What is the CGS Unit of Radioactivity

CGS system of units

The CGS system of units (also CGS system, cgs system, CGS or cgs, from English "centimetre GR.A.M second ") is a metric, coherent system of units based on the units centimeter, Gram and second. The CGS units of the mechanics can be clearly derived from these basic units, but there are several competing extensions of the CGS system for electromagnetic units. The four most common variants are:

Only the Gaussian system of units has significant significance today, with “CGS unit” in modern literature mostly a Gaussian CGS unit is meant.

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 basic units meter, kilogram and second, replaced. The MKS in turn became the basic electromagnetic unit amp expanded (then often referred to as the MKSA system) and finally went in 1960 in Système International d'Unités (SI) on which today also the base units Mole, Candela and Kelvin includes. In most fields, the SI is the only common system of units, but there are areas in which the CGS - especially its expanded forms - is still used.

Because CGS and MKS (or the SI in the field of mechanics) are based on the same size system with the basic sizes length, Dimensions and time the dimensional products of the derived units are the same in both systems. A conversion between units is limited to multiplication with a pure number factor. To simplify matters, there is also the fact that conversion factors only occur in powers of 10, as results from the relationships 100 cm = 1 m and 1000 g = 1 kg. An example: For the force, the derived CGS unit is the dyn (corresponds to 1 g cm s−2) and the derived MBS unit is the Newton (corresponds to 1 kg · m · s−2). The conversion is therefore 1 dyn = 10−5 N.

On the other hand, conversions between electromagnetic units of the CGS and those of the MKSA are quite cumbersome. While the MKSA introduces the ampere as a unit for the electrical current, none of the extensions to the CGS requires an additional base unit. Instead, the proportionality constants are defined by definition in Coulomb's law (electrical permittivity), Ampère's law and Faraday's law of induction. The various sensible options in the definition have led to the various forms of the CGS system. In any case, all electromagnetic units can be traced back to the three purely mechanical base units. However, this not only changes the dimensional products of those derived units, but also the form of physical equations of magnitude in electrodynamics (see e.g. Maxwell's equations). There is therefore no one-to-one correspondence between the electromagnetic units of the MKSA (or the SI) and the CGS, not even between the different CGS variants. In addition to a pure numerical factor, conversions also include the size values ​​of the above constants saved in the CGS.

The principle of fixing natural constants (instead of introducing basic units) can also be transferred to other areas of physics and has led to the development of further systems of units such as the atomic system of units. The SI also relies on this method in its more recent incarnations; In contrast to the CGS and other systems of units, the previous base units are still continued as such.

CGS units of mechanics

As in other systems of units, the CGS units comprise two groups of units, the base units and the derived units. The latter can be written as the product of powers (power product) of the base units. Since the system is coherent ("connected"), there are no further numerical factors in the power products. For any size CGS unit G Does that mean mathematically:

$ [G] = \ mathrm {cm} ^ \ alpha \, \ mathrm {g} ^ \ beta \, \ mathrm {s} ^ \ gamma $

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

$ \ dim G = L ^ \ alpha \, M ^ \ beta \, T ^ \ gamma $

L, M and T are the dimension symbols of the basic quantities length, mass and time time).

Since the MKS system of units uses the same basic quantities, the dimension of a quantity is the same in both systems (the same bases and the same exponents in the dimension product). Because of the two different base units, both base units are correct in the unit equation s only the exponents match. Formally, the conversion is:

$ [G] _ {\ text {MKS}} = \ mathrm {m} ^ \ alpha \, \ mathrm {kg} ^ \ beta \, \ mathrm {s} ^ \ gamma = 10 ^ {2 \ alpha + 3 \ beta} \, \ mathrm {cm} ^ \ alpha \, \ mathrm {g} ^ \ beta \, \ mathrm {s} ^ \ gamma = 10 ^ {2 \ alpha + 3 \ beta} \, [G] _ {\ text {CGS}} $

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

CGS derived units with special names

Some derived CGS units have their own names and unit symbols (symbols) that can be combined with all base and derived units. For example, the CGS unit of power is suitable, that dyn (= g cm / s2) to the unit of energy that erg to be expressed as dynes times centimeters (dyn · cm). The following table lists the named units.

