Definition:Vacuum Permeability/Historical Note

Historical Note on Vacuum Permittivity

Before the redefinition of the SI base units on $20$ May $2019$, the vacuum permeability was defined as exactly $4 \pi \times 10^{-7} \, \mathrm H \, \mathrm m^{-1}$ (henries per metre).

As a consequence, the vacuum permittivity was defined as

$\varepsilon_0 = 8 \cdotp 85418 \, 78176 \, 2039 \times 10^{-12} \, \mathrm F \, \mathrm m^{-1}$ (farads per metre)

which was derived from the equation:

$\varepsilon_0 := \dfrac 1 {\mu_0 c^2}$

where $c$ is the speed of light defined as exactly $299 \, 792 \, 458 \, \mathrm m \, \mathrm s^{-1}$.

However, since $20$ May $2019$, the vacuum permeability has been redefined to be dependent upon the newly redefined electric charge on the electron, as follows:

$\mu_0 = \dfrac {2 \alpha} {e^2} \dfrac h c$

where:

$\alpha$ is the fine-structure constant

$e$ is the elementary charge

$h$ is Planck's constant

$c$ is the speed of light.

As a consequence, $\mu_0$ is now dependent upon the measured quantity $\alpha$, and its value is approximately:

$\mu_0 \approx 4 \pi \times 1 \cdotp 00000 \, 00005 \, 5 (15) \times 10^{-7} \, \mathrm H \, \mathrm m^{-1}$