# Magnetic constant

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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:

μ0 = 4π × 10−7 N/A2 = 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):

${\displaystyle \mathbf {B} =\mu _{0}\ \mathbf {H} .}$

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. Magnetic constant. 2006 CODATA recommended values. NIST. Retrieved on 2007-08-08.
2. Unit of electric current (ampere). Historical context of the SI. NIST. Retrieved on 2007-08-11.
3. Markus Reiher, Alexander Wolf (2009). Relativistic quantum chemistry: the fundamental theory of molecular science. Wiley-VCH, p. 7. ISBN 3527312927.
4. 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").