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The impedance of free space, Z_{0}, is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through free space. That is, Z_{0} = |E|/|H|, where |E| is the electric field strength and |H| magnetic field strength. It has an exact irrational value, given approximately as 376.73031... ohms.^{[1]}
The impedance of free space (more correctly, the wave-impedance of a plane wave in free space) equals the product of the vacuum permeability or magnetic constant μ_{0} and the speed of light in vacuum c_{0}. Since the numerical values of the magnetic constant and of the speed of light are fixed by the definitions of the ampere and the metre respectively, the exact value of the impedance of free space is likewise fixed by definition relative to the S.I. base units.
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 Z_{0} is sometimes referred to as the intrinsic impedance of free space,^{[2]} and given the symbol η_{0}.^{[3]} 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 .
Since 1948, the SI unit ampere has been defined by choosing the numerical value of μ_{0} to be exactly 4π×10^{−7} H/m. Similarly, since 1983 the SI metre has been defined by choosing the value of c_{0} to be 299 792 458 m/s. Consequently
or
It is very common in textbooks and learned papers written before about 1990 to substitute the approximate value for . This is equivalent to taking the speed of light to be 3×10^{8} m/s. For example, Cheng 1989 states^{[3]} 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