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Vacuum permittivity

The physical constant ε0 (pronounced as "epsilon nought" or "epsilon zero"), commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has the CODATA value (as of 2018)

ε0 = 8.8541878128(13)×10−12 F⋅m−1 (farads per metre), with a relative uncertainty of 1.5×10−10.[1]
Value of ε0 Unit
8.854 187 8128(13)×10-12 Fm-1
55.263 494 06 e2GeV-1fm-1
1/(4π) qp2Ep-1lp-1




The value of ε0 is defined by the formula[3]


where c is the defined value for the speed of light in classical vacuum in SI units,[4] and μ0 is the parameter that international Standards Organizations call the "magnetic constant" (commonly called vacuum permeability). Since μ0 has an approximate value 4π × 10−7 H/m,[5] and c has the defined value 299792458 m⋅s−1,[6] it follows that ε0 can be expressed numerically as



Redefinition of the SI unitsEdit

The ampere was redefined by defining the elementary charge as an exact number of coulombs as from 20 May 2019,[9] with the effect that the vacuum electric permeability no longer has an exactly determined value in SI units. The value of the electron charge became a numerically defined quantity, not measured, making μ0 a measured quantity. Consequently, ε0 is not exact. As before, it is defined by the equation ε0 = 1/(μ0c2), and is thus determined by the value of μ0, the magnetic vacuum permeability which in turn is determined by the experimentally determined dimensionless fine-structure constant α:


with e being the elementary charge, h being the Planck constant, and c being the speed of light in vacuum, each with exactly defined values. The relative uncertainty in the value of ε0 is therefore the same as that for the dimensionless fine-structure constant, namely 1.5×10−10.[10]


Historically, the parameter ε0 has been known by many different names. The terms "vacuum permittivity" or its variants, such as "permittivity in/of vacuum",[11][12] "permittivity of empty space",[13] or "permittivity of free space"[14] are widespread. Standards Organizations worldwide now use "electric constant" as a uniform term for this quantity,[7] and official standards documents have adopted the term (although they continue to list the older terms as synonyms).[15][16] In the new SI system, the permittivity of vacuum will not be a constant anymore, but a measured quantity, related to the (measured) dimensionless fine structure constant.

Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity.[17][18] However, in modern usage "dielectric constant" typically refers exclusively to a relative permittivity ε/ε0 and even this usage is considered "obsolete" by some standards bodies in favor of relative static permittivity.[16][19] Hence, the term "dielectric constant of vacuum" for the electric constant ε0 is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.


Historical origin of the parameter ε0Edit


Rationalization of unitsEdit



where Q is a quantity that represents the amount of electricity present at each of the two points, and ke is the Coulomb constant. If one is starting with no constraints, then the value of ke may be chosen arbitrarily.[20] For each different choice of ke there is a different "interpretation" of Q: to avoid confusion, each different "interpretation" has to be allocated a distinctive name and symbol.











Determination of a value for ε0Edit



Permittivity of real mediaEdit








See alsoEdit


  1. ^ "2018 CODATA Value: vacuum electric permittivity". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
  2. ^ "electric constant". Electropedia: International Electrotechnical Vocabulary (IEC 60050). Geneva: International Electrotechnical Commission. Retrieved 26 March 2015..
  3. ^ The approximate numerical value is found at: "Electric constant, ε0". NIST reference on constants, units, and uncertainty: Fundamental physical constants. NIST. Retrieved 22 January 2012. This formula determining the exact value of ε0 is found in Table 1, p. 637 of PJ Mohr; BN Taylor; DB Newell (April–June 2008). "Table 1: Some exact quantities relevant to the 2006 adjustment in CODATA recommended values of the fundamental physical constants: 2006" (PDF). Rev Mod Phys. 80 (2): 633–729. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633.
  9. ^ "Resolution 1 of 24th meeting of the General Conference on Weights and Measures". On the possible future revision of the International System of Units, the SI (PDF). Sèvres, France: International Bureau for Weights and Measures. 21 October 2011.
  10. ^ "2018 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 20 May 2019.
  11. ^ SM Sze & Ng KK (2007). "Appendix E". Physics of semiconductor devices (Third ed.). New York: Wiley-Interscience. p. 788. ISBN 978-0-471-14323-9.
  12. ^ RS Muller, Kamins TI & Chan M (2003). Device electronics for integrated circuits (Third ed.). New York: Wiley. Inside front cover. ISBN 978-0-471-59398-0.
  13. ^ FW Sears, Zemansky MW & Young HD (1985). College physics. Reading, Mass.: Addison-Wesley. p. 40. ISBN 978-0-201-07836-7.
  16. ^ a b Braslavsky, S.E. (2007). "Glossary of terms used in photochemistry (IUPAC recommendations 2006)" (PDF). Pure and Applied Chemistry. 79 (3): 293–465, see p. 348. doi:10.1351/pac200779030293.
  17. ^ "Naturkonstanten". Freie Universität Berlin.
  20. ^ For an introduction to the subject of choices for independent units, see John David Jackson (1999). "Appendix on units and dimensions". Classical electrodynamics (Third ed.). New York: Wiley. pp. 775 et seq. ISBN 978-0-471-30932-1.
  22. ^ Jenö Sólyom (2008). "Equation 16.1.50". Fundamentals of the physics of solids: Electronic properties. Springer. p. 17. ISBN 978-3-540-85315-2.