Editing Gaussian units (section)

=== Unit of charge ===

A major difference between the Gaussian system and the ISQ is in the respective definitions of the quantity charge. In the ISQ, a separate base dimension, electric current, with the associated SI unit, the [[ampere]], is associated with electromagnetic phenomena, with the consequence that a unit of electrical charge (1&nbsp;[[coulomb]]&nbsp;= 1&nbsp;ampere&nbsp;× 1&nbsp;second) is a physical quantity that cannot be expressed purely in terms of the mechanical units (kilogram, metre, second). On the other hand, in the Gaussian system, the unit of electric charge (the [[statcoulomb]], statC) {{em|can}} be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as:

{{block indent|1={{val|1|u=statC}} = {{val|1|u=g<sup>1/2</sup>⋅cm<sup>3/2</sup>⋅s<sup>−1</sup>}}.}}

For example, [[Coulomb's law]] in Gaussian units has no constant:
<math display="block">F = \frac{Q^{_\mathrm{G}}_1 Q^{_\mathrm{G}}_2}{r^2} ,</math>
where {{mvar|F}} is the repulsive force between two electrical charges, {{math|''Q''{{su|p={{small|G}}|b=1|lh=0.8em}}}} and {{math|''Q''{{su|p={{small|G}}|b=2|lh=0.8em}}}} are the two charges in question, and {{mvar|r}} is the distance separating them. If {{math|''Q''{{su|p={{small|G}}|b=1|lh=0.8em}}}} and {{math|''Q''{{su|p={{small|G}}|b=2|lh=0.8em}}}} are expressed in [[statC]] and {{mvar|r}} in [[centimetre]]s, then the unit of {{mvar|F}} that is coherent with these units is the [[dyne]].

The same law in the ISQ is:
<math display="block">F = \frac{1}{4\pi\varepsilon_0} \frac{Q^{_\mathrm{I}}_1 Q^{_\mathrm{I}}_2}{r^2}</math>
where {{math|''ε''{{sub|0}}}} is the [[vacuum permittivity]], a quantity that is not dimensionless: it has dimension ([[electric charge|charge]])<sup>2</sup> ([[time]])<sup>2</sup> ([[mass]])<sup>−1</sup> ([[length]])<sup>−3</sup>. Without {{math|''ε''{{sub|0}}}}, the equation would be dimensionally inconsistent with the quantities as defined in the ISQ, whereas the quantity {{math|''ε''{{sub|0}}}} does not appear in Gaussian equations.  This is an example of how some dimensional [[physical constant]]s can be eliminated from the expressions of [[physical law]] by the choice of definition of quantities.  In the ISQ, {{math|1/''ε''<sub>0</sub>}} converts or scales [[Electric displacement field|electric flux density]], {{math|'''D'''}}, to the corresponding [[electric field]], {{math|'''E'''}} (the latter has dimension of [[force]] per [[electric charge|charge]]), while in the Gaussian system, electric flux density is the same quantity as electric field strength in [[free space]] aside from a dimensionless constant factor.

In the Gaussian system, the [[speed of light]] {{mvar|c}} appears directly in electromagnetic formulas like [[Maxwell's equations]] (see below), whereas in the ISQ it appears via the product {{math|1=''μ''<sub>0</sub>''ε''<sub>0</sub> = 1/''c''<sup>2</sup>}}.