The centimetre-gram-second system (abbreviated CGS or cgs) is a metric system The metric system is an international decimalised system of measurement, first adopted by France in 1791, that is the common system of measuring units used by most of the world. It exists in several variations, with different choices of fundamental units, though the choice of base units does not affect its day-to-day use. Over the last two of physical units A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement based on centimetre A centimetre is a unit of length in the metric system, equal to one hundredth of a metre, which is the current SI base unit of length. Centi is the SI prefix for a factor of 10−2. Hence a centimetre can be written as 10 × 10−3 m (engineering notation) or 1E−2 m (scientific E notation) — meaning 10 × 101 mm or 1 m/100 respectively. The as the unit of length In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire thickness. Another example is FET transistors, in which the channel width may be larger than channel length, gram The Gram , (Greek/Latin root grámma); symbol g, is a unit of mass as a unit of mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties, and second The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock as a unit of time Time is "a nonspatial continuum in which events occur in apparently irreversible succession from the past through the present to the future." It is used to sequence events, to quantify the durations of events and the intervals between them, and to quantify and measure the motions of objects and other changes. Time is quantified in. All CGS mechanical units Mechanics is the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The discipline has its roots in several ancient civilizations (see History of classical mechanics and Timeline of classical mechanics). During the early modern are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism Electromagnetism is one of the four fundamental interactions of nature, along with strong interaction, weak interaction and gravitation. It is the force that causes the interaction between electrically charged particles; the areas in which this happens are called electromagnetic fields, also known as B fields in physics classes.

The CGS system has been largely supplanted by the MKS A physical system of units that expresses any given measurement using fundamental units of the metre, kilogram, and/or second system, based on metre The metre , symbol m, is the base unit of length in the International System of Units (SI). Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole, its definition has been periodically refined to reflect growing knowledge of metrology. Since 1983, it is defined as the distance travelled by light in a, kilogram The kilogram is the base unit of mass in the International System of Units (SI, from the French Le Système International d’Unités),[Note 2] which is the modern standard governing the metric system. The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK),[Note 3] which is almost exactly equal to the mass, and second The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock. MKS was in turn extended and replaced by the International System of Units The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science (SI). The latter adopts the three base units of MKS, plus the ampere The ampere is the SI unit of electric current and is one of the seven SI base units. It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics. In practice, its name is often shortened to amp, mole The mole is the SI base unit of amount of substance; one of a few units used to measure this physical quantity. The name "mole" is an 1897 translation of the German Mol, coined by Wilhelm Ostwald in 1893, although the related concept of equivalent mass had been in use at least a century earlier. The name is assumed to be derived from the, candela The candela is the SI base unit of luminous intensity; that is, power emitted by a light source in a particular direction, weighted by the luminosity function (a standardized model of the sensitivity of the human eye to different wavelengths, also known as the luminous efficiency function). A common candle emits light with a luminous intensity of and kelvin The kelvin is a unit increment of temperature and is one of the seven SI base units. The Kelvin scale is a thermodynamic (absolute) temperature scale referenced to absolute zero, the absence of all thermal energy. So by definition, the temperature of a substance at absolute zero is zero kelvin (0 K). The secondary reference point on the Kelvin. In many fields of science and engineering, SI is the only system of units in use. However, there remain certain subfields where CGS is prevalent.

In measurements of purely mechanical systems (involving units of length In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire thickness. Another example is FET transistors, in which the channel width may be larger than channel length, mass In physics, mass commonly refers to any of three properties of matter, which have been shown experimentally to be equivalent: Inertial mass, active gravitational mass and passive gravitational mass. In everyday usage, mass is often taken to mean weight, but in scientific use, they refer to different properties, force In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a, energy In physics, energy is a quantity that can be assigned to every particle, object, and system of objects as a consequence of the state of that particle, object or system of objects. Different forms of energy include kinetic, potential, thermal, gravitational, sound, elastic, light, and electromagnetic energy. The forms of energy are often named, pressure Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure, etc.), the differences between CGS and SI are straightforward and rather trivial; the unit-conversion factors are all powers Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a: of 10 arising from the relations 100 cm = 1 m and 1000 g = 1 kg. For example, the CGS derived unit of force is the dyne In physics, the dyne (symbol "dyn", from Greek δύναμις meaning power, force) is a unit of force specified in the centimetre-gram-second (CGS) system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µ , equal to 1 g·cm/s2, while the SI derived unit of force is the newton The newton is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics, 1 kg·m/s2. Thus it is straightforward to show that 1 dyne=10−5 newton.

