Centimetre–gram–second system of units

The CGS system of units ( CGS also system cgs system, CGS or cgs, from the English " Centimetre Gram Second" ) is a metric, coherent system of units based on the units of centimeters, grams and seconds. The CGS units of mechanics can be clearly derived from these base units, but there are several competing extensions of the CGS system of electromagnetic units. The four most common variants are:

• The electromagnetic CGS system of units ( EMU ),
• The electrostatic cgs system of units ( ESU),
• The Gaussian system of units and
• The Heaviside - Lorentz system of units.

Considerable importance has now only the Gaussian unit system, with " CGS unit " in modern literature is mostly a Gaussian CGS unit meant.

• 3.1 General formulation of electrodynamics
• 3.2 Electromagnetic units in various CGS systems

Overview

The CGS system was introduced in 1874 by the British Association for the Advancement of Science and in 1889 by the MKS system of units based on the SI units meter, kilogram, and second, detached. The FMD was in turn extended to the electromagnetic base unit ampere ( then often referred to as MKSA system called ) and finally went in 1960 to the Système International d' Unités (SI), which also now includes the basic units of mole, candela and kelvin. In most fields, the SI is the only common unit system, but there are areas where the CGS - especially its extended forms - is still used.

Since CGS and MKS are based (or SI in the field of mechanics) on the same size system with the base units of length, mass and time, the dimension of the products derived units in both systems are the same. A conversion between units is limited to the multiplication by a pure numerical factor. To simplify matters worse, only conversion factors occur in powers of 10, as it is starting 1 kg results of the relations 100 cm = 1 m and 1000 g. An example: For the force the derived CGS unit is the dyne (equivalent to 1 g · cm · s -2) and the derived MKS unit Newton (equivalent to 1 kg · m · s -2). This is the conversion of 1 dyn = 10-5 N.

On the other hand, conversions between electromagnetic units of the CGS and those of MKSA are quite cumbersome. While the MKSA this introduces the ampere as the unit of electric current, none of the extensions of the CGS requires a more basic unit. Instead, the proportionality constant in Coulomb's law ( electric permittivity), defined in the Ampère law and Faraday 's law of induction by definition. The various meaningful choices in the definition have led to the different characteristics of the CGS system. In any case, let all electromagnetic units on the three purely mechanical base units traced. However, this does not change only the dimensions of those products derived units, but also the shape of the physical variable equations of electrodynamics (see eg Maxwell's equations ). There is therefore not a one -to-one correspondence between the electromagnetic units of the MKSA (or SI) and CGS, even between different CGS variants with one another. Conversions include, in addition to a pure numerical factor just the size values ​​of the above, savings in CGS constants.

The principle of codification of fundamental constants (instead of the introduction of basic units ) can also be applied to other areas of physics and has led development of other systems of units such as the atomic unit system. Also, the SI uses in his younger incarnations on this method; In contrast to the CGS and other unit systems, the existing base units will still continue to operate as such.

CGS units of the mechanism

As in other unit systems also, the CGS units include two unit groups, the base units and derived units. The latter can be written respectively as a product of powers ( power product ) of the base units. Since the system is consistent ( " coherent "), is coming to the potency products have no further numerical factors. For the CGS unit of any size G that is mathematically:

Here, cm, g and s is the unit character of the base units centimeter, gram, and second. The exponents α, β, and γ are each a positive or negative integers or zero. Unit above equation can be represented as a corresponding dimension of the equation:

Here, L, M, and T is the dimension sign of base quantities length, mass and time (English time).

Since the MKS unit system uses the same basic parameters is the dimension of a size in both systems (same bases and equal exponents in the Product dimension ). Because of the two different base units agree in the unity equation in addition to the base s match only the exponent. Formal is the translation:

Each CGS unit thus corresponds unambiguously to a MKS unit, they only differ by a numerical factor.

Derived CGS units with special names

Some derived CGS units were assigned their own names and symbols ( symbols) that can be re- combined with all base and derived units themselves. Thus, for example, is the CGS unit of force, the dyne ( = g · cm/s2 ) to the unit of energy, the erg as Dyn times centimeter ( dyn · cm) to express. The following table lists the designated units.

CGS units of electrodynamics

General formulation of electrodynamics

Electrodynamic sizes are linked via several natural laws with mechanical quantities. The electrodynamics itself is completely described by Maxwell's equations, which can be independent of the unit system with the help of two constants of proportionality and formulate:

Wherein the charge density and the electric current density means. As can be seen from the above equations, the constant ( Coulomb's law ), and the constant, the electric charge associated with the electric field strength of the electric current with the magnetic flux density ( law Ampèresches ). The constant ratio and its inverse describes the dependence of the electric and magnetic field when they change over time ( displacement current and induction law ).

Each unit system of mechanics can be extended to describe the electrodynamics by the size values ​​of 2 of the 3 constants, and are determined. Principle, there are three ways to open:

• Introduction of two new basic units of the electric charge and electric current. This will be above constants to the variables that are associated with an uncertainty.
• Election of a new base unit either for or for and the explicit definition of a constant. The remaining constants are then faulty measurements.
• Waiver on new bases by explicit definition of two constants. The third constant is determined thereby and not faulty.

In the SI system, the second way with the introduction of the ampere as a unit and of the definition has been trodden. All extensions of the CGS system set whilst on the third way. The following table summarizes the different systems of units together.

Electromagnetic units in various CGS systems

In the table, the following abbreviations for electromagnetic CGS units are used with special names:

• D = Debye
• Fr = Franklin,
• G = Gaussian,
• Mx = Maxwell