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Vacuum permittivity, commonly denoted ε 0 (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.
Generally, when σ / ωε′ ≪ 1 we consider the material to be a low-loss dielectric (although not exactly lossless), whereas σ / ωε′ ≫ 1 is associated with a good conductor; such materials with non-negligible conductivity yield a large amount of loss that inhibit the propagation of electromagnetic waves, thus are also ...
The name "magnetic constant" was briefly used by standards organizations in order to avoid use of the terms "permeability" and "vacuum", which have physical meanings. The change of name had been made because μ 0 was a defined value, and was not the result of experimental measurement (see below). In the new SI system, the permeability of vacuum ...
Susceptability is the ratio of induced polarisation density to the inducing field. In cgs, the polarisation density is Bi/cm, while the inducing field is in Oe, or Gb/cm. The ratio of Bi/Gb is 4pi Gb = 1 Bi. This is why in CGS, one sees epsilon = epsilon-0 + 4 pi × susceptability. Wendy.krieger 08:53, 4 October 2011 (UTC)
One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define. With SI electromagnetic units, called rationalized, [3] [4] Maxwell's equations have no explicit factors of 4π in the formulae, whereas the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
the Pi function, i.e. the Gamma function when offset to coincide with the factorial; the complete elliptic integral of the third kind; the fundamental groupoid; osmotic pressure; represents: Archimedes' constant (more commonly just called Pi), the ratio of a circle's circumference to its diameter; the prime-counting function
1 q HL 2 / (4πr 2) in the HL system. The unit of charge then connects to 1 dyn⋅cm 2 = 1 statC 2 = 4π HLC 2, where 'HLC' is the HL unit of charge. The HL quantity q HL describing a charge is then √ 4π times larger than the corresponding Gaussian quantity. There are comparable relationships for the other electromagnetic quantities (see below).
Any epsilon number ε has Cantor normal form =, which means that the Cantor normal form is not very useful for epsilon numbers.The ordinals less than ε 0, however, can be usefully described by their Cantor normal forms, which leads to a representation of ε 0 as the ordered set of all finite rooted trees, as follows.