Vacuum permeability

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The vacuum permeability, referred to by international standards organizations as the magnetic constant, and denoted by the symbol μ₀ (also called the permeability of free space and of empty space), is a fundamental physical constant, relating mechanical and electromagnetic units of measurement. In the International System of Units (SI), its value is defined in free space (not measured see defined variables, Table 1 in CODATA report) as:

mu_0  overset{underset{mathrm{def}}{}}{=} 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 the force per unit length between infinitely long parallel wires of zero cross-section in vacuum. For a discussion of this force, see Serway and Jewett, or Monk. See also Ampère's force law.

In vacuum, the magnetic constant defines the value of the magnetic field strength, or H-field (calculated from currents) in terms of the magnetic flux density, or B-field (for calculating Lorentz force):

mathbf{B} = mu_0  mathbf{H}.

See Maxwell's equations.

The magnetic constant μ₀ is related to two other defined constants, the electric constant ε₀ and the speed of light in vacuum c₀ according to the identity:

{c_0}^2 , epsilon_0 , mu_0 = 1

Terminology

Historically, the constant μ₀ has had different names. (In the 1987 IUPAP Red book, for example, this constant was still called permeability of vacuum.) Another, now rather rare and obsolete, term is "magnetic permittivity of vacuum". See, for example, Servant et al. The term "vacuum permeability" (and variations thereof) remains very widespread, but standards organizations have recently moved to magnetic constant as a uniform term for this quantity, although the older term continues to be listed as a synonym.

The term "magnetic constant" avoids the term "permeability" and "vacuum" because it is a defined value, not the result of experimental measurement.

The linear permeability of vacuum is impossible to measure because it defines the ampere, in the same way that the speed of light in vacuum is now impossible to measure because it defines the meter; by definition of the units, the permeability of vacuum is μ₀.

The permeability of vacuum refers to a baseline state in free space. See the free space and vacuum state articles for detail about this ideal reference state.

Vacuum permeability

Terminology

Footnotes

See also