Gaussian units constitute a

metric system The metric system is a system of measurement that succeeded the Decimal, decimalised system based on the metre that had been introduced in French Revolution, France in the 1790s. The historical development of these systems culminated in the d ...

physical units A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multip ...

. This system is the most common of the several electromagnetic unit systems based on cgs (centimetre–gram–second) units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units. The term "cgs units" is ambiguous and therefore to be avoided if possible: there are several variants of cgs with conflicting definitions of electromagnetic quantities and units.

SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...

predominate in most fields, and continue to increase in popularity at the expense of Gaussian units. Alternative unit systems also exist. Conversions between quantities in Gaussian and SI units are direct unit conversions, because the quantities themselves are defined differently in each system. This means that the equations expressing physical laws of electromagnetism—such as

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...

—will change depending on the system of units employed. As an example, quantities that are dimensionless in one system may have dimension in the other.

Alternative unit systems

The Gaussian unit system is just one of several electromagnetic unit systems within CGS. Others include "

electrostatic units The electrostatic system of units (CGS-ESU) is a system of units used to measure quantities of electric charge, electric current, and voltage within the centimetre–gram–second (or "CGS") system of metric units. In electrostatic units, electric ...

", "

electromagnetic units In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...

", and

Heaviside–Lorentz units Heaviside–Lorentz units (or Lorentz–Heaviside units) constitute a system of units (particularly electromagnetic units) within CGS, named for Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that th ...

. Some other unit systems are called " natural units", a category that includes atomic units, Planck units, and others. The

International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

(SI), with the associated International System of Quantities (ISQ), is by far the most common system of units today. In

engineering Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...

and practical areas, SI is nearly universal and has been for decades."CGS"
in ''How Many? A Dictionary of Units of Measurement'', by Russ Rowlett and the

University of North Carolina at Chapel Hill A university () is an institution of higher (or tertiary) education and research which awards academic degrees in several academic disciplines. Universities typically offer both undergraduate and postgraduate programs. In the United States ...

In technical, scientific literature (such as

theoretical physics Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experim ...

and

astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...

), Gaussian units were predominant until recent decades, but are now getting progressively less so. The 8th SI Brochure acknowledges that the CGS-Gaussian unit system has advantages in classical and relativistic electrodynamics, but the 9th SI Brochure makes no mention of CGS systems. Natural units may be used in more theoretical and abstract fields of physics, particularly

particle physics Particle physics or high energy physics is the study of fundamental particles and forces that constitute matter and radiation. The fundamental particles in the universe are classified in the Standard Model as fermions (matter particles) an ...

and

string theory In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interac ...

Major differences between Gaussian and SI systems

"Rationalized" unit systems

One difference between Gaussian and SI units is in the factors of in various formulas. With SI electromagnetic units, called ''rationalized'',Kowalski, Ludwik, 1986
"A Short History of the SI Units in Electricity"
''The Physics Teacher'' 24(2): 97–99
Alternate web link (subscription required)
/ref>

have no explicit factors of in the formulae, whereas the

inverse-square In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understo ...

force laws –

Coulomb's law Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is conventiona ...

and the Biot–Savart law – have a factor of attached to the . With Gaussian units, called ''unrationalized'' (and unlike

), the situation is reversed: two of Maxwell's equations have factors of in the formulas, while both of the inverse-square force laws, Coulomb's law and the Biot–Savart law, have no factor of attached to in the denominator. (The quantity appears because is the

surface area of the sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. A sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

of radius , which reflects the geometry of the configuration. For details, see the articles '' Relation between Gauss's law and Coulomb's law'' and ''

Inverse-square law In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understo ...

''.)

Unit of charge

A major difference between the Gaussian system and the ISQ is in the respective definitions of the quantity charge. In the ISQ, a separate base dimension, electric current, with the associated SI unit, the

ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...

, is associated with electromagnetic phenomena, with the consequence that a unit of electrical charge (1

coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...

