Vacuum permittivity

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Vacuum permittivity is the electric constant ε0 (also known as the permittivity of free space, or by the term dielectric constant of vacuum), which is a fundamental physical constant. The constant ε0 connects mechanical quantities (time, length, mass) to the units for electrical charge, for example in Coulomb's law. Its value in SI units is

\varepsilon_0 \approx 8.854\ 187\ 817\ \cdot 10^{-12} F m-1.[1]

This value is a consequence of the relation ε0 μ0 c ² = 1 with the defined speed of light in vacuum c and with the defined magnetic constant μ0.

The Coulomb force constant or electrostatic constant can thus be expressed as

\frac{1}{ 4 \pi \varepsilon_0} = \frac{\mu_0\ c^2}{4 \pi} = 10^{-7}\ c^2 \approx 8.987\ 551\ 787\ \cdot 10^9 \approx 9\cdot 10^9 N·m²/C².

In other systems of electromagnetic units, it is common to have \varepsilon_0 = 1. This is the case in Gaussian units, Lorentz-Heaviside units, and some choices of natural units (while some other choices set \varepsilon_0 = 1/4\pi e.g. electrostatic cgs units, ).

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Historically, the physical constant ε0 has been known by many different names. Both "electric constant" and "vacuum permittivity" (or its variants, such as "permittivity of free space"[2]) are widespread. Standards organizations now use "electric constant" as a uniform term for this quantity,[1][3] but "vacuum permittivity" and "permittivity of vacuum" continue to be listed as parenthetical synonyms or clarifications in official standards documents.[4][5]

Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity.[6] However, in modern usage "dielectric constant" typically refers exclusively to a relative permittivity \varepsilon / \varepsilon_0 (where the relative permittivity of vacuum is 1 by definition),[7] and even this usage is considered "obsolete" by some standards bodies in favor of "relative permittivity"[5][8]. Hence, the term "dielectric constant of vacuum" for the absolute vacuum permittivity ε0 (as opposed to the relative vacuum permittivity, 1) is likely to be considered obsolete by most modern authors, although occasional examples of continuing usage can be found.[9]

As for notation, the constant can be denoted by either \varepsilon_0\, or \epsilon_0\,, using either of the common glyphs for the letter epsilon.

Therefore, although it is called the "permittivity of vacuum", the value of ε0 (like the speed of light in SI units) is no longer tied to any experimental measurement; its value is precisely determined by the definition of the metre and other units. In principle, it is possible for the experimental ε of a perfect vacuum to vary slightly from ε0 in unusual circumstances, due (e.g.) to quantum corrections to Maxwell's equations, although such deviations have not yet been measured. For example, the theory of quantum electrodynamics predicts that vacuum should exhibit nonlinear effects that will make it behave like a birefringent material with ε slightly greater than ε0 for extremely strong electric fields.[10][11]

  1. ^ a b CODATA. Electric constant. 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
  2. ^ Sam Bowen (1991). What is the significance of permittivity of free space?. Ask a Scientist. Argonne National Laboratory.
  3. ^ National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.
  4. ^ International Bureau of Weights and Measures (2006). The International System of Units (SI) p. 12.
  5. ^ a b Braslavsky, S.E. (2007), "Glossary of terms used in photochemistry (IUPAC recommendations 2006)", Pure and Applied Chemistry 79: p. 293-465; see p. 348., <http://www.iupac.org/publications/pac/2007/pdf/7903x0293.pdf>
  6. ^ King, Ronold W. P. (1963). Fundamental Electromagnetic Theory. New York: Dover, p. 139. 
  7. ^ Jackson, John David (1998). Classical Electrodynamics, 3rd edition. New York: Wiley, p. 154. 
  8. ^ IEEE Standards Board (1997). IEEE Standard Definitions of Terms for Radio Wave Propagation p. 6.
  9. ^ For example in this random patent.
  10. ^ Klein, James J. and B. P. Nigam, "Birefringence of the vacuum," Physical Review vol. 135, p. B1279-B1280 (1964).
  11. ^ Mourou, G. A., T. Tajima, and S. V. Bulanov, "Optics in the relativistic regime," Reviews of Modern Physics vol. 78 (no. 2), 309-371 (2006).
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