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. it can also sometimes be a willy.
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.
This explains why, 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:
However, expressing a CGS derived unit in terms of the SI base units involves a combination of the scale factors that relate the two systems:
|Quantity||Symbol||CGS unit|| CGS unit|
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|
Maxwell's theory of electromagnetism relates these two laws to each other. It states that the ratio of proportionality constants and must obey , where c is the speed of light. Therefore, if one derives the unit of charge from the Coulomb's law by setting , it is obvious that the Ampère's force law will contain a prefactor . Alternatively, deriving the unit of current, and therefore the unit of charge, from the Ampère's force law by setting or , 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:
Furthermore, 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. Then we have (generally) and . The factors λ and λ′ are rationalization constants, which are usually chosen to be 4πkCε0, which is dimensionless. If this quantity equals 1, the system is said to be rationalized. The original CGS system, however, used λ = λ′ = 4π, or, equivalently, kCε0 = 1.
The table below shows the constant values used in some common systems:
(The constant b in SI system is a unit-based scaling factor defined as: .)
|charge||electrostatic unit of charge, franklin, statcoulomb||1 esu = 1 statC = 1 Fr = √(g·cm³/s²)||= 3.33564 × 10−10 C|
|electric current||biot||1 esu/s||= 3.33564 × 10−10 A|
|electric potential||statvolt||1 statV = 1 erg/esu||= 299.792458 V|
|electric field||1 statV/cm = 1 dyn/esu||= 2.99792458 × 104 V/m|
|magnetic field strength H||oersted||1 Oe||= 1000/(4π) A/m = 79.577 A/m|
|magnetic dipole moment||emu||1 emu = 4π × 10-6 Oe||= 10−3 Am²|
|magnetic flux||maxwell||1 Mw = 1 G·cm²||= 10−8 Wb|
|magnetic induction B||gauss||1 G = 1 Mw/cm²||= 10−4 T|
|resistance||1 s/cm||= 8.988 × 1011 Ω|
|resistivity||1 s||= 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|
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
The ESU unit of charge, statcoulomb or esu charge, is therefore defined as follows: In CGS electrostatic units, a statcoulomb is equal to a centimetre times square root of dyne:
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 , , and , where and are the well-known vacuum permittivities and c the corresponding light velocity, whereas and 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 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.
|Atomic mass unit||u||1.660 × 10−24 g|
|Bohr magneton||μB||9.274 × 10−21 erg/G|
|Bohr radius||a0||5.291 × 10−9 cm|
|Boltzmann constant||k||1.380 × 10−16 erg/K|
|Electron mass||me||9.109 × 10−28 g|
|Elementary charge||e||4.803 × 10−10 esu of charge|
|1.602 × 10−19 emu of charge|
|Fine-structure constant||α||7.297 × 10−3|
|Gravitational constant||G||6.674 × 10−8 cm3/(g·s2)|
|Planck constant||h||6.626 × 10−27 erg·s|
|Speed of light in vacuum||c||2.998 × 1010 cm/s|
At the same time, the elimination of and 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 and it has been cause to much mystification how its numerical value should be explained. In SI units with 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 , where the Einstein expression corresponding to , , is an energy, which thus can naturally be expressed in eV ( is Planck's constant divided by ).