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Chapter 3:
Units Associated with Twentieth-Century Electromagnetic Theory
By the beginning of the twentieth century it had become customary to base electromagnetic theory on Maxwell's equations and the Lorentz force law. In principle, any classical electromagnetic formula can be derived from these equations; so, whenever a system of units changes the form of Maxwell's equations or the Lorentz force law, we can expect corresponding changes in the equations and formulas of classical electromagnetism. Perhaps the first set of units to become popular in the twentieth century was the Gaussian system of units. Physicists, always interested in reducing theoretical clutter, liked these units because they removed both ε 0 and μ 0 from electromagnetic equations and formulas. The price paid for this advantage - extra factors of the speed of light in Maxwell's equations and the Lorentz force law - was thought to be well worth the resulting conceptual simplification of electromagnetic theory. The Gaussian system of units, like the esu and emu systems, only recognizes the three fundamental dimensions of mass, length, and time. Although twentieth-century physicists liked Gaussian units, electrical engineers, after a few decades of indecision, chose the rationalized mks system of electromagnetic equations. This system, like the esuq and emuq systems discussed in Chapter 2, recognizes the existence of a fourth fundamental electromagnetic dimension in addition to the three traditional dimensions of mass, length, and time. Like the esuq and emuq systems, both ε 0 and μ 0 are kept as explicit constants; unlike the esuq and emuq systems, a process called "€œrationalization" is used to eliminate all factors of 4π from Maxwell's equations. We start the discussion of twentieth-century electromagnetic units by combining the esu and emu units to create the Gaussian system and then move on to describe a rationalized cousin to the Gaussian units, called the Heaviside-Lorentz system, which has recently become popular with elementary particle physicists. We show how to go from the Gaussian or Heaviside-Lorentz systems to the unrationalized and the rationalized mks systems. The unrationalized mks system, although not in use today and never very popular, is a helpful traditional system when converting equations to and from the rationalized mks system. Just as in Chapter 2, emphasis is placed on how to convert electromagnetic equations and formulas from one system of units to another, explaining as we go the diagrams and tables needed to make the change.
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