Value of Vacuum Permittivity/Proof 1

Proof
The vacuum permittivity is the physical constant denoted $\varepsilon_0$ defined as:


 * $\varepsilon_0 := \dfrac {e^2} {2 \alpha h c}$

where:
 * $e$ is the elementary charge
 * $\alpha$ is the fine-structure constant
 * $h$ is Planck's constant
 * $c$ is the speed of light defined in $\mathrm m \, \mathrm s^{-1}$

$e$ is defined precisely as:
 * $e = 1 \cdotp 60217 \, 6634 \times 10^{-19} \, \mathrm C$ (coulombs)

$\alpha$ has the value determined experimentally as:
 * $\alpha \approx 0 \cdotp 00729 \, 73525 \, 693 (11)$

$h$ is defined precisely as:
 * $h = 6 \cdotp 62607 \, 015 \times 10^{-34} \, \mathrm J \, \mathrm s$ (joule seconds)

$c$ is defined precisely as:
 * $c = 299 \, 792 \, 458 \, \mathrm m \, \mathrm s^{-1}$ (metres per second)

Hence $\varepsilon_0$ can be calculated as: