Difference between revisions of "Electric constant"
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| − | The '''electric constant''' (symbol: '''''ε''<sub>0</sub>'''), also known as the '''vacuum permittivity''' or the '''permittivity of free space''', is a [[physical constant]] that describes the [[force]] between two [[Electric charge|charged]] bodies in [[vacuum]]. The exact definition (and value) depends on the system of quantities used, but in the [[International System of Quantities]] (ISQ) | + | The '''electric constant''' (symbol: '''''ε''<sub>0</sub>'''), also known as the '''vacuum permittivity''' or the '''permittivity of free space''', is a [[physical constant]] that describes the [[force]] between two [[Electric charge|charged]] bodies in [[vacuum]].<ref>{{electropedia | title = electric constant | id = 121-11-03 | accessdate = 2010-04-02}}.</ref> It also appears in Maxwell's equations, which describe the behaviour of [[electromagnetic wave]]s. The exact definition (and value) depends on the system of quantities used, but in the [[International System of Quantities]] (ISQ) it has a defined value of approximately {{nowrap|8.854 187 816{{e|−12}} F m<sup>−1</sup>}}.<ref name="CODATA">{{CODATA 2006|url=http://physics.nist.gov/cgi-bin/cuu/Value?ep0}}.</ref> |
| − | The electric constant is related to the [[magnetic constant]] ''μ''<sub>0</sub> and the [[speed of light]] ''c''<sub>0</sub> by the equation ''c''{{su|b=0|p=2}} = 1/''ε''<sub>0</sub>''μ''<sub>0</sub>. In [[SI units]], the speed of light is exactly {{nowrap|299 792 458 m s<sup>−1</sup>}} (by the definition of the [[metre]]) and the magnetic constant is exactly {{nowrap|4π{{e|−7}} N A<sup>−1</sup>}} (by the definition of the [[ampere]]): hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal). | + | The electric constant is related to the [[magnetic constant]] ''μ''<sub>0</sub> and the [[speed of light]] ''c''<sub>0</sub> by the equation ''c''{{su|b=0|p=2}} = 1/''ε''<sub>0</sub>''μ''<sub>0</sub>. In [[SI units]], the speed of light is exactly {{nowrap|299 792 458 m s<sup>−1</sup>}} (by the definition of the [[metre]]) and the magnetic constant is exactly {{nowrap|4π{{e|−7}} N A<sup>−1</sup>}} (by the definition of the [[ampere]]):<ref>{{SIbrochure8th|pages=112–13}}.</ref> hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal).<ref name="CODATA"/> |
| + | |||
| + | ==International System of Quantities== | ||
| + | The force between two point charges ''Q''<sub>1</sub> and ''Q''<sub>2</sub> in vacuum is given by [[Coulomb's law]], which, in the ISQ, has the form:<ref group="note">This equation is commonly written to give only the magnitude of the force: the version here stresses that the force acts along the line connecting the two particles.</ref> | ||
| + | :'''''F''''' = ''Q''<sub>1</sub>''Q''<sub>2</sub>'''''r'''''/4π''ε''<sub>0</sub>''r''<sup>3</sup> | ||
| + | where '''''r''''' is the vector between the two point charges. The factor of 4π arises here to avoid it appearing in situations of rectangular symmetry:<ref group="note">See, for example, the definition of the [[ampere]], which developed in a non-rationalized quantity system before being incorporated into the SI.</ref> quantity systems in which Coulomb's law is written in this way are said to be "rationalized".<ref name="GreenBook">{{GreenBook2nd|pages=117–19}}.</ref> | ||
| + | |||
| + | ==CGS system== | ||
| + | The different cgs (centimetre–gram–second) quantity systems are non-rationalized.<ref name="GreenBook"/> | ||
| + | |||
| + | ===Electrostatic units=== | ||
| + | The usual approach to treating the electric constant in electrostatic units (esu) is to define it as unity, without dimensions. Coulomb´s law becomes: | ||
| + | :'''''F''''' = ''Q''<sub>1</sub>''Q''<sub>2</sub>'''''r'''''/''r''<sup>3</sup> | ||
| + | Alternatively, the electrostatic unit of charge can be taken as the [[Franklin]] (also called the [[statcoulomb]]), in which case the electric constant is {{nowrap|1 Fr<sup>2</sup> erg<sup>−1</sup> cm<sup>−1</sup>}}.<ref name="GreenBook"/> | ||
| + | |||
| + | ===Electromagnetic units=== | ||
| + | In electromagnetic units (emu), it is the [[magnetic constant]] which is taken as unity. The electric constant, therefore, has the value 1/''c''{{su|p=2|b=0}}.<ref name="GreenBook"/> | ||
==New SI== | ==New SI== | ||
| − | Under the proposals to redefine the [[ampere]] as a fixed number of [[elementary charge]]s per second,<ref>{{citation | contribution = Recommendation E1 | title = Report of the 25th meeting (15–16 March 2007), Consultative Committee for Electricity and Magnetism (CCEM) | url = http://www.bipm.org/utils/common/pdf/CCEM25.pdf | publisher = | + | Under the proposals to redefine the [[ampere]] as a fixed number of [[elementary charge]]s per second,<ref>{{citation | contribution = Recommendation E1 | title = Report of the 25th meeting (15–16 March 2007), Consultative Committee for Electricity and Magnetism (CCEM) | url = http://www.bipm.org/utils/common/pdf/CCEM25.pdf | publisher = International Bureau for Weights and Measures | location = Sèvres, France}}.</ref> the electric constant would no longer have an exact fixed value. Instead, it would be defined by the equation ''ε''<sub>0</sub> = ''e''<sup>2</sup>/2''αhc''<sub>0</sub>,<ref group="note">At present, this equation is used to calculate the [[elementary charge]].</ref> where ''e'' is the elementary charge, ''α'' is the [[fine structure constant]] and ''h'' is the [[Planck constant]]. The relative uncertainty in the value would be the same as that of the fine structure constant, currently 6.8{{e|−10}}.<ref name="CODATA"/> |
