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Vacuum permeability

This article is about the magnetic constant. For the analogous electric constant, see vacuum permittivity.
Value of μ0
1.25663706127(20)×10−6 N⋅A−2

The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum, magnetic constant) is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0 (pronounced "mu nought" or "mu zero"). It quantifies the strength of the magnetic field induced by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.

Since the redefinition of SI units in 2019 (when the values of e and h were fixed as defined quantities), μ0 is an experimentally determined constant, its value being proportional to the dimensionless fine-structure constant, which is known to a relative uncertainty of 1.6×10−10,[1][2][3][4] with no other dependencies with experimental uncertainty. Its value in SI units as recommended by CODATA is:

μ0 = 1.25663706127(20)×10−6 N⋅A−2[5]

From 1948[6] to 2019, μ0 had a defined value (per the former definition of the SI ampere), equal to:[7]

μ0 = 4π×10−7 H/m = 1.25663706143...×10−6 N/A2

The deviation of the recommended measured value from the former defined value is within it uncertainty.

The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872.[8] The modern notation of permeability as μ and permittivity as ε has been in use since the 1950s.

  1. ^ "2022 CODATA Value: fine-structure constant". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  2. ^ "Convocationde la Conférence générale des poids et mesures (26e réunion)" (PDF).
  3. ^ Parker, Richard H.; Yu, Chenghui; Zhong, Weicheng; Estey, Brian; Müller, Holger (2018-04-13). "Measurement of the fine-structure constant as a test of the Standard Model". Science. 360 (6385): 191–195. arXiv:1812.04130. Bibcode:2018Sci...360..191P. doi:10.1126/science.aap7706. ISSN 0036-8075. PMID 29650669. S2CID 4875011.
  4. ^ Davis, Richard S. (2017). "Determining the value of the fine-structure constant from a current balance: Getting acquainted with some upcoming changes to the SI". American Journal of Physics. 85 (5): 364–368. arXiv:1610.02910. Bibcode:2017AmJPh..85..364D. doi:10.1119/1.4976701. ISSN 0002-9505. S2CID 119283799.
  5. ^ "2022 CODATA Value: vacuum magnetic permeability". The NIST Reference on Constants, Units, and Uncertainty. NIST. May 2024. Retrieved 2024-05-18.
  6. ^ Comptes Rendus des Séances de la Neuvième Conférence Générale des Poids et Mesures Réunie à Paris en 1948
  7. ^ Rosen, Joe (2004). "Permeability (Physics)". Encyclopedia of Physics. Facts on File science library. New York: Facts On File. ISBN 9780816049745. Retrieved 2010-02-04.(registration required)
  8. ^ Magnetic Permeability, and Analogues in Electro-static Induction, Conduction of Heat, and Fluid Motion, March 1872.

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