# Gaussian system of units

The Gaussian system of units , also known as the Gaussian CGS system or natural system of units , is a physical system of units that is based on the CGS system and supplements it with electromagnetic units. The Gaussian system of units takes the Coulomb law of force as the starting point for the definition of electromagnetic quantities and not, like the International System of Units (SI) , the Ampère law of force for two parallel conductors through which current flows . It should be clearly pointed out here that the difference between the Gaussian system and the SI is not just a question of the units, but that the quantities are introduced differently in the two systems and are therefore also measured in other units. Strictly speaking, the two systems of terms are different size systems .

In today's practice, the Gaussian system of units is rarely used in its purest form, in particular the units Statvolt and Statcoulomb are rarely used. A mixture of Gaussian units and units from the MKS system is used far more frequently , in which the electric field strength is given in volts per centimeter.

In theoretical physics, the Gaussian system of units is often preferred over the MKSA system because it gives the electrical and magnetic fields identical units, which is more logical, since these fields are just different components of the electromagnetic field strength tensor . They emerge from one another through the Lorentz transformation , so they are only different "forms" of electromagnetism in general and are not principally separable phenomena. Furthermore, the speed of light appears as a factor in this formulation of the Maxwell equations , which is helpful for relativistic considerations.

For some applications, Gaussian units, such as Gaussian for magnetic flux density , are preferred over the corresponding SI units, because then the numerical values ​​are easier to handle. For example, the earth's magnetic field is on the order of 1 Gauss.

## Transformation formulas

The following lists the formulas for transforming a formula given in Gauss' system of terms (without asterisk) into the international system of units (with asterisk). You can see that it's not just a simple change in units.

In addition, two field constants are  required in the SI - the electrical and the magnetic field constant - which do not exist in the Gaussian system. ${\ displaystyle \ varepsilon _ {0}}$ ${\ displaystyle \! \ \ mu _ {0}}$

The relationships apply

 electric field strength ${\ displaystyle {\ vec {E}} = {\ sqrt {4 \ pi \ varepsilon _ {0}}} \ cdot {\ vec {E}} ^ {*}}$ magnetic flux density ${\ displaystyle {\ vec {B}} = {\ sqrt {4 \ pi / \ mu _ {0}}} \ cdot {\ vec {B}} ^ {*}}$ electrical flux density ${\ displaystyle {\ vec {D}} = {\ sqrt {4 \ pi / \ varepsilon _ {0}}} \ cdot {\ vec {D}} ^ {*}}$ magnetic field strength ${\ displaystyle {\ vec {H}} = {\ sqrt {4 \ pi \ mu _ {0}}} \ cdot {\ vec {H}} ^ {*}}$ Space charge density ${\ displaystyle \ rho = {\ cfrac {\ rho ^ {*}} {\ sqrt {4 \ pi \ varepsilon _ {0}}}}}$ electric current density ${\ displaystyle {\ vec {j}} = {\ cfrac {{\ vec {j}} ^ {*}} {\ sqrt {4 \ pi \ varepsilon _ {0}}}}}$ ${\ displaystyle {\ cfrac {1} {c ^ {2}}} = \ varepsilon _ {0} \ mu _ {0}}$

This results in u. a. the conversion formulas for the material quantities electrical polarization and magnetization${\ displaystyle {\ vec {P}}}$ ${\ displaystyle {\ vec {M}}}$

${\ displaystyle {\ vec {D}} = {\ vec {E}} + 4 \ pi {\ vec {P}} \ Leftrightarrow {\ vec {D}} ^ {*} = \ varepsilon _ {0} { \ vec {E}} ^ {*} + {\ vec {P}} ^ {*} \ qquad {\ vec {H}} = {\ vec {B}} - 4 \ pi {\ vec {M}} \ Leftrightarrow {\ vec {H}} ^ {*} = {\ frac {1} {\ mu _ {0}}} {\ vec {B}} ^ {*} - {\ vec {M}} ^ { *}}$

as well as slightly different forms of Maxwell's equations.

## Electromagnetic units - comparison with other systems

Electromagnetic SI units and the corresponding units in three variants of the CGS system
Electromagnetic
quantity
unit Gaussian unit in cgs
SI ESU EMU Gauss
charge Q 1 C 10 −1 c statC 10 −1 ABC 10 −1 c Fr. Fr = statC = g 1/2 cm 3/2 s −1
Amperage I. 1 A 10 −1 c statA 10 −1 abA 10 −1 c statA statA = g 1/2 cm 3/2 s −2
tension U 1 V 10 8 c −1 statV 10 8 abV 10 8 c −1 statV statV = g 1/2 cm 1/2 s −1
electric field strength E. 1 V / m 10 6 c −1 statV / cm 10 6 abV / cm 10 6 c −1 statV / cm statV / cm = g 1/2 cm −1/2 s −1
electric dipole moment p 1 C · m 10 1 c statC · cm 10 1 abC cm 10 19 c D. D = g 1/2 cm 5/2 s −1
magnetic flux density B. 1 T 10 4 c −1 instead of 10 4 G 10 4 G G = g 1/2 cm −1/2 s −1
magnetic field strength H 1 A / m 4π · 10 −3  c statA / cm 4π · 10 −3 Oe 4π · 10 −3 Oe Oe = g 1/2 cm −1/2 s −1
magnetic dipole moment m, μ A · m 2 10 3 c statA cm 2 10 3 abA cm 2 10 3 erg / G G = g 1/2 cm 5/2 s −1
magnetic flooding Θ 1 A 4π · 10 −1 c statA 4π · 10 −1 abA 4π · 10 −1 Gb Gb = g 1/2 cm 1/2 s −1
magnetic river Φ 1 Wb 10 8 c −1 statT cm 2 10 8 G cm 2 10 8 Mx Mx = g 1/2 cm 3/2 s −1
resistance R. 1 Ω 10 9 c −2 s / cm 10 9 abΩ 10 9 c −2 s / cm cm −1 s
specific resistance ρ 1 Ω · m 10 11 c −2 s 10 11 abΩ cm 10 11  c −2 s s
capacity C. 1 F. 10 −9 c 2 cm 10 −9 abF 10 −9 c 2 cm cm
Inductance L. 1 H. 10 9 c −2 cm −1 s 2 10 9 fromH 10 9 c −2 cm −1 s 2 cm −1 s 2
electrical power P 1 V * A = 1 W = 10 7 erg / s 10 7 erg / s 10 7 erg / s erg / s = g cm 2 s −3

The "≙" symbol indicates that this is not a simple conversion of units of measure. The CGS sizes generally have a different dimension than the corresponding size in the SI . That is why it is usually not allowed to simply replace the units in formulas. c is the speed of light .

## literature

• A. Lindner: Basic course in theoretical physics. BG Teubner, Stuttgart 1994, p. 173 f.

## References and footnotes

1. See e.g. BU Krey, A. Owen: Basic Theoretical Physics - A Concise Overview. Springer, Berlin 2007, Chapter 16.1.