# Dictionary Definition

cgs n : system of measurement based on
centimeters and grams and seconds [syn: cgs
system]

# User Contributed Dictionary

## English

### Alternative forms

CGS

- The system of measurement taking the centimeter, gram and second as its fundamental units.

# Extensive Definition

The centimetre-gram-second system (CGS) is a
system of physical
units. It is always the same for mechanical units, but there
are several variants of electric additions. It was replaced by the
MKS,
or metre-kilogram-second system, which in turn was
replaced by the
International System of Units (SI), which has the three base
units of MKS plus the ampere, mole,
candela and kelvin.

The system goes back to a proposal made in 1833
by the German mathematician Carl
Friedrich Gauss and was in 1874 extended by the British
physicists James
Clerk Maxwell and
William Thomson with a set of electromagnetic units. The sizes
(order of magnitude) of many CGS units turned out to be
inconvenient for practical purposes, therefore the CGS system never
gained wide general use outside the field of electrodynamics and
was gradually superseded internationally starting in the 1880s but
not to a significant extent until the mid-20th century by the more
practical MKS (metre-kilogram-second) system, which led eventually
to the modern SI standard units.

CGS units are still occasionally encountered in
technical literature, especially in the United States in the fields
of electrodynamics and
astronomy. SI units
were chosen such that electromagnetic equations concerning spheres
contain 4π, those concerning coils contain 2π and those dealing
with straight wires lack π entirely, which was the most convenient
choice for electrical-engineering applications. In those fields
where formulas concerning spheres dominate (for example, astronomy), it has been argued
that the CGS system can be notationally slightly more
convenient.

Starting from the international adoption of the
MKS standard in the 1940s and the SI standard in the 1960s, the
technical use of CGS units has gradually disappeared worldwide, in
the United
States more slowly than in the rest of the world. CGS units are
today no longer accepted by the house styles of most scientific
journals, textbook publishers and standards bodies, although they
are commonly used in astronomical journals such as the Astrophysical
Journal.

The units gram and centimetre remain useful
within the SI, especially for instructional physics and chemistry
experiments, where they match well the small scales of table-top
setups. In these uses, they are occasionally referred to as the
system of “LAB” units. However, where derived units are needed, the
SI ones are generally used and taught today instead of the CGS
ones.

## CGS units in electromagnetism

While for most units the difference between cgs and SI are just powers of 10, the differences in electromagnetic units are more involved — so much so that formulas for physical laws of electromagnetism are adjusted 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, Electrostatic
units (ESU), 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. What this means specifically is
that in cgs electrostatic units, the unit of charge or statcoulomb, is defined as
such a quantity of charge that the Coulomb
force constant is set to 1. That is, for two point charges,
each with 1 statcoulomb spaced apart by 1 centimetre, the electrostatic
force between them will be, by definition, precisely one dyne. This also has the effect of
eliminating a separate dimension
or fundamental
unit for electric charge. In cgs electrostatic units, a
statcoulomb is the same as a centimetre times square root of dyne.
Dimensionally in the cgs esu system, charge Q is equivalent to
M1/2L3/2T−1 and not an independent dimension of physical quantity.
This reduction of units is an application of the Buckingham
π theorem.

While the proportional constants in cgs simplify
theoretical calculations, they have the disadvantage that the units
in cgs are hard to define through experiment. SI on the other hand
starts with a unit of current, the ampere which is easy to determine
through experiment, but which requires that the constants in the
electromagnetic equations take on odd forms.

Ultimately, relating electromagnetic phenomena to
time, length and mass relies on the forces observed on charges.
There are two fundamental laws in action. The first is Coulomb's
law, which describes the electrostatic force between charges
\left( F = k_C q q^\prime / r^2 \right). The second is Ampère's
force law, which describes the electrodynamic (or
electromagnetic) force between currents ( dF / dl = 2 k_A I
I^\prime / d for two long parallel wires). The proportionality
constants in these two equations are related by k_C / k_A = c^2,
where c is the speed of
light. The static definition of magnetic fields (Biot-Savart
law) yields a third proportionality constant, α, which
establishes convenient dimensions.

If we wish to describe the
electric displacement field \vec D and the magnetic
field \vec H in a medium other than a vacuum, we need to also
define the constants ε0 and μ0, which are the vacuum
permittivity and permeability,
respectively. These two values are related by \sqrt=\alpha / c.
Then we have (generally) \vec D = \epsilon_0 \vec E + \lambda \vec
P and \vec H = \vec B / \mu_0 - \lambda^\prime \vec M. The factors
λ and λ′ are rationalization constants, which are usually chosen to
both be equal to 4πkCε0, which is dimensionless. If this quantity
equals 1, the system is said to be rationalized.

The table below shows the constant values used in
some common systems:

(The b in SI is a scaling factor equal to
107 A2/N = 107 m/H.)