= 1 ampere × 1 second) is a physical quantity that cannot be expressed purely in terms of the mechanical units (kilogram, metre, second). On the other hand, in the Gaussian system, the unit of electric charge (the statcoulomb, statC) be written entirely as a dimensional combination of the non-electrical base units (gram, centimetre, second), as: For example,

in Gaussian units has no constant:

F = \frac ,

where is the repulsive force between two electrical charges, and are the two charges in question, and is the distance separating them. If and are expressed in statC and in centimetres, then the unit of that is coherent with these units is the dyne. The same law in the ISQ is:

F = \frac \frac

where is the

vacuum permittivity Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...

, a quantity that is not dimensionless: it has dimension ( charge)² (

time Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to ...

)² (

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

)⁻¹ (

length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...

)⁻³. Without , the equation would be dimensionally inconsistent with the quantities as defined in the ISQ, whereas the quantity does not appear in Gaussian equations. This is an example of how some dimensional

physical constant A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...

s can be eliminated from the expressions of

physical law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) a ...

by the choice of definition of quantities. In the ISQ,

1/\varepsilon_0

converts or scales

flux density Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

, , to the corresponding

electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

, (the latter has dimension of

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

per charge), while in the Gaussian system, electric flux density is the same quantity as electric field strength in

free space A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...

aside from a dimensionless constant factor. In the Gaussian system, the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...

appears directly in electromagnetic formulas like

(see below), whereas in the ISQ it appears via the product

Units for magnetism

In the Gaussian system, unlike the ISQ, the electric field and the

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

have the same dimension. This amounts to a factor of between how is defined in the two unit systems, on top of the other differences. (The same factor applies to other magnetic quantities such as the

, , and

magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...

, .) For example, in a planar light wave in vacuum, in Gaussian units, while in the ISQ.

Polarization, magnetization

There are further differences between Gaussian system and the ISQ in how quantities related to polarization and magnetization are defined. For one thing, in the Gaussian system, ''all'' of the following quantities have the same dimension: , , , , , and . A further point is that the electric and

magnetic susceptibility In electromagnetism, the magnetic susceptibility (Latin: , "receptive"; denoted ) is a measure of how much a material will become magnetized in an applied magnetic field. It is the ratio of magnetization (magnetic moment per unit volume) to the ap ...

of a material is dimensionless in both Gaussian system and the ISQ, but a given material will have a different numerical susceptibility in the two systems. (Equation is given below.)

List of equations

This section has a list of the basic formulae of electromagnetism, given in both the Gaussian system and the International System of Quantities (ISQ). Most symbol names are not given; for complete explanations and definitions, please click to the appropriate dedicated article for each equation. A simple conversion scheme for use when tables are not available may be found in Garg (2012).A. Garg, 2012, "Classical Electrodynamics in a Nutshell" (Princeton University Press). All formulas except otherwise noted are from Ref.

Maxwell's equations

Here are Maxwell's equations, both in macroscopic and microscopic forms. Only the "differential form" of the equations is given, not the "integral form"; to get the integral forms apply the

divergence theorem In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the vol ...

Kelvin–Stokes theorem Stokes's theorem, also known as the Kelvin–Stokes theorem Nagayoshi Iwahori, et al.:"Bi-Bun-Seki-Bun-Gaku" Sho-Ka-Bou(jp) 1983/12Written in Japanese)Atsuo Fujimoto;"Vector-Kai-Seki Gendai su-gaku rekucha zu. C(1)" :ja:培風館, Bai-Fu-Kan( ...

Other basic laws

Dielectric and magnetic materials

Below are the expressions for the various fields in a dielectric medium. It is assumed here for simplicity that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permittivity is a simple constant. where * and are the

and displacement field, respectively; * is the polarization density; *

\varepsilon

is the permittivity; *

\varepsilon_0

is the

permittivity of vacuum Vacuum permittivity, commonly denoted (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric consta ...

(used in the SI system, but meaningless in Gaussian units); and *

\chi_\mathrm

is the electric susceptibility. The quantities

\varepsilon^\mathrm

and

\varepsilon^\mathrm/\varepsilon_0

are both dimensionless, and they have the same numeric value. By contrast, the electric susceptibility

\chi_\mathrm^\mathrm

and

\chi_\mathrm^\mathrm

are both unitless, but have for the same material:

4\pi \chi_\mathrm^\mathrm = \chi_\mathrm^\mathrm\,.

