have adopted the term (although they continue to list the older terms as synonyms).<ref>{{Cite web|author=[[International Bureau of Weights and Measures]]|url=http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf|title=The International System of Units (SI)|year=2006 |page=12|format=PDF}}</ref><ref name="IUPAC">{{Cite journal|last=Braslavsky |first=S.E. | url=http://www.iupac.org/publications/pac/2007/pdf/7903x0293.pdf |title=Glossary of terms used in photochemistry (IUPAC recommendations 2006) | journal=Pure and Applied Chemistry | volume=79|issue=3 |year=2007 |pages=293–465; see p. 348. |doi=10.1351/pac200779030293 |postscript=<!--None-->}}</ref>
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| Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity.<ref name="Freie Universität Berlin">{{Cite web|title=Naturkonstanten |url=http://www.chemie.fu-berlin.de/chemistry/general/constants.html |publisher=[[Freie Universität Berlin]] }}</ref><ref>{{Cite book
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| | last = King
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| | first = Ronold W. P.
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| | title = Fundamental Electromagnetic Theory
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| | publisher = Dover
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| | year = 1963
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| | location = New York
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| | page = 139}}</ref> However, in modern usage "dielectric constant" typically refers exclusively to a [[relative permittivity]] ''ε''/''ε''<sub>0</sub> and even this usage is considered "obsolete" by some standards bodies in favor of [[relative static permittivity]].<ref name="IUPAC"/><ref>{{Cite web|author=[[IEEE]] Standards Board|url=http://ieeexplore.ieee.org/iel4/5697/15269/00705931.pdf?arnumber=705931|title=IEEE Standard Definitions of Terms for Radio Wave Propagation|year=1997 |page=6}}</ref> Hence, the term "dielectric constant of vacuum" for the electric constant ''ε''<sub>0</sub> is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.
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| As for notation, the constant can be denoted by either <math>\varepsilon_0\,</math> or <math>\epsilon_0\,</math>, using either of the common [[glyph]]s for the letter [[epsilon]].
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| ==Historical origin of the parameter ''ε''<sub>0</sub>==
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| As indicated above, the parameter ''ε''<sub>0</sub> is a measurement-system constant. Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below. But the method of allocating a value to it is a consequence of the result that Maxwell's equations predict that, in free space, electromagnetic waves move with the speed of light. Understanding why ''ε''<sub>0</sub> has the value it does requires a brief understanding of the history.
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| ===Rationalization of units===
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| The experiments of [[Charles-Augustin de Coulomb|Coulomb]] and others showed that the force ''F'' between two equal point-like "amounts" of electricity, situated a distance ''r'' apart in free space, should be given by a formula that has the form
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| :<math> F = \; k_{\mathrm{e}} \frac{Q^2}{r^2}, </math>
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| where ''Q'' is a quantity that represents the amount of electricity present at each of the two points, and ''k''<sub>e</sub> is [[Coulomb's constant]]. If one is starting with no constraints, then the value of ''k''<sub>e</sub> may be chosen arbitrarily.<ref name=Jackson>For an introduction to the subject of choices for independent units, see
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| {{Cite book
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| |author=John David Jackson
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| |title=Classical electrodynamics
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| |edition=Third
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| |chapter=Appendix on units and dimensions
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| |pages=775 ''et seq.''.
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| |publisher= Wiley
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| |location=New York
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| |year=1999
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| |isbn=0-471-30932-X
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| |url=http://worldcat.org/isbn/047130932X}}
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| </ref> For each different choice of ''k''<sub>e</sub> there is a different "interpretation" of ''Q'': to avoid confusion, each different "interpretation" has to be allocated a distinctive name and symbol.
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| In one of the systems of equations and units agreed in the late 19th century, called the "centimetre-gram-second electrostatic system of units" (the cgs esu system), the constant ''k''<sub>e</sub> was taken equal to 1, and a quantity now called "[[Gaussian units#Unit of charge|gaussian electric charge]]" ''q''<sub>s</sub> was defined by the resulting equation
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| :<math> F = \frac{{q_{\text{s}}}^2}{r^2}. </math>
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| The unit of gaussian charge, the [[statcoulomb]], is such that two units, a distance of 1 centimetre apart, repel each other with a force equal to the cgs unit of force, the [[dyne]]. Thus the unit of gaussian charge can also be written 1 dyne<sup>1/2</sup> cm. "Gaussian electric charge" is not the same mathematical quantity as modern (rmks) electric charge and is not measured in coulombs.
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| The idea subsequently developed that it would be better, in situations of spherical geometry, to include a factor 4π in equations like Coulomb's law, and write it in the form:
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| :<math> F = \; k'_{\mathrm{e}} \frac{{q'_{\text{s}}}^2}{4 \pi r^2}. </math>
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| This idea is called "rationalization". The quantities ''q''<sub>s</sub>' and ''k''<sub>e</sub>' are not the same as those in the older convention. Putting ''k''<sub>e</sub>'=1 generates a unit of electricity of different size, but it still has the same dimensions as the cgs esu system.
