Impedance of free space


In electromagnetism, the impedance of free space,, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is,
where is the electric field strength, and 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 is equal to the product of the vacuum permeability and the speed of light in vacuum. Before 2019, the values of both these constants were taken to be exact, 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 while the speed of light in vacuum remains exactly defined, the use of an exact value of as the definition of the ampere has been replaced by a fixed value for the elementary charge, i.e. the charge on the electron.

Terminology

The analogous quantity for a plane wave travelling through a dielectric medium is called the intrinsic impedance of the medium and designated . Hence is sometimes referred to as the intrinsic impedance of free space, and given the symbol. It has numerous other synonyms, including:
From the above definition, and the plane wave solution to Maxwell's equations,
where
The reciprocal of is sometimes referred to as the admittance of free space and represented by the symbol.

Historical exact value

Between 1948 and 2019, the SI unit the ampere was defined by choosing the numerical value of to be exactly. Similarly, since 1983 the SI metre has been defined relative to the second by choosing the value of to be. Consequently, until the 2019 revision,
or
or
This chain of dependencies changed when the ampere was redefined on 20 May 2019.

Approximation as 120π ohms

It is very common in textbooks and papers written before about 1990 to substitute the approximate value 120 ohms for. This is equivalent to taking the speed of light to be precisely in conjunction with the then-current definition of as. For example, Cheng 1989 states that the radiation resistance of a Hertzian dipole is
This practice may be recognized from the resulting discrepancy in the units of the given formula. Consideration of the units, or more formally dimensional analysis, may be used to restore the formula to a more exact form, in this case to