Next, here are the expressions for the various fields in a magnetic medium. Again, it is assumed that the medium is homogeneous, linear, isotropic, and nondispersive, so that the permeability is a simple constant. where * and are the

s; * is

; *

\mu

magnetic permeability In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...

; *

\mu_0

is the permeability of vacuum (used in the SI system, but meaningless in Gaussian units); and *

\chi_\mathrm

is the

. The quantities

\mu^\mathrm

and

\mu^\mathrm/\mu_0

are both dimensionless, and they have the same numeric value. By contrast, the

\chi_\mathrm^\mathrm

and

\chi_\mathrm^\mathrm

are both unitless, but has in the two systems for the same material:

4\pi \chi_\mathrm^\mathrm = \chi_\mathrm^\mathrm

Vector and scalar potentials

The electric and magnetic fields can be written in terms of a vector potential and a scalar potential :

Electrical circuit

where * is the

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...

* is the

electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...

* is the

electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

* is the

magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ( ...

* is the

electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual parallels ...

* is the

capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...

* is the

inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...

Fundamental constants

Electromagnetic unit names

{, class="wikitable plainrowheaders defaultcenter col5left" , + Table 1: Common electromagnetism units in SI vs Gaussian ! scope="col" , Quantity ! scope="col" , Symbol ! scope="col" , SI unit ! scope="col" , Gaussian unit(in base units) ! scope="col" , Conversion factor , - ! scope="row" ,

Electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...

, , C , Fr(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{q^{\mathrm{G}{q^{\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^9 \, \mathrm{Fr{1\, \mathrm{C

, - ! scope="row" ,

Electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...

, , A ,

statA Stata (, , alternatively , occasionally stylized as STATA) is a general-purpose statistical software package developed by StataCorp for data manipulation, visualization, statistics, and automated reporting. It is used by researchers in many fie ...

(cm^3/2⋅g^1/2⋅s⁻²) ,

\frac{I^{\mathrm{G}{I^{\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^9 \, \mathrm{statA{1\, \mathrm{A

, - ! scope="row" ,

Electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

Voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...

, , V , statV(cm^1/2⋅g^1/2⋅s⁻¹) ,

\frac{V^{\mathrm{G}{V^{\mathrm{I} = \sqrt{4\pi\varepsilon_0} \approx \frac{1\, \mathrm{statV{2.998 \times 10^2 \, \mathrm{V

, - ! scope="row" ,

Electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...

, , V/ m , statV/ cm(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{E}^{\mathrm{G}{\mathbf{E}^{\mathrm{I} = \sqrt{4\pi\varepsilon_0} \approx \frac{1 \, \mathrm{statV/cm{2.998 \times 10^4 \, \mathrm{V/m

, - ! scope="row" ,

Electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...

, , C/ m² , Fr/ cm²(cm^−1/2g^1/2s⁻¹) ,

\frac{\mathbf{D}^{\mathrm{G}{\mathbf{D}^{\mathrm{I} = \sqrt{\frac{4\pi}{\varepsilon_0 \approx \frac{4\pi\times 2.998 \times 10^5 \, \mathrm{Fr/cm}^2}{ 1 \, \mathrm{C/m}^2}

, - ! scope="row" ,

Electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...

, , C⋅ m , Fr⋅ cm(cm^5/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{p}^{\mathrm{G}{\mathbf{p}^{\mathrm{I} = \frac{1}{\sqrt{4\pi\varepsilon_0 \approx \frac{2.998 \times 10^{11} \, \mathrm{Fr}{\cdot}\mathrm{cm{1 \, \mathrm{C}{\cdot}\mathrm{m

, - ! scope="row" , Electric flux , , C , Fr(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{\Phi^{\mathrm{G_{\mathrm{e}{\Phi^{\mathrm{I_{\mathrm{e} = \sqrt{\frac{4\pi}{\varepsilon_0 \approx \frac{4\pi\times 2.998 \times 10^9 \, \mathrm{Fr{1 \, \mathrm{C