In system-independent form, Maxwell's
equations can be written

\begin \vec \nabla \cdot \vec E & = & 4
\pi k_C \rho \\ \vec \nabla \cdot \vec B & = & 0 \\ \vec
\nabla \times \vec E & = & \displaystyle \\ \vec \nabla
\times \vec B & = & \displaystyle \end

The mantissas
derived from the speed of
light 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 C between two concentric spheres of radii R and r
is

- \frac.

## Physical constants in CGS units

## Other variants

There were at various points in time about half a dozen systems of electromagnetic units in use, most based on the cgs system. These include electromagnetic units (emu, chosen such that the Biot-Savart law has no constant of proportionality), Gaussian units, and Heaviside-Lorentz units.Further complicating matters is the fact that
some physicists and engineers in
the United States use hybrid units, such as volts per centimetre for electric
field. In fact, this is essentially the same as the SI unit system,
by the variant to translate all lengths used into cm, e.g.
1 m = 100 cm. More difficult is to translate
electromagnetic quantities from SI to cgs, which is also not hard,
e.g. by using the three relations q'=q/\sqrt, \mathbf
E'=\mathbf E\cdot \sqrt, and \mathbf B'=\mathbf B\cdot\sqrt, where
\epsilon_0(\,\,\equiv 1/(c^2\mu_0)) and \mu_0 are the well-known
vacuum permittivities and c the corresponding light velocity,
whereas q, \,\,\mathbf E and \mathbf B are the electrical charge,
electric field, and magnetic induction, respectively, without
primes in a SI system and with primes in a cgs system.

However, the above-mentioned example of hybrid
units can be also simply be seen as a practical example of the
previously described "LAB" units usage since electric fields near
small circuit devices would be measured across distances on the
order of magnitude of one centimetre.

## Pro and contra

A key virtue of the Gaussian CGS system is that electric and magnetic fields have the same units, 4\pi\epsilon_0 is replaced by 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 (with \epsilon_0 equalling 1), 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 4 \pi appearing in the formulas, and it is in Heaviside-Lorentz units that the Maxwell equations take their simplest possible form.At the same time, the elimination of \epsilon_0
and \mu_0 can also be viewed as a major disadvantage of all the
variants of the CGS system. Within classical
electrodynamics, this elimination makes sense because it
greatly simplifies the Maxwell equations. In quantum
electrodynamics, however, the vacuum is no longer just empty
space, but it is filled with virtual particles that interact in
complicated ways. The fine
structure constant in Gaussian CGS is given as \alpha=e^2/\hbar
c and it has been cause to much mystification how its numerical
value \alpha \approx 1/137.036 should be explained. In SI units
with \alpha = e^2/4 \pi \epsilon_0\hbar c it may be clearer that it
is in fact the complicated quantum structure of the vacuum that
gives rise to a non-trivial vacuum permittivity. However, the
advantage would be purely pedagogical, and in practice, SI units
are essentially never used in quantum electrodynamics calculations.
In fact the high energy community uses a system where every
quantity is expressed by only one unit, namely by eV, i.e. lengths
L by the corresponding reciprocal quantity \frac \equiv L=\frac,
where the Einstein expression corresponding to m_L, E_L=m_L\,\,c^2,
is an energy, which thus can naturally be expressed in eV
(\hbar is Plancks constant divided by 2\pi).

## See also

## References

## General references

- Introduction to Electrodynamics (3rd ed.)
- Classical Electrodynamics (3rd ed.)

CGS in Asturian: Sistema Ceguesimal

CGS in Belarusian (Tarashkevitsa): СГС (сыстэма
адзінак вымярэньня)

CGS in Bulgarian: Система
сантиметър-грам-секунда

CGS in Catalan: Sistema CGS

CGS in Czech: Soustava CGS

CGS in German: CGS-Einheitensystem

CGS in Spanish: Sistema Cegesimal de
Unidades

CGS in Esperanto: CGS

CGS in Persian: دستگاه واحدهای
سانتیمتر-گرم-ثانیه

CGS in French: Système CGS

CGS in Galician: Sistema CGS

CGS in Korean: CGS 단위계

CGS in Indonesian: CGS

CGS in Icelandic: CGS-kerfi

CGS in Italian: Sistema CGS

CGS in Hebrew: יחידות cgs

CGS in Dutch: Cgs-systeem

CGS in Japanese: CGS単位系

CGS in Norwegian: CGS-systemet

CGS in Norwegian Nynorsk: CGS-systemet

CGS in Polish: Układ jednostek miar CGS

CGS in Portuguese: Sistema CGS de unidades

CGS in Romanian: Sistemul CGS de unităţi

CGS in Russian: СГС

CGS in Slovak: Sústava CGS

CGS in Finnish: Cgs-järjestelmä

CGS in Swedish: Cgs-systemet

CGS in Turkish: C.G.S.

CGS in Chinese: 厘米-克-秒制