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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 gauss is the unit of magnetic flux density B in the system of Gaussian units and is equal to Mx/cm 2 or g/Bi/s 2, while the oersted is the unit of H-field. One tesla (T) corresponds to 10 4 gauss, and one ampere (A) per metre corresponds to 4π × 10 −3 oersted .
In physics (specifically electromagnetism), Gauss's law, also known as Gauss's flux theorem (or sometimes Gauss's theorem), is one of Maxwell's equations. It is an application of the divergence theorem , and it relates the distribution of electric charge to the resulting electric field .
Electric field from positive to negative charges. Gauss's law describes the relationship between an electric field and electric charges: an electric field points away from positive charges and towards negative charges, and the net outflow of the electric field through a closed surface is proportional to the enclosed charge, including bound charge due to polarization of material.
In both SI and Gaussian units, ε is defined by the equation D = εE. Hence, ε 0 is defined by the equation D = ε 0 E in a vacuum. In Gaussian units, D = E in a vacuum, and so ε 0 = 1. Coulomb's law in SI and Gaussian units is F = q 1 q 2 /(4πε 0 r 2) and F = q 1 q 2 /r 2, respectively.
The equations governing the plasma moments are called the moment or fluid equations. Below the two most used moment equations are presented (in SI units). Deriving the moment equations from the Vlasov equation requires no assumptions about the distribution function.
The magnetic diffusivity has SI units of m²/s and is defined as: [2] =, while in Gaussian units it can be defined as =. In the above, μ 0 {\displaystyle \mu _{0}} is the permeability of free space , c {\displaystyle c} is the speed of light, and σ 0 {\displaystyle \sigma _{0}} is the electrical conductivity of the material in question.
For unit variance, the n-th derivative of the Gaussian is the Gaussian function itself multiplied by the n-th Hermite polynomial, up to scale. Consequently, Gaussian functions are also associated with the vacuum state in quantum field theory. Gaussian beams are used in optical systems, microwave systems and lasers.