On the other hand, in measurements of electromagnetic phenomena (involving units of charge In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. Charges are associated with conserved quantum numbers, electric and magnetic fields, voltage The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. In the more general, etc.), converting between CGS and SI is much more subtle and involved. In fact, formulas for physical laws of electromagnetism (such as Maxwell's equations Maxwell's equations are a set of four partial differential equations that relate the electric and magnetic fields to their sources, charge density and current density. These equations can be combined to show that light is an electromagnetic wave. Individually, the equations are known as Gauss's law, Gauss's law for magnetism, Faraday's law of) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one In mathematics, an injective function is a function which associates distinct arguments with distinct values; that is, every unique argument produces a unique result correspondence between electromagnetic units in SI and those in CGS, as there are for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside-Lorentz. Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units.

Contents

History

The CGS system goes back to a proposal made in 1832 by the German mathematician Carl Friedrich Gauss Johann Carl Friedrich Gauss (pronounced /ˈɡaʊs/; German: Gauß listen , Latin: Carolus Fridericus Gauss) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy.[1] In 1874, it was extended by the British physicists James Clerk Maxwell James Clerk Maxwell was a Scottish theoretical physicist and mathematician. His most important achievement was classical electromagnetic theory, synthesizing all previously unrelated observations, experiments and equations of electricity, magnetism and even optics into a consistent theory. His set of equations—Maxwell's equations—demonstrated and William Thomson William Thomson, 1st Baron Kelvin , OM, GCVO, PC, PRS, PRSE, (26 June 1824 – 17 December 1907) was a Belfast-born mathematical physicist and engineer. At the University of Glasgow he did important work in the mathematical analysis of electricity and formulation of the first and second Laws of Thermodynamics, and did much to unify the emerging with a set of electromagnetic units.

The values (by order of magnitude An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. In its most common usage, the amount being scaled is 10 and the scale is the exponent being applied to this amount. Such differences in order of magnitude can be measured on the logarithmic scale in &) of many CGS units turned out to be inconvenient for practical purposes. For example, many everyday length measurements yield hundreds or thousands of centimetres, such as those of human height When populations share genetic background and environmental factors, average height is frequently characteristic within the group. Exceptional height variation within such a population is usually due to gigantism or dwarfism; which are medical conditions due to specific genes or to endocrine abnormalities[citation needed] and sizes of rooms and buildings. Thus the CGS system never gained wide general use outside the field of electrodynamics and laboratory science. Starting in the 1880s, and more significantly by the mid-20th century, CGS was gradually superseded internationally by the MKS (metre-kilogram-second) system, which in turn became the modern SI The International System of Units is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten. It is the world's most widely used system of measurement, both in everyday commerce and in science standard.

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 declined worldwide, in the United States ^ b. English is the de facto language of American government and the sole language spoken at home by 80% of Americans age five and older. Spanish is the second most commonly spoken language more slowly than elsewhere. CGS units are today no longer accepted by the house styles of most scientific journals, textbook publishers, or standards bodies, although they are commonly used in astronomical journals such as the Astrophysical Journal The Astrophysical Journal is a peer-reviewed scientific journal covering astronomy and astrophysics. It was founded in 1895 by the American astronomers George Ellery Hale and James Edward Keeler. It publishes three 500-page issues per month. CGS units are still occasionally encountered in technical literature, especially in the United States ^ b. English is the de facto language of American government and the sole language spoken at home by 80% of Americans age five and older. Spanish is the second most commonly spoken language in the fields of material science Materials science is an interdisciplinary field involving the properties of matter and its applications to various areas of science and engineering. This science investigates the relationship between the structure of materials at atomic or molecular scales and their macroscopic properties. It includes elements of applied physics and chemistry, electrodynamics Classical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents. It provides an excellent description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible (see and astronomy Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the Earth's atmosphere (such as the cosmic background radiation). It is concerned with the evolution, physics, chemistry, meteorology, and motion of celestial objects, as well as the formation and development of the universe.

