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Concept
Vacuum permittivity
Summary
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. It is an ideal (baseline) physical constant. Its CODATA value is:
(farads per meter), with a relative uncertainty of
It is a measure of how dense of an electric field is "permitted" to form in response to electric charges and relates the units for electric charge to mechanical quantities such as length and force. 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 (known as the Coulomb constant, ke) is approximately 9 × 109 N⋅m2⋅C−2. 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.
The value of ε0 is defined by the formula
where c is the defined value for the speed of light in classical vacuum in SI units, and μ0 is the parameter that international Standards Organizations call the "magnetic constant" (commonly called vacuum permeability or the permeability of free space). Since μ0 has an approximate value 4π × 10−7 H/m, and c has the defined value 299 792 458 m⋅s−1, it follows that ε0 can be expressed numerically as
(or A2⋅s4⋅kg−1⋅m−3 in SI base units, or C2⋅N−1⋅m−2 or C⋅V−1⋅m−1 using other SI coherent units).
The historical origins of the electric constant ε0, and its value, are explained in more detail below.
2019 redefinition of the SI base units
The ampere was redefined by defining the elementary charge as an exact number of coulombs as from 20 May 2019, with the effect that the vacuum electric permittivity no longer has an exactly determined value in SI units.
Official source
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