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From Citizendium, the Citizens' Compendium

The magnetic constant μ₀ (equal to the vacuum permeability, also known as the 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:

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):

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 μ₀ and ε₀ do not enter the theory, only c appears in the equations.

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.^[3] Currently the nomenclature in physics is magnetic constant.^[1][4] The vacuum permeability μ = μ_rμ₀ is equal to μ₀, i.e., for the vacuum μ_r = 1.

Footnotes

1. ↑ ^1.0 1.1 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. ↑ 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").
4. ↑ National Physical Laboratory, UK (1998). Fundamental Physical Constants p. 2.