Magnetic constant

The magnetic constant μ₀ (also known as vacuum permeability or 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.

This value is a consequence of the definition of the ampere in terms of forces between wires, see Ampère's equation. 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):

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

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