Gaussian units

This means that the equations that express physical laws of electromagnetism—such as Maxwell's equations—will change depending on the system of quantities that is employed.

In engineering and practical areas, SI is nearly universal and has been for decades.

[1] In technical, scientific literature (such as theoretical physics and astronomy), Gaussian units were predominant until recent decades, but are now getting progressively less so.

[1][b] The 8th SI Brochure mentions the CGS-Gaussian unit system,[2] but the 9th SI Brochure makes no mention of CGS systems.

One difference between the Gaussian and SI systems is in the factor 4π in various formulas that relate the quantities that they define.

With Gaussian units, called unrationalized (and unlike Heaviside–Lorentz units), the situation is reversed: two of Maxwell's equations have factors of 4π in the formulas, while both of the inverse-square force laws, Coulomb's law and the Biot–Savart law, have no factor of 4π attached to r2 in the denominator.

(The quantity 4π appears because 4πr2 is the surface area of the sphere of radius r, which reflects the geometry of the configuration.

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 coulomb = 1 ampere × 1 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) can be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as: For example, Coulomb's law in Gaussian units has no constant:

where ε0 is the vacuum permittivity, a quantity that is not dimensionless: it has dimension (charge)2 (time)2 (mass)−1 (length)−3.

This amounts to a factor of c between how B is defined in the two unit systems, on top of the other differences.

There are further differences between Gaussian system and the ISQ in how quantities related to polarization and magnetization are defined.

For one thing, in the Gaussian system, all of the following quantities have the same dimension: EG, DG, PG, BG, HG, and MG. A further point is that the electric and magnetic susceptibility of a material is dimensionless in both the Gaussian system and the ISQ, but a given material will have a different numerical susceptibility in the two systems.

Most symbol names are not given; for complete explanations and definitions, please click to the appropriate dedicated article for each equation.

A simple conversion scheme for use when tables are not available may be found in Garg (2012).

It is assumed here for simplicity that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permittivity is a simple constant.

Again, it is assumed that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permeability is a simple constant.

are both unitless, but has different numeric values in the two systems for the same material:

A physical example is: Take a parallel-plate capacitor, which has a "leaky" dielectric with permittivity 1 but a finite resistivity.

After charging it up, the capacitor will discharge itself over time, due to current leaking through the dielectric.

This result is independent of the size, shape, and charge of the capacitor, and therefore this example illuminates the fundamental connection between resistivity and time units.

A number of the units defined by the table have different names but are in fact dimensionally equivalent – i.e., they have the same expression in terms of the base units cm, g, s. (This is analogous to the distinction in SI between newton-metre and joule.)

The different names help avoid ambiguities and misunderstandings as to what physical quantity is being measured.

For example, the electric field of a stationary point charge has the ISQ formula

where r is distance, and the "I" superscript indicates that the electric field and charge are defined as in the ISQ.

If we want the formula to instead use the Gaussian definitions of electric field and charge, we look up how these are related using Table 1, which says:

which is the correct Gaussian-system formula, as mentioned in a previous section.

To convert any formula from the Gaussian system to the ISQ using this table, replace each symbol in the Gaussian column by the corresponding expression in the SI column (vice versa to convert the other way).

[9][10][11][d] After the rules of the table have been applied and the resulting formula has been simplified, replace all combinations