Definition:Impedance of Free Space

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Definition

Impedance of free space is a physical constant relating the magnitudes of the electric and magnetic fields of electromagnetic radiation travelling through a vacuum.

It is defined as:

the quotient of the magnitudes of the electric field and magnetic fields of electromagnetic radiation travelling through a vacuum:
$\dfrac {\size {\mathbf E} } {\size {\mathbf H} }$
the vacuum permeability multiplied by the speed of light:
$\mu_0 c$
the square root of the quotient of the vacuum permeability by the vacuum permittivity:
$\sqrt {\dfrac {\mu_0} {\varepsilon_0} }$


Symbol

$Z_0$

The symbol for the impedance of free space is $Z_0$.


Its $\LaTeX$ code is Z_0 .


Dimension

The impedance of free space has the dimension $\mathsf {M L^2 T^{-3} I^{-2} }$.


This arises from its definition as:

electric field strength per unit magnetic field strength:
$\dfrac {\mathsf {M L T^{-3} I^{-1} } } {\mathsf {I L^{-1} } }$
vacuum permeability multiplied by the speed of light:
$\mathsf {M L T^{-2} I^{-2} } \times \mathsf {L T^{-1} }$
the square root of the quotient of the vacuum permeability by the vacuum permittivity:
$\sqrt {\dfrac {\mathsf {M L T^{-2} I^{-2} } } {\mathsf {M^{-1} L^{-3} T^4 I^2} } } = \sqrt {\mathsf {M^2 L^4 T^{-6} I^{-4} } }$


Units

The SI unit for the impedance of free space is the ohm:

$\Omega$


Value

The value of the impedance of free space expressed in SI units is:

$Z_0 = 376 \cdotp 730313668(57) \, \Omega$


Also known as

Impedance of free space is also variously known as:

  • intrinsic impedance of free space
  • wave impedance of free space
  • the vacuum impedance
  • intrinsic impedance of vacuum
  • characteristic impedance of vacuum
  • characteristic impedance of free space
  • wave resistance of free space


Historical Note

Prior to the redefinition of the SI units in $2019$, the impedance of free space was defined as $\mu_0 c$, where:

$\mu_0$ is the vacuum permeability, defined as (exactly) $4 \pi \times 10^{-7}$ henries per metre
$c$ is the speed of light, defined as (exactly) $299 \, 792 \, 458$ metres per second

leading to a value of:

$Z_0 := 4 \pi \times 29 \cdotp 97924 \, 58 \, \Omega$

that is:

$Z_0 := \pi \times 119 \cdotp 91698 \, 32 \, \Omega$

exactly.

This works out as:

$Z_0 \approx 376 \cdotp 73031 \, 34617 \, 7 \ldots \Omega$


Also, some older books define $Z_0$ to be:

$Z_0 = 120 \pi \, \Omega$

based on:

the above value of $\mu_0$ of $4 \pi \times 10^{-7}$ henries per metre
the popular approximation to $c$ of $3 \times 10^8$ metres per second.


Sources

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