size unit Units-
character
in other CGS units
expressed
in CGS base units
expressed
in SI units
expressed
Gravity accelerationGal Gal cm / s2 cm · s−2 10−2 m · s−2
force dyn dyn g cm / s2 cm g s−2 10−5 N
printBarye Ba dyn / cm2 cm−1· G · s−2 10−1 Pa
Energy, workerg erg dyn · cm cm2· G · s−2 10−7 J
Kinematic viscosity Stokes St. cm2/ s cm2· S−1 10−4 m2· S−1
Dynamic viscosity Poise P. g / (cm s) cm−1· G · s−1 10−1 Pa · s
WavenumberKayser kayser 1 cm cm−1 102 m−1

CGS units of electrodynamics

General formulation of electrodynamics

Electrodynamic quantities are linked to mechanical quantities via several laws of nature. The electrodynamics itself is completely described by Maxwell's equations, which can be formulated independently of the system of units with the help of two proportionality constants $ \ alpha_1 $ and $ \ alpha_2 $:

$ \ begin {align} \ operatorname {div} \, \ vec E & = \ alpha_1 \, \ rho \ ;, & \ operatorname {div} \, \ vec B & = 0 \ ;, \ \ operatorname {red } \, \ vec E & = - \ frac {\ alpha_1} {\ alpha_2} \, \ frac {\ partial \ vec B} {\ partial t} \ ;, & \ operatorname {red} \, \ vec B & = \ frac {1} {c ^ 2} \ alpha_2 \, \ vec j + \ frac {1} {c ^ 2} \, \ frac {\ alpha_2} {\ alpha_1} \, \ frac {\ partial \ vec E} {\ partial t} \ ;, \ end {align} $

where $ \ rho $ means the charge density and $ \ vec j $ means the electric current density. As can be seen from the above equations, the constant $ \ alpha_1 $ connects the electric charge $ Q $ with the electric field strength $ \ vec E $ (Coulomb's law) and the constant $ \ alpha_2 $ the electric current $ I $ with the magnetic flux density $ \ vec B $ (Ampère's law). The constant ratio $ \ alpha_2 / \ alpha_1 $ and its reciprocal value describes the dependence of the electric and magnetic field when these change over time (displacement current and induction law).

Every system of units of mechanics can be extended to describe electrodynamics by defining the size values ​​of 2 of the 3 constants $ \ alpha_1 $, $ \ alpha_2 $ and $ \ alpha_2 / \ alpha_1 $. In principle, there are three ways to do this:

  • Introduction of two new basic units for electrical charge $ Q $ and electrical current $ I $. As a result, the above constants become measured variables that are subject to a measurement uncertainty.
  • Choice of a new base unit for either $ Q $ or $ I $ and the explicit definition of a constant. The remaining constants are then faulty measured variables.
  • Dispensing with new base units by explicitly defining two constants. This also defines the third constant and does not contain errors.

In the SI, the second approach was taken with the introduction of the ampere as a unit of $ I $ and the definition $ \ alpha_2 / \ alpha_1 = 1 $. All extensions to the CGS system, however, rely on the third way. The following table summarizes the different systems of units.

System of units $ \ alpha_1 $$ \ alpha_2 $$ \ alpha_2 / \ alpha_1 $
Electrostatic CGS system $ 4 \ pi $$ 4 \ pi $ 1
Electromagnetic CGS system $ 4 \ pi c ^ 2 $$ 4 \ pi c ^ 2 $ 1
Gaussian CGS system$ 4 \ pi $$ 4 \ pi c $$ c $
Heaviside-Lorentz unit system 1 $ c $$ c $
International System of Units (SI)[E 1]$ 4 \ pi \ cdot 10 ^ {- 7} \ mathrm {\ frac {N} {A ^ 2}} \ cdot c ^ 2 $$ 4 \ pi \ cdot 10 ^ {- 7} \ mathrm {\ frac {N} {A ^ 2}} \ cdot c ^ 2 $ 1
  1. ↑ The SI introduces the ampere (A) as an independent base unit. The official definition of the ampere implies a definition of $ \ mu_0 $ = 4π · 10−7 N / A2. The following also applies: $ \ alpha_1 = \ alpha_2 = \ mu_0c ^ 2 $.

Electromagnetic units in various CGS systems

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

literature

  • Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins. 3. Edition. Springer, 2004, ISBN 1-85233-682-X.