The impedance of free space, , is a

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant ...

relating the magnitudes of the electric and magnetic fields of

electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...

travelling through

free space A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often ...

. That is, , where is the electric field strength and is the magnetic field strength. Its presently accepted value is :. Where Ω is the

ohm Ohm (symbol Ω) is a unit of electrical resistance named after Georg Ohm. Ohm or OHM may also refer to: People * Georg Ohm (1789–1854), German physicist and namesake of the term ''ohm'' * Germán Ohm (born 1936), Mexican boxer * Jörg Ohm (bor ...

, the

SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallel ...

. The impedance of free space (that is the wave impedance of a

plane wave In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. For any position \vec x in space and any time t, ...

in free space) is equal to the product of the

vacuum permeability The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, ...

and the

speed of light in vacuum The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

. Before 2019, the values of both these constants were taken to be exact (they were given in the definitions of the

ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...

and the

metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pre ...

respectively), and the value of the impedance of free space was therefore likewise taken to be exact. However, with the

redefinition of the SI base units In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144t ...

that came into force on 20 May 2019, the impedance of free space is subject to experimental measurement because only the speed of light in vacuum retains an exactly defined value.

Terminology

The analogous quantity for a

travelling through a

dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the ma ...

medium Medium may refer to: Science and technology Aviation * Medium bomber, a class of war plane * Tecma Medium, a French hang glider design Communication * Media (communication), tools used to store and deliver information or data * Medium ...

is called the ''

intrinsic impedance The wave impedance of an electromagnetic wave is the ratio of the transverse components of the electric and magnetic fields (the transverse components being those at right angles to the direction of propagation). For a transverse-electric-magnetic ...

'' of the medium, and designated (

eta Eta (uppercase , lowercase ; grc, ἦτα ''ē̂ta'' or ell, ήτα ''ita'' ) is the seventh letter of the Greek alphabet, representing the close front unrounded vowel . Originally denoting the voiceless glottal fricative in most dialects, ...

). Hence is sometimes referred to as the ''intrinsic impedance of

'', and given the symbol . It has numerous other synonyms, including: * ''wave impedance of free space'', * ''the vacuum impedance'', * ''intrinsic impedance of vacuum'', * ''characteristic impedance of vacuum'', * ''wave resistance of free space''.

Relation to other constants

From the above definition, and the

solution to

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...

Z_0 = \frac = \mu_0 c = \sqrt = \frac

where * is the

magnetic constant The vacuum magnetic permeability (variously ''vacuum permeability'', ''permeability of free space'', ''permeability of vacuum''), also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constan ...

, also known as the permeability of free space ≈ Henries/meter, * is the

electric constant Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric const ...

, also known as the permittivity of free space ≈ Farads/meter, * is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...

."Current practice is to use to denote the speed of light in vacuum according to

ISO 31 ISO 31 ( Quantities and units, International Organization for Standardization, 1992) is a superseded international standard concerning physical quantities, units of measurement, their interrrelationships and their presentation. It was revised and ...

. In the original Recommendation of 1983, the symbol was used for this purpose." Quote fro
NIST ''Special Publication 330'', Appendix 2, p. 45
. 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

was defined by ''choosing'' the numerical value of to be exactly . Similarly, since 1983 the SI

has been defined relative to the second by ''choosing'' the value of to be . Consequently until the 2019 redefinition, :

Z_0 = \mu_0 c = 4\pi \times 29.979\,2458~\Omega

''exactly'', or :

Z_0 = \mu_0 c = \pi \times 119.916\,9832~\Omega

''exactly'', or :

Z_0 = 376.730\,313\,461\,77\ldots~\Omega.

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 Radiation resistance, \ R_\mathsf\ or \ R_\mathsf\ , is proportional to the part of an antenna's feedpoint electrical resistance that is caused by power loss from the emission of radio waves from the antenna. Radiation resistance is an ''effecti ...

of a Hertzian dipole is :

R_r \approx 80 \pi^2 \left( \frac\right)^2

(''result in ohms; not exact''). 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 In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measure (such as mi ...

, may be used to restore the formula to a more exact form, in this case to :

R_r = \frac Z_0 \left( \frac\right)^2.

Terminology

Relation to other constants

Historical exact value

Approximation as 120π ohms

See also

References and notes

Further reading