Vacuum permeability

The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0 (pronounced "mu nought" or "mu zero"). Its purpose is to quantify the strength of the magnetic field emitted by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.

This article is about the magnetic constant. For the analogous electric constant, see vacuum permittivity.
Value of μ0Unit
1.25663706212(19)×10−6N⋅A−2

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, with no other dependencies with experimental uncertainty. Its value in SI units as recommended by CODATA 2018 (published in May 2019) is:

μ0 = 1.25663706212(19)×10−6 N⋅A−2

From 1948 to 2019, μ0 had a defined value (per the former definition of the SI ampere), equal to:

μ0 = 4π×10−7 H/m = 1.25663706143...×10−6 N/A2 (1 henry per metre = 1 newton per square ampere = 1 tesla metre per ampere)

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.

The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872. The modern notation of permeability as μ and permittivity as ε has been in use since the 1950s.

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