Download centimetre-gram-second system (CGS) is a system of physical units

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 1832 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gradually superseded internationally starting in the 1880s but not to a significant extent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 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.
The e.m.u. system within which the abvolt, etc., were defined was itself based on the
setting of the value of magnetic permeability to 1; in 1901 it was realized that, were
permeability set at 10-7 rather than 1, the whole array of practical terms shown above
fitted unchanged into the metric m.k.s. system without any multipliers. Thus, what began
as part of a c.g.s. system became very readily part of the m.k.s. system, which was
increasingly favoured, and ultimately the like-structured SI system.
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
. The second is Ampère's law, which describes the electrodynamic (or
electromagnetic) force between currents
for two long parallel
wires). The proportionality constants in these two equations are related by kC / kA = c2,
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 and the magnetic field 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
. Then we have (generally)
and
. 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:
system
electrostatic (esu)
electromagnetic (emu)
Gaussian
Heaviside-Lorentz
SI
kC
1
c2
1
1/4π
c2/b
α
1
1
c
c
1
ε0
1
c-2
1
1
b/(4πc2)
Electrostatic units
The electrostatic system of units is a system of units used to measure electrical quantities
of electric charge, current, and voltage, within the centimeter gram second (or "CGS")
metric system of units. In electrostatic units, electrical charge is defined via the force it
exerts on other charges. Although CGS units have mostly been supplanted by the MKS or
"International System of Units" (SI) units, electrostatic units are still in use in some
applications, most notably physics.
The main electrostatic units are:



Statcoulomb or "esu" for charge
Statvolt for voltage
Gauss for magnetic induction
Dimension
Unit
Definition
SI
electrostatic unit of charge, 1 esu = 1 statC = 1 Fr
charge
= 3.33564 × 10−10 C
franklin, statcoulomb
= √(g·cm³/s²)
= 3.33564 × 10−10
electric current biot
1 esu/s
C/s
electric potential statvolt
1 statV = 1 erg/esu = 299.792458 V
1 statV/cm = 1
= 2.99792458 × 104
electric field
dyn/esu
V/m
magnetic field
= 1000/(4π) A/m =
oersted
1 Oe
strength H
79.577 A/m
magnetic flux maxwell
1 Mw = 1 G·cm²
= 10−8 Wb
magnetic
gauss
1 G = 1 Mw/cm²
= 10−4 T
induction B
resistance
1 s/cm
= 8.988 × 1011 Ω
resistivity
1s
= 8.988 × 109 Ω·m
capacitance
1 cm
= 1.113 × 10−12 F
inductance
statH
= 8.988 × 1011 H
wavenumber kayser
1 /cm
= 100 /m
The mantissas derived from the speed of light are more precisely 299
Mks system of units
A physical system of units that expresses any given measurement using fundamental
units of the meter, kilogram, and/or second (mks). Historically the mks system of units
led to the International System of Units. The SI system now serves as the international
standard. Therefore the exact composition of the mks system is a historical issue. As a
matter of historical record the mks system encorporated fundamental units other than the
meter, kilogram, and second in addition to derived units. An incomplete list of the
fundamental/derived units appears below. If the mks system of units never had a
governing body to rule on a standard definition then this list might depend on different
conventions and different times.



cycle (This dimensionless quantity became synonymous with the term "cycle per
second" as an abbreviation. This circumstance confused the exact definition of the
term cycle. Therefore the term "cycle per meter" became ill-defined. The cycle
did not become an SI unit.)
cycle per second [1]
cycle per meter (This measure of wavenumber became ill-defined due to the
abbrevitiation of "cycle per second" as "cycle".)