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The units describing the kinematics and dynamics of mechanical objects are straightforward to learn and use. Different units of length are always the same kind of unit, differing only in size; different energy units are always the same kind of unit, differing only in how much energy is specified; and so on. One happy consequence of this pattern is that all the equations of classical Newtonian physics have the same form no matter what system of units is being used. Indeed, it seems intuitively absurd that any other pattern could exist, that two different units for the same physical quantity could be different in kind as well as size. Nevertheless, an idea can be intuitively absurd without being mathematically absurd, and there are times when it is not clear what kind of unit best describes a well-understood physical quantity. This book will show that the equations and formulas of classical electromagnetic theory routinely change form when expressed in different units exactly because the physical intuition of scientists has been different, leading them to create units that are different in kind as well as size to measure the same electromagnetic quantities. The idea of many different “kinds” of units for the same physical quantity may seem strange at first, but like most ideas involving units it is really rather simple once the right perspective is adopted. Fortunately, there do exist procedures using elementary mechanical units that are analogous to what goes on when we change the kinds of units used in electromagnetic theory; we can use this analogy to introduce the appropriate perspective for understanding electromagnetic units. This chapter begins by presenting material with which the reader is probably already familiar—what a unit is, what a dimension is, the rules for manipulating units inside equations—and then moves on to describe the procedures applied to standard mechanical units in quantum mechanics and relativistic physics to simplify the forms of complicated equations. It should be emphasized that all these equations are presented as “given,” with no expectation that the reader will gain or have any particular knowledge of how the equation is derived; we just show how to simplify the equation by changing the units in which it is expressed. By the end of the chapter the reader will have acquired the rules and terminology needed to describe how and why the equations of classical electromagnetism change form when moving from one system of units to another.
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