Impedance of free space

In electromagnetism, the impedance of free space, Z₀, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, $${\displaystyle Z_{0}={\frac {|\mathbf {E} |}{|\mathbf {H} |}},}$$ where |E| is the electric field strength, and |H| is the magnetic field strength. Its presently accepted value is

where Ω is the ohm, the SI unit of electrical resistance. The impedance of free space (that is, the wave impedance of a plane wave in free space) is equal to the product of the vacuum permeability μ₀ and the speed of light in vacuum c₀. Before 2019, the values of both these constants were taken to be exact (they were given in the definitions of the ampere and the metre respectively), and the value of the impedance of free space was therefore likewise taken to be exact. However, with the revision of the SI that came into force on 20 May 2019, the impedance of free space as expressed with an SI unit is subject to experimental measurement because only the speed of light in vacuum c₀ retains an exactly defined value.

The analogous quantity for a plane wave travelling through a dielectric medium is called the intrinsic impedance of the medium and designated η (eta). Hence Z₀ is sometimes referred to as the intrinsic impedance of free space, and given the symbol η₀. It has numerous other synonyms, including:

From the above definition, and the plane wave solution to Maxwell's equations, $${\displaystyle Z_{0}={\frac {|\mathbf {E} |}{|\mathbf {H} |}}=\mu _{0}c={\sqrt {\frac {\mu _{0}}{\varepsilon _{0}}}}={\frac {1}{\varepsilon _{0}c}},}$$ where

The reciprocal of Z₀ is sometimes referred to as the admittance of free space and represented by the symbol Y₀.

Between 1948 and 2019, the SI unit the ampere was defined by choosing the numerical value of μ₀ to be exactly 4π × 10⁻⁷ H/m. Similarly, since 1983 the SI metre has been defined relative to the second by choosing the value of c₀ to be 299792458 m/s. Consequently, until the 2019 revision,

or

or