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| The next step was to treat the quantity representing "amount of electricity" as a fundamental quantity in its own right, denoted by the symbol ''q'', and to write Coulomb's Law in its modern form:
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| :<math>\ F = \frac{1}{4 \pi \varepsilon_0} \frac{q^2}{r^2}. </math>
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| The system of equations thus generated is known as the rationalized metre-kilogram-second (rmks) equation system, or "metre-kilogram-second-ampere (mksa)" equation system. This is the system used to define the SI units.<ref>{{Cite web|author=[[International Bureau of Weights and Measures]]|url=http://www.bipm.org/en/si/si_brochure/chapter1/1-2.html|title=The International System of Units (SI) and the corresponding system of quantities}}</ref> | |
| The new quantity ''q'' is given the name "rmks electric charge", or (nowadays) just "electric charge". Clearly, the quantity ''q''<sub>s</sub> used in the old cgs esu system is related to the new quantity ''q'' by
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| :<math>\ q_{\text{s}} = \frac{q}{\sqrt{4 \pi \varepsilon_0}}.</math>
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| ===Determination of a value for ''ε''<sub>0</sub>===
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| One now adds the requirement that one wants force to be measured in newtons, distance in metres, and charge to be measured in the engineers' practical unit, the coulomb, which is defined as the charge accumulated when a current of 1 ampere flows for one second. This shows that the parameter ''ε''<sub>0</sub> should be allocated the unit
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| C<sup>2</sup>·N<sup>−1</sup>·m<sup>−2</sup> (or equivalent units - in practice "farads per metre").
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| In order to establish the numerical value of ''ε''<sub>0</sub>, one makes use of the fact that if one uses the rationalized forms of Coulomb's law and [[Ampère's force law]] (and other ideas) to develop [[Maxwell's equations]], then the relationship stated above is found to exist between ''ε''<sub>0</sub>, ''μ''<sub>0</sub> and ''c''<sub>0</sub>. In principle, one has a choice of deciding whether to make the coulomb or the ampere the fundamental unit of electricity and magnetism. The decision was taken internationally to use the ampere. This means that the value of ''ε''<sub>0</sub> is determined by the values of ''c''<sub>0</sub> and ''μ''<sub>0</sub>, as stated above. For a brief explanation of how the value of ''μ''<sub>0</sub> is decided, see the article about [[vacuum permeability|''μ''<sub>0</sub>]].
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| ==Permittivity of real media==
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| By convention, the electric constant ''ε''<sub>0</sub> appears in the relationship that defines the [[electric displacement field]] '''D''' in terms of the [[electric field]] '''E''' and classical electrical [[polarization density]] '''P''' of the medium. In general, this relationship has the form:
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| :<math>\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P}</math>.
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| For a linear dielectric, '''P''' is assumed to be proportional to '''E''', but a delayed response is permitted and a spatially non-local response, so one has:<ref name=Sólyom>
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| {{cite book |title=Fundamentals of the physics of solids: Electronic properties |author=Jenö Sólyom |url=http://books.google.com/books?id=XSo-a2n43xEC&pg=PA17 |page=17 |chapter=Equation 16.1.50 |isbn=3-540-85315-4 |year=2008 |publisher=Springer}}
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| </ref>
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| :<math>\mathbf D (\mathbf r , \ t) = \int_{-\infty}^t dt' \int d^3\mathbf r' \ \varepsilon (\mathbf r, \ t ; \mathbf r' ,\ t') \mathbf E(\mathbf r', \ t') \ . </math>
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| In the event that nonlocality and delay of response are not important, the result is:
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| :<math>\mathbf{D} = \varepsilon \mathbf{E} = \varepsilon_{\text{r}} \varepsilon_0 \mathbf{E}</math>
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| where ''ε'' is the [[permittivity]] and ''ε''<sub>r</sub> the [[relative static permittivity]]. In the [[Vacuum#In electromagnetism|vacuum of classical electromagnetism]], the polarization '''P''' = '''0''', so ''ε''<sub>r</sub> = 1 and ''ε'' = ''ε''<sub>0</sub>.
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| ==See also==
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| *[[Casimir effect]]
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| *[[Coulomb's law]]
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| *[[Electromagnetic wave equation]]
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| *[[ISO 31-5]]
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| *[[Mathematical descriptions of the electromagnetic field]]
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| *[[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]
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| *[[Wave impedance]]
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| ==Notes==
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| {{reflist|2}}
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| {{Use dmy dates|date=September 2010}}
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| {{DEFAULTSORT:Vacuum Permittivity}}
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| [[Category:Electromagnetism]]
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| [[Category:Fundamental constants]]
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| [[ar:سماحية الفراغ]]
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| [[ca:Permitivitat del buit]]
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| [[el:Διηλεκτρική σταθερά]]
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| [[fr:Constante électrique]]
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| [[he:מקדם דיאלקטרי#מקדם דיאלקטרי של הריק]]
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| [[pl:Przenikalność elektryczna]]
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| [[uk:Електрична константа]]
| |
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HONG LEONG HOLDINGS RESTRICTED (HLH) was established in 1968 as the group's privately held property investment and property holding automobile. It has developed about 40 residential properties to date and markets/manages 12 business projects. The data includes both residential and business properties. But the common value of the purchases apartment For sale China is the bottom of all the nations, which suggests numerous the deals are for residential property. Valuation payment for the security property (charges will differ depending on property kind) The remainder of the inhabitants live in private housing, akin to apartments, condominiums and landed properties. Components that determine Singapore's property market A Look Again on 2011 and Looking Ahead to 2012 (at Propwise.sg)