, - ! scope="row" , Permittivity , , F/ m , cm/cm ,

\frac{\varepsilon^{\mathrm{G}{\varepsilon^{\mathrm{I} = \frac{1}{\varepsilon_0} \approx \frac{4\pi \times 2.998^2 \times 10^{9} \, \mathrm{cm/cm{1 \, \mathrm{F/m

, - ! scope="row" , Magnetic B field , , T , G(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{B}^{\mathrm{G}{\mathbf{B}^{\mathrm{I} = \sqrt{\frac{4\pi}{\mu_0 \approx \frac{10^4 \, \mathrm{G{1 \, \mathrm{T

, - ! scope="row" , Magnetic H field , , A/ m , Oe(cm^−1/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{H}^{\mathrm{G}{\mathbf{H}^{\mathrm{I} = \sqrt{4\pi\mu_0} \approx \frac{4\pi \times 10^{-3} \, \mathrm{Oe{1 \, \mathrm{A/m

, - ! scope="row" ,

Magnetic dipole moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...

, , A⋅ m² ,

erg The erg is a unit of energy equal to 10−7joules (100 nJ). It originated in the Centimetre–gram–second system of units (CGS). It has the symbol ''erg''. The erg is not an SI unit. Its name is derived from (), a Greek word meaning 'work' o ...

/ G(cm^5/2⋅g^1/2⋅s⁻¹) ,

\frac{\mathbf{m}^{\mathrm{G}{\mathbf{m}^{\mathrm{I} = \sqrt{\frac{\mu_0}{4\pi \approx \frac{10^3 \, \mathrm{erg/G{1 \, \mathrm{A}{\cdot}\mathrm{m}^2}

, - ! scope="row" ,

Magnetic flux In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B over that surface. It is usually denoted or . The SI unit of magnetic flux is the weber ( ...

, , Wb , Mx(cm^3/2⋅g^1/2⋅s⁻¹) ,

\frac{\Phi^{\mathrm{G_{\mathrm{m}{\Phi^{\mathrm{I_{\mathrm{m} = \sqrt{\frac{4\pi}{\mu_0 \approx \frac{10^8 \, \mathrm{Mx{1 \, \mathrm{Wb

, - ! scope="row" , Permeability , , H/ m , cm/cm ,

\frac{\mu^{\mathrm{G}{\mu^{\mathrm{I} = \frac{1}{\mu_0} \approx \frac{1 \, \mathrm{cm/cm{4\pi \times 10^{-7} \, \mathrm{H/m

, - ! scope="row" ,

Resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...

, , Ω , s/ cm ,

\frac{R^{\mathrm{G}{R^{\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s/cm{2.998^2 \times 10^{11}  \, \Omega}

, - ! scope="row" , Resistivity , , Ω⋅ m , s ,

\frac{\rho^{\mathrm{G}{\rho^{\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s{2.998^2 \times 10^{9}  \, \Omega{\cdot}\mathrm{m

, - ! scope="row" ,

Capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...

, , F , cm ,

\frac{C^{\mathrm{G}{C^{\mathrm{I} = \frac{1}{4\pi\varepsilon_0} \approx \frac{2.998^2 \times 10^{11} \, \mathrm{cm{1 \, \mathrm{F

, - ! scope="row" ,

Inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...

, , H , s²/ cm ,

\frac{L^{\mathrm{G}{L^{\mathrm{I} = 4\pi\varepsilon_0 \approx \frac{1 \, \mathrm{s}^2/\mathrm{cm{2.998^2 \times 10^{11} \, \mathrm{H

Note: The SI quantities

\varepsilon_0

and

\mu_0

satisfy The conversion factors are written both symbolically and numerically. The numerical conversion factors can be derived from the symbolic conversion factors by dimensional analysis. For example, the top row says \approx {2.998 \times 10^9 \,\mathrm{Fr \,/\, {1\,\mathrm{C, a relation which can be verified with dimensional analysis, by expanding

\varepsilon_0

and

s (C) in SI base units, and expanding statcoulombs (or franklins, Fr) in Gaussian base units. It is surprising to think of measuring capacitance in centimetres. One useful example is that a centimetre of capacitance is the capacitance between a sphere of radius 1 cm in vacuum and infinity. Another surprising unit is measuring resistivity in units of seconds. A physical example is: Take a parallel-plate capacitor, which has a "leaky" dielectric with permittivity 1 but a finite resistivity. After charging it up, the capacitor will discharge itself over time, due to current leaking through the dielectric. If the resistivity of the dielectric is seconds, the half-life of the discharge is seconds. This result is independent of the size, shape, and charge of the capacitor, and therefore this example illuminates the fundamental connection between resistivity and time units.