The units gram The Gram , (Greek/Latin root grámma); symbol g, is a unit of mass and centimetre A centimetre is a unit of length in the metric system, equal to one hundredth of a metre, which is the current SI base unit of length. Centi is the SI prefix for a factor of 10−2. Hence a centimetre can be written as 10 × 10−3 m (engineering notation) or 1E−2 m (scientific E notation) — meaning 10 × 101 mm or 1 m/100 respectively. The remain useful as prefixed The International System of Units specifies a set of unit prefixes known as SI prefixes or metric prefixes. An SI prefix is a name that precedes a basic unit of measure to indicate a decimal multiple or fraction of the unit. Each prefix has a unique symbol that is prepended to the unit symbol. The SI prefixes are standardized by the International units within the SI system, especially for instructional physics and chemistry experiments, where they match the small scale of table-top setups. However, where derived units The International System of Units specifies a set of seven base units from which all other units of measurement are formed. These other units are called SI derived units and are also considered part of the standard are needed, the SI ones are generally used and taught instead of the CGS ones today. For example, a physics lab course might ask students to record lengths in centimeters, and masses in grams, but force (a derived unit) in newtons The newton is the SI derived unit of force, named after Isaac Newton in recognition of his work on classical mechanics, a usage consistent with the SI system.

Definition of CGS units in mechanics

In mechanics, the CGS and SI systems of units are built in an identical way. The two systems differ only in the scale of two out of the three base units (centimetre versus metre and gram versus kilogram, respectively), while the third unit (second The second , sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time. It may be measured using a clock as the unit of time) is the same in both systems.

There is a one-to-one In mathematics, an injective function is a function which associates distinct arguments with distinct values; that is, every unique argument produces a unique result correspondence between the base units of mechanics in CGS and SI, and the laws of mechanics are not affected by the choice of units. The definitions of all derived units in terms of the three base units are therefore the same in both systems, and there is an unambiguous one-to-one correspondence of derived units:

(definition of velocity)
(Newton's second law of motion)
(energy defined in terms of work)
(pressure defined as force per unit area)
(dynamic viscosity defined as shear stress per unit velocity gradient).

Thus, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time:

1 unit of pressure = 1 unit of force/(1 unit of length)2 = 1 unit of mass/(1 unit of length·(1 unit of time)2)
1 Ba = 1 g/(cm·s2)
1 Pa = 1 kg/(m·s2).

Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems:

1 Ba = 1 g/(cm·s2) = 10-3 kg/(10-2 m·s2) = 10-1 kg/(m·s2) = 10-1 Pa.

Definitions and conversion factors of CGS units in mechanics

Quantity Symbol CGS unit CGS unit abbreviation Definition Equivalent in SI units
length, position L, x centimetre cm 1/100 of metre = 10−2 m
mass m gram g 1/1000 of kilogram = 10−3 kg
time t second s 1 second = 1 s
velocity v centimetre per second cm/s cm/s = 10−2 m/s
force F dyne dyn g cm / s2 = 10−5 N
energy E erg erg g cm2 / s2 = 10−7 J
power P erg per second erg/s g cm2 / s3 = 10−7 W
pressure p barye Ba g / (cm s2) = 10−1 Pa
dynamic viscosity η poise P g / (cm s) = 10−1 Pa·s
wavenumber k kayser cm−1 cm−1 = 100 m−1

Derivation of CGS units in electromagnetism

CGS approach to electromagnetic units

The conversion factors relating electromagnetic units in the CGS and SI systems are much more involved — so much so that formulas for physical laws of electromagnetism are adjusted depending on what system of units one uses. This illustrates the fundamental difference in the ways the two systems are built:

,
therefore unit of electric charge, coulomb (C), is defined as 1 C = 1 A·s.

