- Terminology
- Relation to other constants
- Exact value
- Approximation as 120π ohms
- See also
- References and notes
- Further reading
The impedance of free space, {{math|Z0}}, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, {{math|1=Z0 = {{sfrac|{{abs|E}}|{{abs|H}}}}}}, where {{math|{{abs|E}}}} is the electric field strength and {{math|{{abs|H}}}} is the magnetic field strength. It currently has an exactly defined value
The impedance of free space (more correctly, the wave impedance of a plane wave in free space) equals the product of the vacuum permeability {{math|μ0}} and the speed of light in vacuum {{math|c0}}. Since the values of these constants are exact (they are given in the definitions of the ampere and the metre respectively), the value of the impedance of free space is likewise exact. However, with the redefinition of the SI base units which are going into force on May 20, 2019, this value is subject to experimental measurement.
Terminology
The analogous quantity for a plane wave travelling through a dielectric medium is called the intrinsic impedance of the medium, and designated {{math|η}} (eta). Hence {{math|Z0}} is sometimes referred to as the intrinsic impedance of free space,[1] and given the symbol {{math|η0}}.[2] It has numerous other synonyms, including:
- wave impedance of free space,[2]
- the vacuum impedance,[3]
- intrinsic impedance of vacuum,[4]
- characteristic impedance of vacuum,[5]
- wave resistance of free space.[6]
Relation to other constants
From the above definition, and the plane wave solution to Maxwell's equations,
where
{{math|μ0}} is the magnetic constant,
{{math|ε0}} is the electric constant,
{{math|c0}} is the speed of light in free space.[7][8]
The reciprocal of {{math|Z0}} is sometimes referred to as the admittance of free space and represented by the symbol {{math|Y0}}.
Exact value
Since 1948, the definition of the SI unit ampere has relied upon choosing the numerical value of {{math|μ0}} to be exactly {{nowrap|4{{pi}} × {{val|e=-7|u=H/m}}}}. Similarly, since 1983 the SI metre has been defined relative to the second by choosing the value of {{math|c0}} to be {{val|299792458|u=m/s}}. Consequently,
exactly,
or
This chain of dependencies will change when the ampere is redefined on 20 May 2019. See New SI definitions.
Approximation as 120π ohms
It is very common in textbooks and papers written before about 1990 to substitute the approximate value 120{{pi}} ohms for {{math|Z0}}. This is equivalent to taking the speed of light {{math|c0}} to be precisely {{val|3|e=8|u=m/s}} in conjunction with the current definition of {{math|μ0}}. For example, Cheng 1989 states[2] that the radiation resistance of a Hertzian dipole is
(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
See also
- Electromagnetic wave equation
- Mathematical descriptions of the electromagnetic field
- Near and far field
- Planck impedance
- Sinusoidal plane-wave solutions of the electromagnetic wave equation
- Space cloth
- Vacuum
- Wave impedance
References and notes
Further reading
- {{cite book
|author=John David Jackson
|title=Classical electrodynamics
|edition=Third
|publisher= Wiley
|location=New York
|year=1998
|isbn=0-471-30932-X
|url=http://worldcat.org/isbn/047130932X}}
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