The CGS System of Units

The centimetre-gram-second system (abbreviated CGS or cgs) is a metric system of physical units propsed by the German mathematician Gauss, based on the centimetre as the length unit, the gram as the mass unit, and second as the time unit, as opposed to the metre, Kg and second in the internationally accepted SI system. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.

The CGS system has been largely supplanted by the MKS system, based on metre, kilogram, and second. MKS was in turn extended and replaced by the International System of Units (SI). The latter adopts the three base units of MKS, plus the ampere, mole, candela and kelvin. In many fields of science and engineering, SI is the only system of units in use but there remain niche areas where the CGS system is prevalent.

In measurements of purely mechanical systems (involving units of length, mass, force, energy, pressure, and so on.), the differences between CGS and SI are straightforward and rather trivial; the unit-conversion factors are all powers of 10 arising from the relations 100 cm = 1m and 1000 g = 1 kg. For example, the CGS derived unit of force is the dyne, equal to 1g·cm/s 2 , while the SI derived unit of force is the newton, 1kg·m/s 2 . It is straightforward to show that 1 dyne =10 −5 Newtons:

On the other hand, in measurements of electromagnetic phenomena (involving units of charge, electric and magnetic fields, voltage, and so on), converting between CGS and SI is much more subtle and involved. In fact, formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case 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.

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