Editing Gaussian units (section)

=== "Rationalized" unit systems ===

One difference between the Gaussian and SI systems is in the factor {{math|4''π''}} in various formulas that relate the quantities that they define. With SI electromagnetic units, called ''rationalized'',<ref name=Littlejohn>{{cite web | url=http://bohr.physics.berkeley.edu/classes/221/1112/notes/emunits.pdf | title=Gaussian, SI and Other Systems of Units in Electromagnetic Theory | work=Physics 221A, University of California, Berkeley lecture notes|author-link1=Robert Grayson Littlejohn | author=Littlejohn, Robert | date=Fall 2017 | access-date=2018-04-18 }}</ref><ref name=Kowalski>Kowalski, Ludwik, 1986, [http://alpha.montclair.edu/~kowalskiL/SI/SI_PAGE.HTML "A Short History of the SI Units in Electricity"], {{webarchive |url=https://web.archive.org/web/20090429035624/http://alpha.montclair.edu/~kowalskiL/SI/SI_PAGE.HTML |date=2009-04-29 }}  ''The Physics Teacher'' 24(2): 97–99. [https://dx.doi.org/10.1119/1.2341955 Alternate web link (subscription required)]</ref> [[Maxwell's equations]] have no explicit factors of {{math|4''π''}} in the formulae, whereas the [[inverse-square law|inverse-square]] force laws &ndash; [[Coulomb's law]] and the [[Biot–Savart law]] &ndash; {{em|do}} have a factor of {{math|4''π''}} attached to the {{math|''r''{{i sup|2}}}}. With Gaussian units, called ''unrationalized'' (and unlike [[Heaviside–Lorentz units]]), the situation is reversed: two of Maxwell's equations have factors of {{math|4''π''}} in the formulas, while both of the inverse-square force laws, Coulomb's law and the Biot–Savart law, have no factor of {{math|4''π''}} attached to {{math|''r''{{i sup|2}}}} in the denominator.

(The quantity {{math|4''π''}} appears because {{math|4''πr''{{i sup|2}}}} is the [[sphere#Surface area|surface area of the sphere]] of radius {{mvar|r}}, which reflects the geometry of the configuration. For details, see the articles ''[[Gauss's law#Relation to Coulomb's law|Relation between Gauss's law and Coulomb's law]]'' and ''[[Inverse-square law]]''.)