epsilonzero

The vacuum permittivity, denoted ε0 and also called the absolute permittivity, is a fundamental physical constant that characterizes how electric fields propagate through free space. It appears in Coulomb's law, Maxwell's equations, and the expression for the energy stored in electric fields. In vacuum, the electric displacement field D is proportional to the electric field E by D = ε0 E.

In the International System of Units (SI), ε0 has a value of approximately 8.854187817 × 10^-12 farads per meter (F/m). This value is derived from measurements of the speed of light and the vacuum permeability, μ0. Since the 2019 redefinition of SI units, the speed of light c is defined exactly, while μ0 is a measured quantity; ε0 is thus determined through the relation ε0 = 1/(μ0 c^2).

Key relationships involving ε0 include Coulomb's law, where the force between point charges q1 and q2 separated by a distance r is F = (1/(4π ε0)) q1 q2 / r^2. The force constant k = 1/(4π ε0) is about 8.9875 × 10^9 N m^2 C^-2. In Maxwell's equations, Gauss's law in differential form is ∇·E = ρ/ε0, and the energy density of the electric field is u_E = (1/2) ε0 E^2. The speed of light satisfies c^2 = 1/(μ0 ε0), and the impedance of free space is Z0 = √(μ0/ε0) ≈ 377 ohms.

ε0 thus plays a central role in linking electric phenomena to the fabric of space, setting the scale for how electric fields interact in vacuum.