electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge via electromagnetic fields. The electromagnetic force is one of the four fundamental forces of nature. It is the dominant force in the interacti ...

, the impedance of free space, , is a

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...

relating the magnitudes of the

electric Electricity is the set of physical phenomena associated with the presence and motion of matter possessing an electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described by Maxwel ...

and

magnetic field A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular ...

s of

electromagnetic radiation In physics, electromagnetic radiation (EMR) is a self-propagating wave of the electromagnetic field that carries momentum and radiant energy through space. It encompasses a broad spectrum, classified by frequency or its inverse, wavelength ...

travelling through

free space A vacuum (: vacuums or vacua) is space devoid of matter. The word is derived from the Latin adjective (neuter ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressur ...

. That is,

Z_0 = \frac,

where is the

electric field strength An electric field (sometimes called E-field) is a field (physics), physical field that surrounds electrically charged particles such as electrons. In classical electromagnetism, the electric field of a single charge (or group of charges) descri ...

, and is the

magnetic field strength A magnetic field (sometimes called B-field) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicula ...

. 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 (1 ...

, the

SI unit The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of units of measurement, system of measurement. It is the only system ...

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 paral ...

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

plane wave In physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of ...

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'', ''magnetic constant'') is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally ...

and the

speed of light in vacuum The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

. 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 1 c ...

and the

metre The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of ...

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 retains an exactly defined value.

Terminology

The analogous quantity for a

travelling through a

dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electric ...

medium Medium may refer to: Aircraft *Medium bomber, a class of warplane * Tecma Medium, a French hang glider design Arts, entertainment, and media Films * ''The Medium'' (1921 film), a German silent film * ''The Medium'' (1951 film), a film vers ...

is called the '' intrinsic impedance'' of the medium and designated (

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

). 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 plane wave 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, Electrical network, electr ...

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

where : H/ m is the

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

, also known as the permeability of free space, : F/m 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, : is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

in free space,"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 interrelationships and their presentation. It was revised and re ...

. 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 revision, :

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 is that part of an antenna's feedpoint electrical resistance caused by the emission of radio waves from the antenna. A radio transmitter applies a radio frequency alternating current to an antenna, which radiates the energy ...

of a

Hertzian dipole In radio and telecommunications a dipole antenna or doublet is one of the two simplest and most widely used types of antenna; the other is the monopole. The dipole is any one of a class of antennas producing a radiation pattern approxima ...

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, 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