Cegesimal System of Units
The Cegesimal System of Units, also called the CGS system or Gaussian system, is a system of units based on the centimeter, the gram and the second. Its name is the acronym for these three units.
It was proposed by Gauss in 1832, and implemented by the British Association for the Advancement of Science (BAAS, now BA) in 1874 including the rules for forming a system made up of base units and derived units.
The CGS system has been almost completely replaced by the International System of Units (SI). However, its use still persists in some very specific scientific and technical fields, with advantageous results in some contexts. Thus, many of the formulas of electromagnetism have a simpler form when expressed in CGS units, making it simpler to expand the terms into v/c.
The International Office of Weights and Measures, regulator of the SI, values and recognizes these facts and includes in its bulletins references and equivalences of some electromagnetic units of the Gaussian CGS system, although it advises against their use.
Electromagnetic Units
Unlike the SI, the CGS system does not determine whether there should be an additional dimension for electromagnetic quantities (in the SI is the current). Hence there are several cegesimale systems depending on how constants are treated ε ε 0{displaystyle epsilon} and μ μ 0{displaystyle mu _{0}}. The equations are adjusted according to the concrete system adopted, although in practice it is only used more than that of Gauss, where both constants are taken as 1 and in turn appears explicitly c. The dimensions, so, can have semi-enteran exponents.
In the SI, electric current is defined by the intensity of the magnetic field it presents, and electric charge is defined as electric current per unit of time. In one variety of CGS, the ues or electrostatic units, charge is defined as the force exerted on other charges, and current is defined as charge per unit time. One consequence of this method is that Coulomb's law does not contain a constant of proportionality.
Finally, when relating electromagnetic phenomena to time, length, and mass, they depend on the observed forces on charges. There are two fundamental laws at work: Coulomb's law, which describes the electrostatic force between charges, and Ampère's law (also known as the Biot-Savart law), which describes the electrodynamic force (or electromagnetic) between currents.
Each of them contains the constants of k1{displaystyle k_{1},!} and k2{displaystyle k_{2},!}. The static definition of magnetic field has another constant, α α {displaystyle alpha ,!}. The first two constants relate to each other through the speed of light, c{displaystyle c,!} (the reason between k1{displaystyle k_{1},!} and k2{displaystyle k_{2},!} must be equal to c2{displaystyle c^{2},!}).
This way you have several options:
| k1{displaystyle k_{1},!} | k2{displaystyle k_{2},!} | α α {displaystyle alpha ,!} | System |
|---|---|---|---|
| 1{displaystyle 1,!} | 1/c2{displaystyle 1/c^{2},!} | 1{displaystyle 1,!} | Electrostatic GS |
| c2{displaystyle c^{2},!} | 1{displaystyle 1,!} | 1{displaystyle 1,!} | Electromagnetic CGS |
| 1{displaystyle 1,!} | 1/c2{displaystyle 1/c^{2},!} | 1/c{displaystyle 1/c,!} | CGS Gausiano |
| 14π π ε ε 0{displaystyle {frac {1}{4pi epsilon _{0}}}}{,!} | μ μ 04π π {displaystyle {frac {mu _{0}}{4pi }}{,!} | 1{displaystyle 1,!} | Yes |
A feature of the Gaussian CGS system is that the electric field and magnetic field have the same units. There are about half a dozen electromagnetic drive systems in use, most based on the CGS system. These include the EMU or electromagnetic units (chosen such that the Biot-Savart law has no constant of proportionality), Gaussian, and Heaviside-Lorentz units. To further complicate matters, some engineers use hybrid units for the electric field, such as volts per centimeter.
In the old system of electromagnetic units based on the CGS that was used to study magnetic induction, the unit of current is not the statampere, but the abampere (=10 amps), which allows us to define the gauss as unit of magnetic flux density.
In the following table you will find the statampere and the gauss as belonging to the modern CGS system; this is inaccurate: the gauss is not a CGS quantity, but an electromagnetic one.
Units of the cegesimal system
| Magnitude | Unit | Symbol | Definition | Equivalence in S.I. |
|---|---|---|---|---|
| length | centimeter | cm | 0.01 m | |
| mass | gram | g | 0.001 kg | |
| time | Second | s | 1 s | |
| Acceleration | gal | Gal | cm/s2 | 0.01 m/s2 |
| strength | d | dyn | g.cm/s2 | 10−5 N |
| energy | ergio | erg | dyn cm | 10−7 J |
| power | Ergio per second | erg/s | erg s−1 | 10−7 W |
| Pressure | baria | baria | dyn/cm2 | 0.1 Pa |
| dynamic viscosity | poise | P | g (cm s)−1 | 0.1 Pa s |
| cinematic viscosity | stokes | St. | cm2−1 | 10−4 m2s−1 |
| electric charge | Franklin | Fr | dyn1⁄2cm | 3,336 641 × 10−10 C |
| electric potential | statvoltio | statV | erg Fr−1 | 299,7925 V |
| electric field | statvoltio per centimeter | statV/cm | stat−1 | 2.9979 V m−1 |
| magnetic flow | maxwell | Mx | G cm2 | 10−8 Wb |
| Magnetic flow density | gauss | G | Mx cm−2 | 10−4 T |
| magnetic field intensity | oersted | Oe | (103/4π) A/m | |
| current intensity | Estatamperio | statA | 3.335 641 × 10−10 A | |
| resistance | statohmio | statΩ | 8.987 552 × 1011 Ω | |
| electrical capacity | or «centimeter» | «cm» | 1,113 × 10−12 F | |
| inductance | estathenrio | statH | 8,988 × 1011 H | |
| wave number | kayser | K | 1 cm−1 | 100 m−1 |
The coefficients 2998, 3336, 1113 and 8988 are derived from the speed of light; They are exactly worth 299792458, 333564095198152, 1112650056 and 89875517873681764.
A "centimeter" of capacitance is the capacitance of a conducting sphere, 1 cm in radius, in a vacuum.
In the CGS (Gauss) system, inductance has dimensions of length, and therefore, the unit of inductance is called centimeter (1H = 109 cm). And, conversely, 1 cm of CGS inductance is equal to 9.174 mH in the International System of Measurements.
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