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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.
For example, the CGS unit of force is the dyne, which is defined as 1 g⋅cm/s 2, so the SI unit of force, the newton (1 kg⋅m/s 2), is equal to 100 000 dynes. On the other hand, in measurements of electromagnetic phenomena (involving units of charge , electric and magnetic fields, voltage , and so on), converting between CGS and SI is less ...
Carl Friedrich Gauß in 1828, aged 50 years old. The gauss (symbol: G, sometimes Gs) is a unit of measurement of magnetic induction, also known as magnetic flux density.The unit is part of the Gaussian system of units, which inherited it from the older centimetre–gram–second electromagnetic units (CGS-EMU) system.
Coulomb's law in the CGS-Gaussian system takes the form =, where F is the force, q G 1 and q G 2 are the two electric charges, and r is the distance between the charges. This serves to define charge as a quantity in the Gaussian system.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).
The equations given above for the electric potential (and all the equations used here) are in the forms required by SI units. In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.
It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.
The integral version of Gauss's equation can thus be rewritten as = Since Ω is arbitrary (e.g. an arbitrary small ball with arbitrary center), this is satisfied if and only if the integrand is zero everywhere. This is the differential equations formulation of Gauss equation up to a trivial rearrangement.