Dimensionally equivalent units

A number of the units defined by the table have different names but are in fact dimensionally equivalent – i.e., they have the same expression in terms of the base units cm, g, s. (This is analogous to the distinction in SI between becquerel and Hz, or between

newton-metre The newton-metre (also newton metre or newton meter; symbol N⋅m or N m) is the unit of torque (also called ) in the International System of Units (SI). One newton-metre is equal to the torque resulting from a force of one newton applie ...

and

joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied ...

.) The different names help avoid ambiguities and misunderstandings as to what physical quantity is being measured. In particular, of the following quantities are dimensionally equivalent in Gaussian units, but they are nevertheless given different unit names as follows: {, class="wikitable plainrowheaders" style="text-align: center;" , + Dimensionally equivalent units , - ! scope="col" , Quantity ! scope="col" , Gaussian symbol ! scope="col" , In Gaussian
base units ! scope="col" , Gaussian unit
of measure , - ! scope="row" ,

, , cm^−1/2⋅g^1/2⋅s⁻¹ , statV/cm , - ! scope="row" ,

, , cm^−1/2⋅g^1/2⋅s⁻¹ , statC/cm² , - ! scope="row" , Polarization density , , cm^−1/2⋅g^1/2⋅s⁻¹ , statC/cm² , - ! scope="row" , Magnetic flux density , , cm^−1/2⋅g^1/2⋅s⁻¹ , G , - ! scope="row" , Magnetizing field , , cm^−1/2 g^1/2⋅s⁻¹ , Oe , - ! scope="row" ,

Magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Di ...

, , cm^−1/2⋅g^1/2⋅s⁻¹ , dyn/ Mx

General rules to translate a formula

Any formula can be converted between Gaussian and SI units by using the symbolic conversion factors from Table 1 above. For example, the electric field of a stationary point charge has the ISQ formula

\mathbf{E}^{\mathrm{I = \frac{q^{\mathrm{I}{4\pi \varepsilon_0 r^2} \hat{\mathbf{r ,

where is distance, and the "" superscript indicates that the electric field and charge are defined as in the ISQ. If we want the formula to instead use the Gaussian definitions of electric field and charge, we look up how these are related using Table 1, which says:

\begin{align}
\frac{\mathbf{E}^{\mathrm{G}{\mathbf{E}^{\mathrm{I} &= \sqrt{4\pi\varepsilon_0}\,, \\
\frac{q^{\mathrm{G}{q^\mathrm{I &= \frac{1}{\sqrt{4\pi\varepsilon_0\,.
\end{align}

Therefore, after substituting and simplifying, we get the Gaussian-system formula:

\mathbf{E}^{\mathrm{G = \frac{q^{\mathrm{G}{r^2}\hat{\mathbf{r\,,

which is the correct Gaussian-system formula, as mentioned in a previous section. For convenience, the table below has a compilation of the symbolic conversion factors from Table 1. To convert any formula from Gaussian system to the ISQ using this table, replace each symbol in the Gaussian column by the corresponding expression in the SI column (vice versa to convert the other way). This will reproduce any of the specific formulas given in the list above, such as Maxwell's equations, as well as any other formula not listed. {, class="wikitable plainrowheaders" , + Table 2A: Replacement rules for translating formulas from Gaussian to ISQ , - ! scope="col" , Name ! scope="col" , Gaussian system ! scope="col" , , - ! scope="row" ,

electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...

\left(\mathbf{E}^{\mathrm{G, \varphi^{\mathrm{G, \mathcal E^{\mathrm G}\right)

\sqrt{4\pi\varepsilon_0}\left(\mathbf{E}^{\mathrm{I, \varphi^{\mathrm{I, \mathcal E^{\mathrm I}\right)

, - ! scope="row" ,

electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...

