FACTOID # 21: 15% of Army recruits from South Dakota are Native American, which is roughly the same percentage for female Army recruits in the state.

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Encyclopedia > Gaussian units

CGS is an acronym for centimetre-gram-second. This is a system of physical units which preceded, and has largely been replaced by, the standard SI system (SI was based on the metre-kilogram-second system of units, hence the unofficial but occasionally used name mks). The cgs system is still in use; this is largely because many electromagnetic formulas are simpler in cgs units, but also because much of the older physics literature uses these units, and in some cases because they are more convenient in a particular context. Additionally, cgs units are still widely used in astronomy.

While for most units the difference between cgs and SI is a mere power of 10, the differences in electromagnetic units are considerable; so much so that formulas for physical laws need to be changed depending on what system of units one uses. In SI, electric current is defined via the magnetic force it exerts and charge is then defined as current multiplied with time. In one variant of the cgs system, esu, or electrostatic units, charge is defined via the force it exerts on other charges, and current is then defined as charge per time. One consequence of this approach is that Coulomb's law does not contain a constant of proportionality.

Ultimately, relating electromagnetic phenomena to time, length and mass relies on the forces observed on charges. There are two fundamental laws in action: Coulomb's law, which describes the electrostatic force between charges, and Ampère's law (also known as Biot-Savart's law), which describes the electrodynamic (or electromagnetic) force between currents. Each of these includes one fudge factor, the proportionality constants and . The static definition of magnetic fields yields a third proportionality constant, . The first two constants are related to each other through the speed of light, (the ratio of over must equal ).

We then have several choices:

yields
electrostatic cgs system
electromagnetic cgs system
Gaussian cgs system
SI

There are actually about half a dozen systems of electromagnetic units in use, most based on the cgs system. These include emu, or electromagnetic units (chosen such that the Biot-Savart Law has no constant of proportionality), Gaussian, and Heaviside-Lorentz units. A key virtue of the Gaussian CGS system is that electric and magnetic fields have the same units, both ε0 and μ0 are 1, and the only dimensional constant appearing in the equations is c, the speed of light. The Heaviside-Lorentz system has these desirable properties as well, but is a "rationalized" system (as is SI) in which the charges and fields are defined in such a way that there are many fewer factors of appearing in the formulas, and it is in Heaviside-Lorentz units that the Maxwell equations take their simplest possible form.

Further complicating matters is the fact that some physicists and engineers use hybrid units, such as volts per centimetre for electric field.

## Units

The units of cgs (specifically esu) are as follows:

The mantissas 2998, 3336, 1113, and 8988 are derived from the speed of light and are more precisely 299792458, 333564095198152, 1112650056, and 89875517873681764.

A centimetre of capacitance is the capacitance between a sphere of radius 1 cm in vacuum and infinity. The capacitance Cbetween two spheres of radii R and r is

. By taking the limit as R goes to infinity we see C equals r.

Results from FactBites:

 Units (741 words) In 1960 physicists throughout the world adopted the so-called S.I. system of units, whose standard measures of length, mass, time, and electric charge are the meter, kilogram, second, and coloumb, respectively. Admittedly, this is mostly an Anglo-Saxon phenomenon; the Gaussian system is most prevalent in the U.S., followed by Britain (although, the Gaussian system is rapidly dying out in Britain under the benign influence of the European Community). Incidentally, the standard units of length, mass, time, and electric charge in the Gaussian system are the centimeter, gram, second, and statcoloumb, respectively.
 PlanetMath: Gaussian integer (152 words) of all Gaussian integers is a subring of This is version 6 of Gaussian integer, born on 2001-10-15, modified 2003-10-08. For instance, they are a subring of the complex numbers, their graph on the complex plane forms a lattice of "squares", and they are a Euclidean domain.
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