Electric constant

The electric constant (also: vacuum permittivity or permittivity of free space), designated ε₀, is a physical constant, an electromagnetic property of classical vacuum, appearing in equations relating electrical charge to mechanical quantities in the SI system of units, for example in Coulomb's law. In scalar form, Coulomb's law can be given as:

$F={\frac {1}{4\pi \varepsilon _{0}}}\ {\frac {\left|q_{1}q_{2}\right|}{r^{2}}}$,

where F is the magnitude of the force between two point charges q₁ and q₂, separated by a distance r and located in an idealized medium sometimes called simply "vacuum" (although it is not intended to imply that this ideal medium is in fact physically realizable as some real "vacuum") and sometimes called free space.

Its value is given by

$\varepsilon _{0}={\frac {1}{\mu _{0}c^{2}}}$,

where c is the speed of light in vacuum and μ₀ is the magnetic constant. In the SI system of units, c is defined and μ₀ is a consequence of the definition of the ampere: μ₀ = 4π × 10⁻⁷ N/A². Consequently, ε₀ has an exact value and to ten digits is expressed by:

$\varepsilon _{0}={\frac {10^{7}{\mbox{ A}}^{2}{\mbox{/N}}}{4\pi \,c^{2}}}=8.854\;187\;817...10^{-12}{\mbox{ F/m}}$ ;

Alternatively, the electric constant is sometimes given in the form of the constant factor that appears in Coulomb's law,

${\frac {1}{4\pi \varepsilon _{0}}}=8.987\ 551\ 787...10^{9}$ N m²/C².

The uncertainty denoted by dots after the last digits is not related to some experimental uncertainty, but is a consequence of the impossibility of expressing an irrational number with a finite number of decimal figures. Despite the sometimes used name of "vacuum permittivity", this defined value cannot be interpreted as a measured property of any real medium that one might refer to as a "vacuum".

Terminology

Historically, the physical constant ε₀ has had different names. One of these was dielectric constant of vacuum. Although still in use, "dielectric constant" is now deemed obsolete. In the 1987 IUPAP Red book this constant was called permittivity of vacuum. Currently the nomenclature is electric constant. The vacuum permittivity ε = ε_r ε₀ is equal to the electric constant ε₀.