Gaussian units

Gaussiancgs-Gaussian unitsGaussian-cgs unitscgscgs unitsGaussian cgs unitscgs (Gaussian) system of unitsCGS-GaussianGaussian cgsgaussian electric charge
Gaussian units constitute a metric system of physical units.wikipedia
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Lorentz–Heaviside units

Heaviside–Lorentz unitsLorentz-Heaviside unitsHeaviside–Lorentz
Others include "electrostatic units", "electromagnetic units", and Lorentz–Heaviside units.
They share with CGS-Gaussian units the property that the electric constant

Centimetre–gram–second system of units

CGScgs unitsCGS unit
Others include "electrostatic units", "electromagnetic units", and Lorentz–Heaviside units. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units.
Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian units, "ESU", "EMU", and Lorentz–Heaviside units.

Natural units

natural unitGeometric variableshas been set to one
Some other unit systems are called "natural units", a category that includes atomic units, Planck units, and others.
, and in Gaussian units (also called "non-rationalized"), Coulomb's law is

Statcoulomb

esufranklinelectrostatic unit
On the other hand, in Gaussian units, the unit of electrical charge (the statcoulomb, statC) can be written entirely as a dimensional combination of the mechanical units (gram, centimetre, second), as:
This repulsion is governed by Coulomb's law, which in the Gaussian-cgs system states:

Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
On the other hand, the inverse-square force laws – Coulomb's law and the Biot–Savart law – do have a factor of 4π attached to the r 2.
Gaussian units and Lorentz–Heaviside units are both CGS unit systems.

Planck units

Planck scalePlanck epochPlanck density
Some other unit systems are called "natural units", a category that includes atomic units, Planck units, and others.
However, since the non-rationalized gravitational constant, G, is set to 1, a natural extension of Planck units to a unit of electric charge is to also set the non-rationalized Coulomb constant, k e, to 1 as well.

Hartree atomic units

atomic unitsatomic unita.u.
Some other unit systems are called "natural units", a category that includes atomic units, Planck units, and others.
There are two common variants of atomic units, one where they are used in conjunction with SI units for electromagnetism, and one where they are used with Gaussian-CGS units.

Magnetic field

magnetic fieldsmagneticmagnetic flux density
In Gaussian units, unlike SI units, the electric field E and the magnetic field B have the same dimension.
In Gaussian-cgs units,

Coulomb constant

Coulomb's constantCoulomb force constantelectrostatic constant
where ε 0 is the vacuum permittivity, a quantity with dimension, namely (charge) 2 (time) 2 (mass) −1 (length) −3, and k e is Coulomb's constant.
has an exact numeric value; in Gaussian units

Lorentz force

magnetic forceLorentz force lawLorentz
In cgs-Gaussian units, which are somewhat more common among theoretical physicists as well as condensed matter experimentalists, one has instead

Magnetic susceptibility

susceptibilitymagnetic susceptibilitiesvolume magnetic susceptibility
Another important point is that the electric and magnetic susceptibility of a material is dimensionless in both Gaussian and SI units, but a given material will have a different numerical susceptibility in the two systems.
However, many tables of magnetic susceptibility give cgs values (more specifically emu-cgs, short for electromagnetic units, or Gaussian-cgs; both are the same in this context).

Vacuum

free spaceevacuatedhigh vacuum
In SI, 1/ε 0, converts or scales flux density, D, to electric field, E (the latter has dimension of force per charge), while in rationalized Gaussian units, flux density is the very same as electric field in free space, not just a scaled copy.

Gauss (unit)

gaussGkG
The gauss, symbol G, sometimes Gs, is the cgs unit of measurement of magnetic flux density (or "magnetic induction") (B).

Vacuum permittivity

permittivity of free spaceelectric constantvacuum electric permittivity
where ε 0 is the vacuum permittivity, a quantity with dimension, namely (charge) 2 (time) 2 (mass) −1 (length) −3, and k e is Coulomb's constant.
In one of the systems of equations and units agreed in the late 19th century, called the "centimetre–gram–second electrostatic system of units" (the cgs esu system), the constant k e was taken equal to 1, and a quantity now called "gaussian electric charge" q s was defined by the resulting equation

Magnetic moment

magnetic dipole momentmagnetic momentsdipole moment
For example, in SI units, a loop of current with current I and area A has magnetic moment IA (see below), but in Gaussian units the magnetic moment is

Ampère's circuital law

Ampère's lawAmpere's lawAmpere's circuital law
In cgs units, the integral form of the equation, including Maxwell's correction, reads

Stokes' theorem

Stokes theoremStokes's theoremKelvin–Stokes theorem
Only the "differential form" of the equations is given, not the "integral form"; to get the integral forms apply the divergence theorem or Kelvin–Stokes theorem.
In other systems of units, such as CGS or Gaussian units, the scaling factors for the terms differ.

Electric potential

electrical potentialelectrostatic potentialCoulomb potential
In some other (less common) systems of units, such as CGS-Gaussian, many of these equations would be altered.

Magnetic potential

magnetic vector potentialvector potentialmagnetic scalar potential
In particular, in abstract index notation, the set of Maxwell's equations (in the Lorenz gauge) may be written (in Gaussian units) as follows:

Metric system

metricmetric unitsmetric unit
Gaussian units constitute a metric system of physical units.

Unit of measurement

unitunits of measurementweights and measures
Gaussian units constitute a metric system of physical units.