Vacuum permeability

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The vacuum permeability, referred to by international standards organizations as the magnetic constant,[1][2] and denoted by the symbol μ0 (also called the permeability of free space and of empty space), is a fundamental physical constant, relating mechanical and electromagnetic units of measurement. In the International System of Units (SI), its value is defined in free space (not measured see defined variables, Table 1 in CODATA report[3]) as:

\mu_0 \ \overset{\underset{\mathrm{def}}{}}{=}\ 4 \pi\ \times \ 10^{-7}\ N/A2 = 4π×10−7 H/m, or approximately 1.2566×10−6 H/m (or T·m/A) [1]

This value is a consequence of the definition of the ampere in terms of the force per unit length between infinitely long parallel wires of zero cross-section in vacuum.[4] For a discussion of this force, see Serway and Jewett,[5] or Monk.[6] See also Ampère's force law.

In vacuum, the magnetic constant defines the value of the magnetic field strength, or H-field (calculated from currents) in terms of the magnetic flux density, or B-field (for calculating Lorentz force):[7]

\mathbf{B} = \mu_0 \ \mathbf{H}.

See Maxwell's equations.

The magnetic constant μ0 is related to two other defined constants, the electric constant ε0 and the speed of light in vacuum c0 according to the identity:[8]

{c_0}^2 \, \epsilon_0 \, \mu_0 = 1.

[edit] Terminology

Historically, the constant μ0 has had different names. (In the 1987 IUPAP Red book, for example, this constant was still called permeability of vacuum.)[9] Another, now rather rare and obsolete, term is "magnetic permittivity of vacuum". See, for example, Servant et al.[10] The term "vacuum permeability" (and variations thereof) remains very widespread, but standards organizations have recently moved to magnetic constant as a uniform term for this quantity, although the older term continues to be listed as a synonym.[3]

The term "magnetic constant" avoids the term "permeability" and "vacuum" because it is a defined value, not the result of experimental measurement.

The linear permeability of vacuum is impossible to measure because it defines the ampere, in the same way that the speed of light in vacuum is now impossible to measure because it defines the metre; by definition of the units, the permeability of vacuum is μ0.[11]

The permeability of vacuum refers to a baseline state in free space. See the free space and vacuum state articles for detail about this ideal reference state.

[edit] Footnotes

  1. ^ a b Magnetic constant. 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
  2. ^ BIPM
  3. ^ a b CODATA Recommended Values of the Fundamental Physical Constants: 2006. Committee on Data for Science and Technology (CODATA): See Table 1. NIST.
  4. ^ Unit of electric current (ampere). Historical context of the SI. NIST. Retrieved on 2007-08-11.
  5. ^ Raymond A Serway & Jewett JW (2006). Serway's principles of physics: a calculus based text, Fourth Edition, Belmont, CA: Thompson Brooks/Cole, p. 746. ISBN 053449143X. 
  6. ^ Paul M. S. Monk, Physical Chemistry: Understanding our Chemical World, John Wiley and Sons, 2004 online.
  7. ^ The B-field is considered more fundamental than the H-field; see B and H
  8. ^ Quote from NIST: "Current practice is to use c0 to denote the speed of light in vacuum according to ISO 31. In the original Recommendation of 1983, the symbol c was used for this purpose." See NIST Special Publication 330, Appendix 2, p. 45
  9. ^ SUNAMCO Commission (1987), “Recommended values of the fundamental physical constants”, Symbols, Units, Nomenclature and Fundamental Constants in Physics, pp. p.54, <http://www-v2.sp.se/metrology/IUPAP_SUNAMCO/IUPAP%20SUNAMCO%20Commission_files/IUPAP_Red_book_1987/SUNAMCO%20Red%20book%201987/6_Recommended_fundamental_constants_iupap_sunamco_red_book_1987.pdf> ; (the IUPAP "Red book").
  10. ^ J R Lalanne, F Carmona & L Servant (1999). Optical spectroscopies of electronic absorption., World Scientific series in contemporary chemical physics, vol. 17., Singapore;London: World Scientific, p. 10. ISBN 9810238614. 
  11. ^ John David Jackson (1998). Classical electrodynamics, Third Edition, New York: Wiley, p. 154. ISBN 047130932X. 

[edit] See also