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 has a defined value of approximately {{nowrap|8.854 187 816{{e|−12}} F m<sup>−1</sup>}}. | + | 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 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 defined (by the definition of the [[metre]]) as {{nowrap|299 792 458 m s<sup>−1</sup>}} and the magnetic constant is defined (by the definition of the [[ampere]]) as {{nowrap|4π{{e|−7}} N A<sup>−1</sup>}}: 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 defined (by the definition of the [[metre]]) as {{nowrap|299 792 458 m s<sup>−1</sup>}} and the magnetic constant is defined (by the definition of the [[ampere]]) as {{nowrap|4π{{e|−7}} N A<sup>−1</sup>}}: hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal). | ||
==New SI== | ==New SI== | ||
| − | Under the proposals to redefine the [[ampere]] as a fixed number of [[elementary charge]]s per second, 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>, 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, 6.8{{e|−10}} at present. | + | 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 = Internation 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>, 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, 6.8{{e|−10}} at present.<ref name="CODATA"/> |
==References== | ==References== | ||
Revision as of 18:53, 31 March 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. The exact definition (and value) depends on the system of quantities used, but in the International System of Quantities (ISQ), the electric constant has a defined value of approximately 8.854 187 816 × 10−12 F m−1.[1]
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 defined (by the definition of the metre) as 299 792 458 m s−1 and the magnetic constant is defined (by the definition of the ampere) as 4π × 10−7 N A−1: hence, the electric constant is also fixed, and can be calculated to any desired precision (although the numerical value is a non-repeating decimal).
New SI
Under the proposals to redefine the ampere as a fixed number of elementary charges per second,[2] the electric constant would no longer have an exact fixed value. Instead, it would be defined by the equation ε0 = e2/2αhc0, 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, 6.8 × 10−10 at present.[1]
References
- ↑ 1.0 1.1 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.
- ↑ Recommendation E1. In Report of the 25th meeting (15–16 March 2007), Consultative Committee for Electricity and Magnetism (CCEM); Internation 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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