Vacuum permeability

The vacuum magnetic permeability (variously vacuum permeability, permeability of free space, permeability of vacuum, 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"), approximately equal to 4π × 10⁻⁷ H/m (by the former definition of the ampere). It quantifies the strength of the magnetic field induced 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, H·m⁻¹, or T·m·A⁻¹, which are all equivalent.

Since the revision of the SI 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 1.6×10⁻¹⁰,^[1][2][3][4] with no other dependencies with experimental uncertainty. Its value in SI units as recommended by CODATA is:

This is equal to 4π × [1 − (1.3 ± 1.6) × 10⁻¹⁰] × 10⁻⁷ N/A², with a relative deviation (of order 10⁻¹⁰, i.e. less than a part per billion) from the former defined value that is within its uncertainty.

The terminology of permeability and susceptibility was introduced by William Thomson, 1st Baron Kelvin in 1872.^[6] The modern notation of permeability as μ and permittivity as ε has been in use since the 1950s.