Magnetic constant: Difference between revisions
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The '''magnetic constant''' ''μ''<sub>0</sub> ( | The '''magnetic constant''' ''μ''<sub>0</sub> (also known as '''vacuum permeability''' or '''permeability of [[Free space (electromagnetism)|free space]]''') is a universal [[physical constant]], an electromagnetic property of [[classical vacuum]], relating mechanical and electromagnetic units of measurement. In the [[International System of Units]] (SI), its value is ''exactly'' expressed by: | ||
:<math>\mu_0 = 4 \pi\ \times \ 10^{-7}\ </math> [[newton|N]]/[[ampere|A]]<sup>2</sup> = 4π×10<sup>−7</sup> [[Henry (inductance)| | <!-- :<math>\mu_0 = 4 \pi\ \times \ 10^{-7}\ </math> --> | ||
:μ<sub>0</sub> = 4π × 10<sup>−7</sup> [[newton|N]]/[[ampere|A]]<sup>2</sup> = 4π×10<sup>−7</sup> [[Henry (inductance)|henry]]/[[metre]] (H/m) , or approximately 1.2566×10<sup>−6</sup> H/m.<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 forces between wires.<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> | This value is a consequence of the definition of the [[ampere]] in terms of forces between wires, see [[Ampere's_equation#Two straight, infinite, and parallel wires|Ampère's equation]].<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> | ||
In vacuum, the magnetic constant is the ratio of the | In vacuum, the magnetic constant is the ratio of the [[magnetic induction|magnetic '''B'''-field]] (entering the expression for the [[Lorentz force]]) to the [[magnetic field|magnetic '''H'''-field]] | ||
(the field inside a [[solenoid]]): | |||
:<math>\mathbf{B} = \mu_0 \ \mathbf{H}.</math> | :<math>\mathbf{B} = \mu_0 \ \mathbf{H}.</math> | ||
In SI units the magnetic constant ''μ''<sub>0</sub> is related to the [[electric constant]] ''ε''<sub>0</sub> and to the [[speed of light in vacuum | In SI units the magnetic constant ''μ''<sub>0</sub> is related to the [[electric constant]] ''ε''<sub>0</sub> and to the [[speed of light]] in vacuum by ''c'' ² ε<sub>0</sub> μ<sub>0</sub> = 1. | ||
In [[Gaussian units]], the symbols ''μ''<sub>0</sub> and ''ε''<sub>0</sub> do not appear.<ref name=Wolf> | |||
{{cite book |title=Relativistic quantum chemistry: the fundamental theory of molecular science |author=Markus Reiher, Alexander Wolf |url=http://books.google.com/books?id=tpsHi7F16dMC&pg=PA7 |pages=p. 7 |isbn=3527312927 |publisher=Wiley-VCH |year=2009}} | |||
</ref> Also, in Gaussian units, the speed of light is a measured, not a defined quantity. | |||
==Terminology== | ==Terminology== | ||
Historically, the constant μ<sub>0</sub> has had different names. A now rather obsolete term is "''magnetic permittivity of vacuum''". In the 1987 [[IUPAP]] Red book this constant was 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> | Historically, the constant μ<sub>0</sub> has had different names. A now rather obsolete term is "''magnetic permittivity of vacuum''". In the 1987 [[IUPAP]] Red book this constant was 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> | ||
Currently the [[nomenclature]] in physics is ''magnetic constant''.<ref name="NIST"/><ref>{{cite web |author=[[National Physical Laboratory, UK]]|url=http://www.npl.co.uk/reference/fundamental_constants.pdf |title=Fundamental Physical Constants |year=1998 |pages=p. 2}}</ref> | Currently the [[nomenclature]] in physics is ''magnetic constant''.<ref name="NIST"/><ref>{{cite web |author=[[National Physical Laboratory, UK]]|url=http://www.npl.co.uk/reference/fundamental_constants.pdf |title=Fundamental Physical Constants |year=1998 |pages=p. 2}}</ref> | ||
The | The [[permeability (electromagnetism)|permeability]] μ ≡ μ<sub>r</sub> μ<sub>0</sub> is equal to μ<sub>0</sub> for the vacuum, i.e., for the vacuum the ''relative permeability'' μ<sub>r</sub> = 1. | ||
== Footnotes == | == Footnotes == | ||
<references/> | <references/>[[Category:Suggestion Bot Tag]] | ||
Latest revision as of 16:01, 14 September 2024
The magnetic constant μ0 (also known as vacuum permeability or permeability of free space) is a universal physical constant, an electromagnetic property of classical vacuum, relating mechanical and electromagnetic units of measurement. In the International System of Units (SI), its value is exactly expressed by:
This value is a consequence of the definition of the ampere in terms of forces between wires, see Ampère's equation.[2] In vacuum, the magnetic constant is the ratio of the magnetic B-field (entering the expression for the Lorentz force) to the magnetic H-field (the field inside a solenoid):
In SI units the magnetic constant μ0 is related to the electric constant ε0 and to the speed of light in vacuum by c ² ε0 μ0 = 1.
In Gaussian units, the symbols μ0 and ε0 do not appear.[3] Also, in Gaussian units, the speed of light is a measured, not a defined quantity.
Terminology
Historically, the constant μ0 has had different names. A now rather obsolete term is "magnetic permittivity of vacuum". In the 1987 IUPAP Red book this constant was called permeability of vacuum.[4] Currently the nomenclature in physics is magnetic constant.[1][5] The permeability μ ≡ μr μ0 is equal to μ0 for the vacuum, i.e., for the vacuum the relative permeability μr = 1.
Footnotes
- ↑ 1.0 1.1 Magnetic constant. 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
- ↑ Unit of electric current (ampere). Historical context of the SI. NIST. Retrieved on 2007-08-11.
- ↑ Markus Reiher, Alexander Wolf (2009). Relativistic quantum chemistry: the fundamental theory of molecular science. Wiley-VCH, p. 7. ISBN 3527312927.
- ↑ SUNAMCO Commission (1987), Recommended values of the fundamental physical constants, Symbols, Units, Nomenclature and Fundamental Constants in Physics, at p.54; (the IUPAP "Red book").
- ↑ National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.