# 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).

### Gauss's law for magnetism

**Gauss' law for magnetismGauss's lawfor magnetism**

### 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.

### Oersted

**megagauss oerstedsOeOERSTEDS**

### 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.