Vacuum permeability
Value of μ0 | Unit |
---|---|
1.25663706212(19)×10−6 | N⋅A−2 |
The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum), also known as the magnetic constant, is the
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 about 1.5×10−10,[1][2][3] with no other dependencies with experimental uncertainty. Its value in SI units as recommended by
From 1948[5] to 2019, μ0 had a defined value (per the former definition of the SI ampere), equal to:[6][7]
The deviation of the recommended measured value from the former defined value is statistically significant, at about 3.6σ, listed as μ0/(4π×10−7 N⋅A−2) − 1 = (5.5±1.5)×10−10.[4]
The terminology of
Ampere-defined vacuum permeability
Two thin, straight, stationary, parallel wires, a distance r apart in
From 1948 until 2019 the ampere was defined as "that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length". This is equivalent to a definition of of exactly 4π×10−7 H/m.[a], since
Terminology
Standards organizations have recently moved to magnetic constant as the preferred name for μ0, although the older name continues to be listed as a synonym. The term "vacuum permeability" (and variations thereof, such as "permeability of free space") remains very widespread.
The name "magnetic constant" was used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. This change of preferred name had been made because μ0 was a defined value, and was not the result of experimental measurement (see below). In the new SI system, the permeability of vacuum no longer has a defined value, but is a measured quantity, with an uncertainty related to that of the (measured) dimensionless fine structure constant.
Systems of units and historical origin of value of μ0
In principle, there are several equation systems that could be used to set up a system of electrical quantities and units.[13] Since the late 19th century, the fundamental definitions of current units have been related to the definitions of mass, length, and time units, using Ampère's force law. However, the precise way in which this has "officially" been done has changed many times, as measurement techniques and thinking on the topic developed. The overall history of the unit of electric current, and of the related question of how to define a set of equations for describing electromagnetic phenomena, is very complicated. Briefly, the basic reason why μ0 has the value it does is as follows.
Ampère's force law describes the experimentally-derived fact that, for two thin, straight, stationary, parallel wires, a distance r apart, in each of which a current I flows, the force per unit length, Fm/L, that one wire exerts upon the other in the vacuum of
In the old "electromagnetic (emu)" system of equations defined in the late 19th century, km was chosen to be a pure number, 2, distance was measured in centimetres, force was measured in the cgs unit dyne, and the currents defined by this equation were measured in the "electromagnetic unit (emu) of current" (also called the "abampere"). A practical unit to be used by electricians and engineers, the ampere, was then defined as equal to one tenth of the electromagnetic unit of current.
In another system, the "rationalized metre–kilogram–second (rmks) system" (or alternatively the "metre–kilogram–second–ampere (mksa) system"), km is written as μ0/2π, where μ0 is a measurement-system constant called the "magnetic constant".[b]
The value of μ0 was chosen such that the rmks unit of current is equal in size to the ampere in the emu system: μ0 was defined to be 4π × 10−7
Historically, several different systems (including the two described above) were in use simultaneously. In particular, physicists and engineers used different systems, and physicists used three different systems for different parts of physics theory and a fourth different system (the engineers' system) for laboratory experiments. In 1948, international decisions were made by standards organizations to adopt the rmks system, and its related set of electrical quantities and units, as the single main international system for describing electromagnetic phenomena in the International System of Units.
Significance in electromagnetism
The magnetic constant μ0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources. In particular, it appears in relationship to quantities such as permeability and magnetization density, such as the relationship that defines the magnetic H-field in terms of the magnetic B-field. In real media, this relationship has the form:
In the International System of Quantities (ISQ), the speed of light in vacuum, c,[14] is related to the magnetic constant and the electric constant (vacuum permittivity), ε0, by the equation:
Conversely, as the permittivity is related to the
In the
See also
- Characteristic impedance of vacuum
- Electromagnetic wave equation
- Mathematical descriptions of the electromagnetic field
- New SI definitions
- Sinusoidal plane-wave solutions of the electromagnetic wave equation
- Vacuum permittivity
Notes
- ^ NIST. Retrieved 2007-08-11.
- ^ The decision to explicitly include the factor of 2π in km stems from the "rationalization" of the equations used to describe physical electromagnetic phenomena.
References
- ^ "Convocationde la Conférence générale des poids et mesures (26e réunion)" (PDF).
- S2CID 4875011.
- S2CID 119283799.
- ^ a b NIST SP 961 (May 2019)
- ^ Comptes Rendus des Séances de la Neuvième Conférence Générale des Poids et Mesures Réunie à Paris en 1948
- National Institute of Standards and Technology.
- )
- ^ Magnetic Permeability, and Analogues in Electro-static Induction, Conduction of Heat, and Fluid Motion, March 1872.
- ISBN 978-0-87901-434-6.
- .
- SUNAMCO (1987). "Recommended values of the fundamental physical constants"(PDF). Symbols, Units, Nomenclature and Fundamental Constants in Physics. p. 54.
- ^
Lalanne, J.-R.; Carmona, F.; Servant, L. (1999). Optical spectroscopies of electronic absorption. World Scientific Series in Contemporary Chemical Physics. Vol. 17. p. 10. ISBN 978-981-02-3861-2.
- ^
For an introduction to the subject of choices for independent units, see
John David Jackson (1998). Classical electrodynamics (Third ed.). New York: Wiley. p. 154. ISBN 978-0-471-30932-1.
- ^ "2018 CODATA Value: speed of light in vacuum". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
- ^ The exact numerical value is found at: "Electric constant, ε0". NIST reference on constants, units, and uncertainty: Fundamental physical constants. NIST. Retrieved 2012-01-22. This formula determining the exact value of ε0 is found in Table 1, p. 637 of Mohr, Peter J; Taylor, Barry N; Newell, David B (2008). "CODATA recommended values of the fundamental physical constants: 2006" (PDF). Reviews of Modern Physics. 80 (2): 633–730. .