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While for most units the difference between cgs and SI is a mere power of 10, the differences in electromagnetic units are considerable, so much so that formulas for physical laws need to be changed 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 the cgs system, charge is defined via the force it exerts on other charges, and current is then defined as charge per time. This latter approach has as one consequence that Coulomb's law does not contain a constant of proportionality in the cgs system.
Actually, the above gives an incomplete picture of the difficulties with electromagnetic units in the cgs system. There are actually about half a dozen systems of electromagnetic units in use, most based on the cgs system. The most common system of electromagnetic units based on the cgs system is known as esu, or electrostatic units. This is the system described above and has units chosen such that Coulomb's Law, the fundamental law of electrostatics, has no constant of proportionality. Other systems of electromagnetic units based on the cgs system include emu, or electromagnetic units (chosen such that BiotSavart's Law has no constant of proportionality), Gaussian, and HeavisideLorentz units. Further complicating matters is the fact that both physicists and engineers use hybrid units, such as volts per centimeter for electric field.
The units of cgs (specifically esu) are as follows:
The mantissas 2998, 3336, 1113, and 8988 are derived from the speed of light and are more precisely 299792458, 333564095198152, 1112650056, and 89875517873681764.
A centimeter is the capacitance between a 1cm sphere in vacuum and infinity. The capacitance between two spheres of radii R and r is
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