# Magnetic constant

*13 January 2011*.

The **magnetic constant** *μ*_{0} (also known as **vacuum permeability** or **permeability of free space**) is a universal physical constant, relating mechanical and electromagnetic units of measurement. In the International System of Units (SI), its value is *exactly* expressed by:

- μ
_{0}= 4π × 10^{−7}N/A^{2}= 4π×10^{−7}henry/metre (H/m) , or approximately 1.2566×10^{−6}H/m.^{[1]}

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 *μ*_{0} is related to the electric constant *ε*_{0} and to the speed of light in vacuum by *c* ² ε_{0} μ_{0} = 1.

In Gaussian units, the symbols *μ*_{0} and *ε*_{0} do not appear.^{[3]} Also, in Gaussian units, the speed of light is a measured, not a defined quantity.

## [edit] Terminology

Historically, the constant μ_{0} 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 ≡ μ_{r} μ_{0} is equal to μ_{0} for the vacuum, i.e., for the vacuum the *relative permeability* μ_{r} = 1.

## [edit] 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*, 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"). - ↑ National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.