\mathbf{D}^{\mathrm{G

\sqrt{\frac{4\pi}{\varepsilon_0\mathbf{D}^{\mathrm{I

, - ! scope="row" , charge,

charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in co ...

, current,

current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...

, polarization density,

electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...

\left(q^{\mathrm{G, \rho^{\mathrm{G, I^{\mathrm{G, \mathbf{J}^{\mathrm{G,\mathbf{P}^{\mathrm{G, \mathbf{p}^{\mathrm{G\right)

\frac{1}{\sqrt{4\pi\varepsilon_0\left(q^{\mathrm{I, \rho^{\mathrm{I, I^{\mathrm{I, \mathbf{J}^{\mathrm{I,\mathbf{P}^{\mathrm{I,\mathbf{p}^{\mathrm{I\right)

, - ! scope="row" , magnetic field,

magnetic vector potential In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: \nabla \times \mathbf = \mathbf. Together with the electric potential ''φ'', the magnetic v ...

\left(\mathbf{B}^{\mathrm{G, \Phi_\mathrm{m}^{\mathrm{G,\mathbf{A}^{\mathrm{G\right)

\sqrt{\frac{4\pi}{\mu_0\left(\mathbf{B}^{\mathrm{I, \Phi_\mathrm{m}^{\mathrm{I,\mathbf{A}^{\mathrm{I\right)

, - ! scope="row" , magnetic field, magnetic scalar potential, magnetomotive force ,

\left(\mathbf{H}^{\mathrm{G, \psi^{\mathrm G}, \mathcal F^{\mathrm G}\right)

\sqrt{4\pi\mu_0}\left(\mathbf{H}^{\mathrm{I, \psi^{\mathrm I}, \mathcal F^{\mathrm I}\right)

, - ! scope="row" ,

magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...

magnetic pole strength In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...

\left(\mathbf{m}^{\mathrm{G, \mathbf{M}^{\mathrm{G, p^{\mathrm G}\right)

\sqrt{\frac{\mu_0}{4\pi\left(\mathbf{m}^{\mathrm{I, \mathbf{M}^{\mathrm{I, p^{\mathrm I}\right)

, - ! scope="row" , permittivity,
permeability ,

\left(\varepsilon^{\mathrm{G, \mu^{\mathrm{G\right)

\left(\frac{\varepsilon^{\mathrm{I}{\varepsilon_0}, \frac{\mu^{\mathrm{I}{\mu_0}\right)

, - ! scope="row" , electric susceptibility,

\left(\chi_\mathrm{e}^{\mathrm{G, \chi_\mathrm{m}^{\mathrm{G\right)

\frac{1}{4\pi}\left(\chi_\mathrm{e}^{\mathrm{I, \chi_\mathrm{m}^{\mathrm{I\right)

, - ! scope="row" , conductivity, conductance,

\left(\sigma^{\mathrm{G, S^{\mathrm{G, C^{\mathrm{G\right)

\frac{1}{4\pi\varepsilon_0}\left(\sigma^{\mathrm{I,S^{\mathrm{I,C^{\mathrm{I\right)

, - ! scope="row" , resistivity,

resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''T ...

, memristance, impedance ,

\left(\rho^{\mathrm{G,R^{\mathrm{G,L^{\mathrm{G,M^{\mathrm{G,Z^{\mathrm{G\right)

4\pi\varepsilon_0\left(\rho^{\mathrm{I,R^{\mathrm{I,L^{\mathrm{I,M^{\mathrm{I,Z^{\mathrm{I\right)

, - ! scope="row" , magnetic reluctance ,

\mathcal{R}^{\mathrm G}

\mu_0\mathcal{R}^{\mathrm I}

{, class="wikitable plainrowheaders" , + Table 2B: Replacement rules for translating formulas from ISQ to Gaussian , - ! scope="col" , Name ! scope="col" , ! scope="col" , Gaussian system , - ! scope="row" ,

\left(\mathbf{E}^{\mathrm{I, \varphi^{\mathrm{I, \mathcal E^{\mathrm I}\right)

