constant

vacuum permittivity

Permittivity of free space, a fundamental constant
Value
\(\varepsilon_0 = 8.8541878128 \times 10^{-12}\)farad per metre
14 related articles · 3 formulas

Description

Vacuum 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).

History

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.

How it works

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.

In practice

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.

Fun fact

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.

Concept graph →

Formulas

$$V(z) = \phi - eFz - \frac{e^2}{4\pi\epsilon_0 z}$$
Potential energy for electron emission including work function and field.
What is in the formula
Vvariablepotential energy of electron — potential energy joule
zvariabledistance from the metal surface — position metre
φvariablework function of the metal — work function joule
Fvariableapplied electric field strength — electric field volt per metre
econstantcharge of a single proton — elementary charge = 1.602176634e-19 coulomb
ε0constantability of vacuum to permit electric field lines — vacuum permittivity = 8.8541878128e-12 farad per metre
$$V_{\text{dep}} = \frac{P d}{\varepsilon_0 \varepsilon_r}$$
Voltage opposing polarization in a dielectric film of thickness d.
What is in the formula
V_depvariableDepolarizing field voltage — voltage volt
PvariablePolarization of the dielectric — polarization coulomb per metre squared
dvariableThickness of the dielectric film — thickness metre
ε₀constantPermittivity of free space, a fundamental constant — vacuum permittivity = 8.8541878128e-12 farad per metre
εᵣconstantDimensionless ratio of the material's permittivity to vacuum permittivity — relative permittivity
$$\omega_p = \sqrt{\frac{n e^2}{m \epsilon_0}}$$
Natural frequency of charge density oscillations.
What is in the formula
\omega_pvariableplasma angular frequency — angular frequency radian per second
nvariableelectron number density — number density per cubic metre
evariableelementary charge — electric charge coulomb
mvariableelectron mass — mass kilogram
\epsilon_0constantpermittivity of free space — vacuum permittivity = 8.8541878128e-12 farad per metre
\sqrt{}operatortakes the square root — square root

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