
Permittivity of free space, a fundamental constantVacuum permittivity, denoted ε₀, is a fundamental constant that describes how much electric field is generated per unit charge in a vacuum. It appears in Coulomb's law and Maxwell's equations, setting the strength of the electric force between charges. Its value is approximately 8.854×10^-12 farads per meter, and it is one of the defining constants of the International System of Units (SI).
The concept of permittivity was developed in the 19th century by Michael Faraday and James Clerk Maxwell, who introduced ε₀ in his formulation of electromagnetism. Its precise value was historically determined experimentally, but since 2019 it is defined exactly in terms of the speed of light and the fine-structure constant.
In classical electromagnetism, ε₀ relates the electric displacement field D to the electric field E in a vacuum via D = ε₀E. It also appears in the speed of light in vacuum, c = 1/√(ε₀μ₀), where μ₀ is the vacuum permeability. The constant essentially measures how much 'resistance' the vacuum offers to the formation of an electric field.
It is essential in designing capacitors, transmission lines, and antennas, as it determines the capacitance of structures and the impedance of free space. It also appears in the calculation of the fine-structure constant, which governs atomic spectra.
The vacuum permittivity is so fundamental that its value was redefined in 2019 to be exactly 8.8541878128×10^-12 F/m, tying it to the speed of light and the elementary charge.
| V | variable | potential energy of electron — potential energy joule |
| z | variable | distance from the metal surface — position metre |
| φ | variable | work function of the metal — work function joule |
| F | variable | applied electric field strength — electric field volt per metre |
| e | constant | charge of a single proton — elementary charge = 1.602176634e-19 coulomb |
| ε0 | constant | ability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre |
| V_dep | variable | Depolarizing field voltage — voltage volt |
| P | variable | Polarization of the dielectric — polarization coulomb per metre squared |
| d | variable | Thickness of the dielectric film — thickness metre |
| ε₀ | constant | Permittivity of free space, a fundamental constant — vacuum permittivity = 8.8541878128e-12 farad per metre |
| εᵣ | constant | Dimensionless ratio of the material's permittivity to vacuum permittivity — relative permittivity |
| \omega_p | variable | plasma angular frequency — angular frequency radian per second |
| n | variable | electron number density — number density per cubic metre |
| e | variable | elementary charge — electric charge coulomb |
| m | variable | electron mass — mass kilogram |
| \epsilon_0 | constant | permittivity of free space — vacuum permittivity = 8.8541878128e-12 farad per metre |
| \sqrt{} | operator | takes the square root — square root |





