Magnetic constant

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:

$\mu _{0}=4\pi \ \times \ 10^{-7}\$ N/A² = 4π×10⁻⁷ H/m, or approximately 1.2566×10⁻⁶ H/m.

This value is a consequence of the definition of the ampere in terms of forces between wires. In vacuum, the magnetic constant is the ratio of the magnetic B-field (for calculating Lorentz force) to the H-field (calculated from currents):

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

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.

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