Alternate derivations of CGS units in electromagnetism

Electromagnetic relationships to length, time and mass may be derived by equally appealing methods. Two of them rely on the forces observed on charges. Two fundamental laws relate (independently of each other) the electric charge or its rate of change (electric current) to a mechanical quantity such as force. They can be written[3] in system-independent form as follows:

Maxwell's theory of electromagnetism relates these two laws to each other. It states that the ratio of proportionality constants kC and kA must obey kC / kA = c2, where c is the speed of light. Therefore, if one derives the unit of charge from the Coulomb's law by setting kC = 1, it is obvious that the Ampère's force law will contain a prefactor 2 / c2. Alternatively, deriving the unit of current, and therefore the unit of charge, from the Ampère's force law by setting kA = 1 or kA = 1 / 2, will lead to a constant prefactor in the Coulomb's law.

Indeed, both of these mutually-exclusive approaches have been practiced by the users of CGS system, leading to the two independent and mutually-exclusive branches of CGS, described in the subsections below. However, the freedom of choice in deriving electromagnetic units from the units of length, mass, and time is not limited to the definition of charge. While the electric field can be related to the work performed by it on a moving electric charge, the magnetic force is always perpendicular to the velocity of the moving charge, and thus the work performed by the magnetic field on any charge is always zero. This leads to a choice between two laws of magnetism, each relating magnetic field to mechanical quantities and electric charge:

where r and are the length and the unit vector in the direction of vector r.

These two laws can be used to derive Ampère's force law, resulting in the relationship: . Therefore, if the unit of charge is based on the Ampère's force law such that kA = 1, it is natural to derive the unit of magnetic field by setting . However, if it is not the case, a choice has to be made as to which of the two laws above is a more convenient basis for deriving the unit of magnetic field.

Furthermore, if we wish to describe the electric displacement field D and the magnetic field 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. Then we have[3] (generally) and , where P and M are polarization density and magnetization vectors. The factors λ and λ′ are rationalization constants, which are usually chosen to be 4πkCε0, a dimensionless quantity. If λ = λ′ = 1, the system is said to be "rationalized":[4] the laws for systems of spherical geometry contain factors of 4π (e.g. point charges), those of cylindrical geometry — factors of 2π (e.g. wires), and those of planar geometry contain no factors of π (e.g. parallel-plate capacitors). However, the original CGS system used λ = λ′ = 4π, or, equivalently, kCε0 = 1. Therefore, Gaussian, ESU, and EMU subsystems of CGS (described below) are not rationalized.

Various extensions of the CGS system to electromagnetism

The table below shows the values of the above constants used in some common CGS subsystems:

system kC αB ε0 μ0 λ'
Electrostatic[3] CGS (ESU, esu, or stat-) 1 c−2 1 c−2 c−2 1 4π 4π
Electromagnetic[3] CGS (EMU, emu, or ab-) c2 1 c−2 1 1 1 4π 4π
Gaussian[3] CGS 1 c−1 1 1 c−2 c−1 4π 4π
Heaviside-Lorentz[3] CGS 1 1 c−1 1 1
SI 1 1 1

The constant b in SI system is a unit-based scaling factor defined as: .

Also, note the following correspondence of the above constants to those in Jackson[3] and Leung[5]:

kC = k1 = kE
kA = k2 = kE / c2
αL = k3 = kF

In system-independent form, Maxwell's equations in vacuum can be written as:[3][5]

Note that of all these variants, only in Gaussian and Heaviside-Lorentz systems αL equals c − 1 rather than 1. As a result, vectors and of an electromagnetic wave propagating in vacuum have the same units and are equal in magnitude in these two variants of CGS.

Electrostatic units (ESU)

Main article: Electrostatic units

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. It is done by setting the Coulomb force constant kC = 1, so that Coulomb's law does not contain an explicit prefactor.

The ESU unit of charge, franklin (Fr), also known as statcoulomb or esu charge, is therefore defined as follows:[6]

two equal point charges spaced 1 centimetre apart are said to be of 1 franklin each if the electrostatic force between them is 1 dyne.

Therefore, in electrostatic CGS units, a franklin is equal to a centimetre times square root of dyne:

.

The unit of current is defined as:

.

Dimensionally in the ESU CGS system, charge q is therefore equivalent to m1/2L3/2t−1. Neither charge nor current are therefore an independent dimension of physical quantity in ESU CGS. This reduction of units is an application of the Buckingham π theorem.

