Centimetre–gram–second system of units: Difference between revisions

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=== CGS approach to electromagnetic units ===
The conversion factors relating [[electromagnetism|electromagnetic]] units in the CGS and SI systems are made more complex by the differences in the formulaeformulas expressing physical laws of electromagnetism as assumed by each system of units, specifically in the nature of the constants that appear in these formulaeformulas. This illustrates the fundamental difference in the ways the two systems are built:
* In SI, the unit of [[electric current]], the ampere (A), was historically defined such that the [[magnetism|magnetic]] force exerted by two infinitely long, thin, parallel wires 1&nbsp;[[metre]] apart and carrying a current of 1&nbsp;[[ampere]] is exactly {{val|2|e=-7|u=[[newton (unit)|N]]/[[metre|m]]}}. This definition results in all [[International System of Units#Derived units|SI electromagnetic units]] being numerically consistent (subject to factors of some [[integer]] powers of 10) with those of the CGS-EMU system described in further sections. The ampere is a base unit of the SI system, with the same status as the metre, kilogram, and second. Thus the relationship in the definition of the ampere with the metre and newton is disregarded, and the ampere is not treated as dimensionally equivalent to any combination of other base units. As a result, electromagnetic laws in SI require an additional constant of proportionality (see ''[[Vacuum permeability]]'') to relate electromagnetic units to kinematic units. (This constant of proportionality is derivable directly from the above definition of the ampere.) All other electric and magnetic units are derived from these four base units using the most basic common definitions: for example, [[charge (physics)|electric charge]] ''q'' is defined as current ''I'' multiplied by time ''t'', <math display="block">q = I \, t,</math> resulting in the unit of electric charge, the [[coulomb]] (C), being defined as 1&nbsp;C = 1&nbsp;A⋅s.
* The CGS system variant avoids introducing new base quantities and units, and instead defines all electromagnetic quantities by expressing the physical laws that relate electromagnetic phenomena to mechanics with only dimensionless constants, and hence all units for these quantities are directly derived from the centimetre, gram, and second.