Centimetre gram second system of units Totally Explained

Everything about Cgs totally explained

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.

Dimension	Unit	Definition	SI
length	centimetre	1/100 of metre	= 10⁻² m
mass	gram	1/1000 of kilogram	= 10⁻³ kg
time	second	1 second	= 1 s
force	dyne	g cm / s²	= 10⁻⁵ N
energy	erg	g cm² / s²	= 10⁻⁷ J
power	erg per second	g cm² / s³	= 10⁻⁷ W
pressure	barye	g / (cm s²)	= 10⁻¹ Pa
dynamic viscosity	poise	g / (cm s)	= 10⁻¹ Pa·s

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purposes, therefore the CGS system never gained wide general use outside the field of electrodynamics and was gradually superseded internationally starting in the 1880s but not to a significant extent until the mid-20th century by the more practical MKS (metre-kilogram-second) system,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're 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're 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 doesn't 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 M^1/2L^3/2T⁻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've 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 
ight)

. 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

, 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

2pi

Further Information

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