ESU notation

All electromagnetic units in ESU CGS system that do not have proper names are denoted by a corresponding SI name with an attached prefix "stat" or with a separate abbreviation "esu".[6]

Electromagnetic units (EMU)

In another variant of the CGS system, Electromagnetic units (EMU), current is defined via the force existing between two thin, parallel, infinitely long wires carrying it, and charge is then defined as current multiplied by time. (This approach was eventually used to define the SI unit of ampere as well). In the EMU CGS subsystem, is done by setting the Ampere force constant kA = 1, so that Ampère's force law simply contains 2 as an explicit prefactor (this prefactor 2 is itself a result of integrating a more general formulation of Ampère's law over the length of the infinite wire).

The EMU unit of current, biot (Bi), also known as abampere or emu current, is therefore defined as follows:[6]

The biot is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one centimetre apart in vacuo, would produce between these conductors a force equal to two dynes per centimetre of length.

Therefore, in electromagnetic CGS units, a biot is equal to a square root of dyne:

.

The unit of charge in CGS EMU is:

.

Dimensionally in the EMU CGS system, charge q is therefore equivalent to m1/2L1/2. Neither charge nor current are therefore an independent dimension of physical quantity in EMU CGS.

EMU notation

All electromagnetic units in EMU CGS system that do not have proper names are denoted by a corresponding SI name with an attached prefix "ab" or with a separate abbreviation "emu".[6]

Relations between ESU and EMU units

The ESU and EMU subsystems of CGS are connected by the fundamental relationship kC / kA = c2 (see above), where c = 29,979,245,800 ≈ 3·1010 is the speed of light in vacuum in cm/s. Therefore, the ratio of the corresponding “primary″ electrical and magnetic units (e.g. current, charge, voltage, etc. — quantities proportional to those that enter directly into Coulomb's law or Ampère's force law) is equal either to c-1 or c:[6]

and

.

Units derived from these may have ratios equal to higher powers of c, for example:

.

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.[7] These also include 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.

Electromagnetic units in various CGS systems

Conversion of SI units in electromagnetism to ESU, EMU, and Gaussian subsystems of CGS[6] c = 29,979,245,800 ≈ 3·1010
Quantity Symbol SI unit ESU unit EMU unit Gaussian unit
electric charge q 1 C = (10-1 c) statC = (10-1) abC = (10-1 c) Fr
electric current I 1 A = (10-1 c) statA = (10-1) abA = (10-1 c) Fr·s-1
electric potential voltage φ V 1 V = (108 c-1) statV = (108) abV = (108 c-1) statV
electric field E 1 V/m = (106 c-1) statV/cm = (106) abV/cm = (106 c-1) statV/cm
magnetic induction B 1 T = (104 c-1) statT = (104) G = (104) G
magnetic field strength H 1 A/m = (4π 10-3 c) statA/cm = (4π 10-3) Oe = (4π 10-3) Oe
magnetic dipole moment μ 1 A·m² = (103 c) statA·cm² = (103) abA·cm² = (103) erg/G
magnetic flux Φm 1 Wb = (108 c-1) statT·cm² = (108) Mw = (108) G·cm²
resistance R 1 Ω = (109 c-2) s/cm = (109) abΩ = (109 c-2) s/cm
resistivity ρ 1 Ω·m = (1011 c-2) s = (1011) abΩ·cm = (1011 c-2) s
capacitance C 1 F = (10-9 c2) cm = (10-9) abF = (10-9 c2) cm
inductance L 1 H = (109 c-2) cm-1·s-2 = (109) abH = (109 c-2) cm-1·s2

In this table, c = 29,979,245,800 ≈ 3·1010 is the speed of light in vacuum in the CGS units of cm/s.

One can think of the SI value of the Coulomb constant kC as:

This explains why SI to ESU conversions involving factors of c2 lead to significant simplifications of the ESU units, such as 1 statF = 1 cm and 1 statΩ = 1 s/cm: this is the consequence of the fact that in ESU system kC=1. For example, 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 in ESU CGS system is:

.