\frac{1}{\sqrt{4\pi\varepsilon_0\left(\mathbf{E}^{\mathrm{G, \varphi^{\mathrm{G, \mathcal E^{\mathrm G}\right)

, - ! scope="row" ,

\mathbf{D}^{\mathrm{I

\sqrt{\frac{\varepsilon_0}{4\pi\mathbf{D}^{\mathrm{G

, - ! scope="row" , charge,

, current,

, polarization density,

\left(q^{\mathrm{I, \rho^{\mathrm{I, I^{\mathrm{I, \mathbf{J}^{\mathrm{I,\mathbf{P}^{\mathrm{I, \mathbf{p}^{\mathrm{I\right)

\sqrt{4\pi\varepsilon_0}\left(q^{\mathrm{G, \rho^{\mathrm{G, I^{\mathrm{G, \mathbf{J}^{\mathrm{G,\mathbf{P}^{\mathrm{G,\mathbf{p}^{\mathrm{G\right)

, - ! scope="row" , magnetic field,

\left(\mathbf{B}^{\mathrm{I, \Phi_\mathrm{m}^{\mathrm{I,\mathbf{A}^{\mathrm{I\right)

\sqrt{\frac{\mu_0}{4\pi\left(\mathbf{B}^{\mathrm{G, \Phi_\mathrm{m}^{\mathrm{G,\mathbf{A}^{\mathrm{G\right)

, - ! scope="row" , magnetic field, magnetic scalar potential, magnetomotive force ,

\left(\mathbf{H}^{\mathrm{I, \psi^{\mathrm I}, \mathcal F^{\mathrm I}\right)

\frac{1}{\sqrt{4\pi\mu_0\left(\mathbf{H}^{\mathrm{G, \psi^{\mathrm G}, \mathcal F^{\mathrm G}\right)

, - ! scope="row" ,

\left(\mathbf{m}^{\mathrm{I, \mathbf{M}^{\mathrm{I, p^{\mathrm I}\right)

\sqrt{\frac{4\pi}{\mu_0\left(\mathbf{m}^{\mathrm{G, \mathbf{M}^{\mathrm{G, p^{\mathrm G}\right)

, - ! scope="row" , permittivity,
permeability ,

\left(\varepsilon^{\mathrm{I, \mu^{\mathrm{I\right)

\left(\varepsilon_0\varepsilon^{\mathrm{G, \mu_0\mu^{\mathrm{G\right)

, - ! scope="row" , electric susceptibility,

\left(\chi_\mathrm{e}^{\mathrm{I, \chi_\mathrm{m}^{\mathrm{I\right)

4\pi \left(\chi_\mathrm{e}^{\mathrm{G, \chi_\mathrm{m}^{\mathrm{G\right)

, - ! scope="row" , conductivity, conductance,

\left(\sigma^{\mathrm{I, S^{\mathrm{I, C^{\mathrm{I\right)

4\pi\varepsilon_0\left(\sigma^{\mathrm{G,S^{\mathrm{G,C^{\mathrm{G\right)

, - ! scope="row" , resistivity,

, memristance, impedance ,

\left(\rho^{\mathrm{I,R^{\mathrm{I,L^{\mathrm{I,M^{\mathrm{I,Z^{\mathrm{I\right)

\frac{1}{4\pi\varepsilon_0}\left(\rho^{\mathrm{G,R^{\mathrm{G,L^{\mathrm{G,M^{\mathrm{G,Z^{\mathrm{G\right)

, - ! scope="row" , magnetic reluctance ,

\mathcal{R}^{\mathrm I}

\frac{1}{\mu_0}\mathcal{R}^{\mathrm G}

Once all occurrences of the product

\varepsilon_0 \mu_0

have been replaced by

1/c^2

, there should be no remaining quantities in the equation that have an ISQ electromagnetic dimension (or, equivalently, that have an SI electromagnetic unit).

Notes

References

External links

Comprehensive list of Gaussian unit names, and their expressions in base units

The evolution of the Gaussian Units
by Dan Petru Danescu {{Carl Friedrich Gauss Centimetre–gram–second system of units Systems of units Carl Friedrich Gauss