Definition:Vacuum Permittivity/Historical Note

Historical Note on Vacuum Permittivity
Before the redefinition of the SI base units on $20$ May $2019$, the vacuum permittivity was:


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

which was derived from the equation:
 * $\varepsilon_0 := \dfrac 1 {\mu_0 c^2}$

where:
 * $\mu_0$ is the vacuum permeability defined as exactly $4 \pi \times 10^{-7} \, \mathrm H \, \mathrm m^{-1}$ (henries per metre)
 * $c$ 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:
 * $\mu_0 \approx 4 \pi \times 1 \cdotp 00000 \, 00005 \, 5 (15) \times 10^{-7} \, \mathrm H \, \mathrm m^{-1}$

Some older sources interject the following:
 * $\varepsilon_0 = \dfrac 1 {36 \pi} \times 10^{-9}$

based on the well-known estimate of the speed of light $3 \times 10^8 \mathrm {m \, s^{-1} }$.

This works out at:
 * $\varepsilon_0 \approx 8 \cdotp 84194 \, 1283 \ldots$