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Permittivity of Free Space (ε₀)

A fundamental physical constant representing the ability of a vacuum to permit electric fields, crucial in Coulomb's Law.
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The statement of the theorem

In the vacuum (r⃗∈R3\vec{r} \in \mathbb{R}^3, t=0t=0), the electric displacement field D⃗\vec{D} is defined by the linear constitutive relation D⃗=ϵ0E⃗\vec{D} = \epsilon_0 \vec{E}, where E⃗\vec{E} is the electric field. The constant ϵ0\epsilon_0 is rigorously determined by the requirement that the electric field energy density ueu_e must satisfy the Hamiltonian density formulation derived from the Lagrangian density L\mathcal{L}: ue=12D⃗⋅E⃗=12ϵ0E⃗2u_e = \frac{1}{2} \vec{D} \cdot \vec{E} = \frac{1}{2} \epsilon_0 \vec{E}^2 Furthermore, ϵ0\epsilon_0 is related to the vacuum permeability μ0\mu_0 and the speed of light cc by the fundamental identity derived from Maxwell's equations: ϵ0=1μ0c2\epsilon_0 = \frac{1}{\mu_0 c^2}
Source: Wikipedia