Vacuum permeability
4602964
219332913
2008-06-14T18:52:54Z
Biblbroks
1337363
/* See also */ changed catČ [[Category:Fundamental constants]]
The '''vacuum [[permeability (electromagnetism)|permeability]]''', referred to by international standards organizations as the '''magnetic constant''',<ref name ="NIST"/><ref>[http://www.bipm.org/en/si/si_brochure/chapter2/2-1/ampere.html BIPM]</ref> and denoted by the symbol ''μ''<sub>0</sub> (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<ref name="CODATA">{{cite web |url=http://physics.nist.gov/cuu/Constants/codata.pdf |title=CODATA Recommended Values of the Fundamental Physical Constants: 2006 |work=Committee on Data for Science and Technology (CODATA): See Table 1 |publisher=[[NIST]]}}</ref>) as:
:<math>\mu_0 \ \overset{\underset{\mathrm{def}}{}}{=}\ 4 \pi\ \times \ 10^{-7}\ </math> [[newton|N]]/[[ampere|A]]<sup>2</sup> = 4π×10<sup>−7</sup> [[Henry (unit)|H]]/[[metre|m]], or approximately 1.2566×10<sup>−6</sup> [[Henry (unit)|H]]/[[metre|m]] (or [[Tesla (unit)|T]]·[[metre|m]]/[[Ampere|A]]) <ref name="NIST">{{cite web |url=http://physics.nist.gov/cgi-bin/cuu/Value?mu0 |title=Magnetic constant |accessdate=2007-08-08 |work=2006 [[CODATA]] recommended values |publisher=[[NIST]] }}</ref>
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.<ref name="NIST amp hist">{{cite web |url=http://physics.nist.gov/cuu/Units/ampere.html |title=Unit of electric current (ampere) |accessdate=2007-08-11 |work=Historical context of the SI |publisher=[[NIST]] }}</ref> For a discussion of this force, see Serway and Jewett,<ref name=Serway>{{cite book
|author=Raymond A Serway & Jewett JW
|title=Serway's principles of physics: a calculus based text
|url=http://books.google.com/books?id=1DZz341Pp50C&pg=RA1-PA746&dq=wire+%22magnetic+force%22&lr=&as_brr=0&sig=4vMV_CH6Nm8ZkgjtDJFlupekYoA#PRA1-PA746,M1 |publisher=Thompson Brooks/Cole
|edition=Fourth Edition
|location=Belmont, CA
|year=2006
|page=p. 746
|isbn=053449143X}}</ref> or Monk.<ref>Paul M. S. Monk, ''Physical Chemistry: Understanding our Chemical World'', John Wiley and Sons, 2004 [http://books.google.com/books?vid=ISBN0471491802&id=LupAi35QjhoC&pg=PA16&lpg=PA16&ots=IMiGyIL-67&dq=ampere+definition+si&sig=9Y0k0wgvymmLNYFMcXodwJZwvAM online].</ref> 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|'''B'''-field]] (for calculating [[Lorentz force]]):<ref>The '''B'''-field is considered more fundamental than the '''H'''-field; see [[Magnetic field#B and H|B and H]]</ref>
:<math>\mathbf{B} = \mu_0 \ \mathbf{H}.</math>
See [[Maxwell's equations#In vacuum, without charges or currents|Maxwell's equations]].
The magnetic constant ''μ''<sub>0</sub> is related to two other defined constants, the [[electric constant]] ''ε''<sub>0</sub> and the [[speed of light in vacuum]] ''c''<sub>0</sub> according to the identity:<ref> Quote from NIST: "Current practice is to use ''c''<sub>0</sub> 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 [http://physics.nist.gov/Pubs/SP330/sp330.pdf NIST ''Special Publication 330'', Appendix 2, p. 45 ]</ref>
:<math>{c_0}^2 \, \epsilon_0 \, \mu_0 = 1</math>.
==Terminology==
Historically, the constant μ<sub>0</sub> has had different names. (In the 1987 [[IUPAP]] Red book, for example, this constant was still called ''permeability of vacuum''.)<ref>{{citation|author=[[SUNAMCO Commission]]| chapter=Recommended values of the fundamental physical constants | url=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 |title=[http://www-v2.sp.se/metrology/IUPAP_SUNAMCO/IUPAP%20SUNAMCO%20Commission_files/IUPAP_Red_book_1987/SUNAMCO%20Red%20book%201987/index_red_book_iupap_sunamco_1987.htm Symbols, Units, Nomenclature and Fundamental Constants in Physics] |year=1987 | pages=p.54 }}; (the [[IUPAP]] "Red book").</ref> Another, now rather rare and obsolete, term is "''magnetic permittivity of vacuum''". See, for example, Servant ''et al.''<ref name=Servant>{{cite book
|author=J R Lalanne, F Carmona & L Servant
|title=Optical spectroscopies of electronic absorption.
|edition=World Scientific series in contemporary chemical physics, vol. 17.
|page=p. 10
|publisher= World Scientific
|location=Singapore;London
|year=1999
|isbn=9810238614
|url=http://books.google.com/books?id=7rWD-TdxKkMC&pg=PA10&lpg=PA10&dq=+%22magnetic+permittivity%22&source=web&ots=w62tNR56Yg&sig=YECrYWXFJWZS29tdZ_7Gr92LZ7M}}
</ref>
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.<ref name="CODATA"/>
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 μ<sub>0</sub>.<ref name=Jackson>{{cite book
|author=John David Jackson
|title=Classical electrodynamics
|edition=Third Edition
|page=p. 154
|publisher= Wiley
|location=New York
|year=1998
|isbn=047130932X
|url=http://worldcat.org/isbn/047130932X}}</ref>
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.
== Footnotes ==
<references/>
==See also==
*[[Electric constant]] (Vacuum permittivity)
*[[Speed of light in vacuum]]
*[[Free space]]
*[[Characteristic impedance of vacuum]]
*[[Maxwell's equations]]
*[[Electromagnetic wave equation]]
*[[Sinusoidal plane-wave solutions of the electromagnetic wave equation]]
*[[Mathematical descriptions of the electromagnetic field]]
[[Category:Fundamental constants]]
[[ca:Permeabilitat del buit]]
[[de:Magnetische Feldkonstante]]
[[et:Magnetiline konstant]]
[[fa:ثابت تراوایی خلاء]]
[[fr:Constante magnétique]]
[[lt:Magnetinė konstanta]]
[[nl:Magnetische veldconstante]]
[[ru:Магнитная постоянная]]
[[sv:Magnetiska konstanten]]
[[uk:Магнітна проникність вакууму]]
[[zh:真空磁导率]]