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

Physical constants in CGS units

Commonly used physical constants in CGS units[8]
Constant Symbol Value
Atomic mass unit u 1.660 538 782 × 10−24 g
Bohr magneton μB 9.274 009 15 × 10−21 erg/G (EMU, Gaussian)
2.780 278 00 × 10−10 statA·cm2 (ESU)
Bohr radius a0 5.291 772 0859 × 10−9 cm
Boltzmann constant k 1.380 6504 × 10−16 erg/K
Electron mass me 9.109 382 15 × 10−28 g
Elementary charge e 4.803 204 27 × 10−10 Fr (ESU, Gaussian)
1.602 176 487 × 10−20 abC (EMU)
Fine-structure constant α ≈ 1/137 7.297 352 570 × 10−3
Gravitational constant G 6.674 28 × 10−8 cm3/(g·s2)
Planck constant h 6.626 068 85 × 10−27 erg·s
1.054 5716 × 10−27 erg·s
Speed of light in vacuum c ≡ 2.997 924 58 × 1010 cm/s

Pro and contra

While the absence of explicit prefactors in some CGS subsystems simplifies some theoretical calculations, it has the disadvantage that sometimes the units in CGS are hard to define through experiment. Also, lack of unique unit names leads to a great confusion: thus “15 emu” may mean either 15 abvolt, or 15 emu units of electric dipole moment, or 15 emu units of magnetic susceptibility, sometimes (but not always) per gram or per mole. On the other hand, SI starts with a unit of current, the ampere, which is easier to determine through experiment, but which requires extra prefactors in the electromagnetic equations. With its system of unique named units, SI also removes any confusion in usage: 1 ampere is a fixed quantity of a specific variable, and so are 1 henry and 1 ohm.

A key virtue of the Gaussian CGS system is that electric and magnetic fields have the same units, 4πε0 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 ε0 equaling 1), but it 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 4π appearing in the formulas, and it is in Heaviside-Lorentz units that the Maxwell equations take their simplest form.

In SI, and other rationalized systems (e.g. Heaviside-Lorentz), the unit of current was chosen such that electromagnetic equations concerning charged spheres contain 4π, those concerning coils of current and straight wires contain 2π and those dealing with charged surfaces 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 non-rationalized CGS system can be somewhat more convenient notationally.

In fact, in certain fields, specialized unit systems are used to simplify formulas even further than either SI or CGS, by using some system of natural units. For example, the particle physics community uses a system where every quantity is expressed by only one unit, the eV, with lengths, times, etc. all converted into eV's by inserting factors of c and . This unit system is very convenient for particle-physics calculations, but would be impractical in other contexts.

See also

References and notes

  1. ^ Hallock, William; Wade, Herbert Treadwell (1906). Outlines of the evolution of weights and measures and the metric system. New York: The Macmillan Co. p. 200. http://books.google.com/books?id=NVZKAAAAMAAJ.
  2. ^ For historical reasons, 1 ampere is chosen such that the magnetic force exerted by two infinitely long, thin, parallel wires 1 m apart and carrying this current is exactly 2×10–7 N/m. This definition makes all SI electromagnetic units consistent (up to some integer powers of 10) with the EMU CGS system described in further sections.
  3. ^ a b c d e f g h Jackson, John David (1999). Classical Electrodynamics (3rd ed.). New York: Wiley. pp. 775–784. ISBN 0-471-30932-X.
  4. ^ Cardarelli, F. (2004). Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins (2nd ed.). Springer. p. 20. ISBN 1-8523-3682-X. http://books.google.com/books?id=6KCx8Ww75VkC.
  5. ^ a b Leung, P. T. (2004). "A note on the 'system-free' expressions of Maxwell's equations". European Journal of Physics 25 (2): N1–N4. doi:10.1088/0143-0807/25/2/N01.
  6. ^ a b c d e f Cardarelli, F. (2004). Encyclopaedia of Scientific Units, Weights and Measures: Their SI Equivalences and Origins (2nd ed.). Springer. pp. 20–25. ISBN 1-8523-3682-X. http://books.google.com/books?id=6KCx8Ww75VkC.
  7. ^ Bennett, L. H.; Page, C. H.; and Swartzendruber, L. J. (1978). "Comments on units in magnetism". Journal of Research of the National Bureau of Standards 83 (1): 9–12.
  8. ^ A.P. French, Edwind F. Taylor (1978). An Introduction to Quantum Physics. W.W. Norton & Company.

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Categories: Systems of units | Centimetre gram second system of units

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