| + | |||
| + | ==Notes and references== | ||
| + | ===Notes=== | ||
| + | {{reflist|group=note}} | ||
| − | ==References== | + | ===References=== |
{{reflist}} | {{reflist}} | ||
Latest revision as of 06:16, 2 April 2010
The electric constant (symbol: ε0), also known as the vacuum permittivity or the permittivity of free space, is a physical constant that describes the force between two charged bodies in vacuum.[1] It also appears in Maxwell's equations, which describe the behaviour of electromagnetic waves. The exact definition (and value) depends on the system of quantities used, but in the International System of Quantities (ISQ) it has a defined value of approximately 8.854 187 816 × 10−12 F m−1.[2]
The electric constant is related to the magnetic constant μ0 and the speed of light c0 by the equation c20 = 1/ε0μ0. In SI units, the speed of light is exactly 299 792 458 m s−1 (by the definition of the metre) and the magnetic constant is exactly 4π × 10−7 N A−1 (by the definition of the ampere):[3] hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal).[2]
Contents
International System of Quantities
The force between two point charges Q1 and Q2 in vacuum is given by Coulomb's law, which, in the ISQ, has the form:[note 1]
- F = Q1Q2r/4πε0r3
where r is the vector between the two point charges. The factor of 4π arises here to avoid it appearing in situations of rectangular symmetry:[note 2] quantity systems in which Coulomb's law is written in this way are said to be "rationalized".[4]
CGS system
The different cgs (centimetre–gram–second) quantity systems are non-rationalized.[4]
Electrostatic units
The usual approach to treating the electric constant in electrostatic units (esu) is to define it as unity, without dimensions. Coulomb´s law becomes:
- F = Q1Q2r/r3
Alternatively, the electrostatic unit of charge can be taken as the Franklin (also called the statcoulomb), in which case the electric constant is 1 Fr2 erg−1 cm−1.[4]
Electromagnetic units
In electromagnetic units (emu), it is the magnetic constant which is taken as unity. The electric constant, therefore, has the value 1/c20.[4]
New SI
Under the proposals to redefine the ampere as a fixed number of elementary charges per second,[5] the electric constant would no longer have an exact fixed value. Instead, it would be defined by the equation ε0 = e2/2αhc0,[note 3] where e is the elementary charge, α is the fine structure constant and h is the Planck constant. The relative uncertainty in the value would be the same as that of the fine structure constant, currently 6.8 × 10−10.[2]
Notes and references
Notes
- ↑ This equation is commonly written to give only the magnitude of the force: the version here stresses that the force acts along the line connecting the two particles.
- ↑ See, for example, the definition of the ampere, which developed in a non-rationalized quantity system before being incorporated into the SI.
- ↑ At present, this equation is used to calculate the elementary charge.
References
- ↑ electric constant. In Electropedia: International Electrotechnical Vocabulary (IEC 60050); International Electrotechnical Commission: Geneva, <http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=121-11-03>. (accessed 2 April 2010).
- ↑ 2.0 2.1 2.2 Mohr, Peter J.; Taylor, Barry N.; Newell, David B. CODATA Recommended Values of the Fundamental Physical Constants: 2006. Rev. Mod. Phys. 2008, 80 (2), 633–730. doi:10.1103/RevModPhys.80.633, <http://physics.nist.gov/cuu/Constants/codata.pdf>. Direct link to value.
- ↑ The International System of Units (SI), 8th ed.; International Bureau of Weights and Measures: Sèvres, France, 2006; pp 112–13. ISBN 92-822-2213-6, <http://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf>.
- ↑ 4.0 4.1 4.2 4.3 Quantities, Units and Symbols in Physical Chemistry, 2nd ed.; Blackwell Science: Oxford, 1993; pp 117–19. ISBN 0-63203-5838, <http://old.iupac.org/publications/books/gbook/green_book_2ed.pdf>.
- ↑ Recommendation E1. In Report of the 25th meeting (15–16 March 2007), Consultative Committee for Electricity and Magnetism (CCEM); International Bureau for Weights and Measures: Sèvres, France, <http://www.bipm.org/utils/common/pdf/CCEM25.pdf>.
External links
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See also the corresponding article on Wikipedia. |
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