Vacuum permittivity, commonly denoted ε0 (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum.
It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum.
[2] For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:
Here, q1 and q2 are the charges, r is the distance between their centres, and the value of the constant fraction
Likewise, ε0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources.
In electrical engineering, ε0 itself is used as a unit to quantify the permittivity of various dielectric materials.
where c is the defined value for the speed of light in classical vacuum in SI units,[4]: 127 and μ0 is the parameter that international standards organizations refer to as the magnetic constant (also called vacuum permeability or the permeability of free space).
The historical origins of the electric constant ε0, and its value, are explained in more detail below.
The ampere was redefined by defining the elementary charge as an exact number of coulombs as from 20 May 2019,[4] with the effect that the vacuum electric permittivity no longer has an exactly determined value in SI units.
with e being the elementary charge, h being the Planck constant, and c being the speed of light in vacuum, each with exactly defined values.
The relative uncertainty in the value of ε0 is therefore the same as that for the dimensionless fine-structure constant, namely 1.6×10−10.
Standards organizations also use "electric constant" as a term for this quantity.
[14][15] However, in modern usage "dielectric constant" typically refers exclusively to a relative permittivity ε/ε0 and even this usage is considered "obsolete" by some standards bodies in favor of relative static permittivity.
[13][16] Hence, the term "dielectric constant of vacuum" for the electric constant ε0 is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.
As for notation, the constant can be denoted by either ε0 or ϵ0, using either of the common glyphs for the letter epsilon.
Its presence in the equations now used to define electromagnetic quantities is the result of the so-called "rationalization" process described below.
But the method of allocating a value to it is a consequence of the result that Maxwell's equations predict that, in free space, electromagnetic waves move with the speed of light.
The experiments of Coulomb and others showed that the force F between two, equal, point-like "amounts" of electricity that are situated a distance r apart in free space, should be given by a formula that has the form
where Q is a quantity that represents the amount of electricity present at each of the two points, and ke depends on the units.
If one is starting with no constraints, then the value of ke may be chosen arbitrarily.
In one of the systems of equations and units agreed in the late 19th century, called the "centimetre–gram–second electrostatic system of units" (the cgs esu system), the constant ke was taken equal to 1, and a quantity now called "Gaussian electric charge" qs was defined by the resulting equation
The idea subsequently developed that it would be better, in situations of spherical geometry, to include a factor 4π in equations like Coulomb's law, and write it in the form:
Putting ke′ = 1 generates a unit of electricity of different size, but it still has the same dimensions as the cgs esu system.
The next step was to treat the quantity representing "amount of electricity" as a fundamental quantity in its own right, denoted by the symbol q, and to write Coulomb's law in its modern form:
In the 2019 revision of the SI, the elementary charge is fixed at 1.602176634×10−19 C and the value of the vacuum permittivity must be determined experimentally.
[18]: 132 One now adds the requirement that one wants force to be measured in newtons, distance in metres, and charge to be measured in the engineers' practical unit, the coulomb, which is defined as the charge accumulated when a current of 1 ampere flows for one second.
In order to establish the numerical value of ε0, one makes use of the fact that if one uses the rationalized forms of Coulomb's law and Ampère's force law (and other ideas) to develop Maxwell's equations, then the relationship stated above is found to exist between ε0, μ0 and c0.
In principle, one has a choice of deciding whether to make the coulomb or the ampere the fundamental unit of electricity and magnetism.
In the event that nonlocality and delay of response are not important, the result is:
In the vacuum of classical electromagnetism, the polarization P = 0, so εr = 1 and ε = ε0.