chapter 4, Two Standard Shortcuts Used to Transform Electromagnetic Equations

Excerpt

The last several chapters have explained how the standard rules for changing units apply to electromagnetic physical quantities. Having become familiar with these rules, we are now sure that electromagnetic equations and formulas transform in a way that makes sense when going from one system of units to another. We also know, however, that following these rules can be algebraically cumbersome, forcing us always to watch for the appearance or disappearance of constants ε₀ and μ₀ as we recognize or refuse to recognize charge as a new dimension. Engineers and physicists are no more eager than anyone else to do unnecessary work; consequently, they have come up with both the free-parameter method and substitution tables, two shortcuts that can greatly reduce the time required to convert electromagnetic equations and formulas from one system of units to another. Unfortunately, neither shortcut is perfect: substitution tables can give ambiguous answers in unusual situations, and to apply the free-parameter method we must first relate our equation or formula to one or more of a predefined list of equations and formulas. Nevertheless, these shortcuts often provide a quick and easy way of transforming electromagnetic expressions; and whenever there is any doubt about the result, the transformation can be checked using the procedures explained in the previous chapters.

4.1 The free-parameter method

Table 4.1 lists Maxwell's equations and the Lorentz force law for the six major electromagnetic systems discussed in this book. As pointed out at the beginning of Chapter 3, any classical electromagnetic formula can be derived from Maxwell's equations and the Lorentz force law. This means we can consult Table 4.1, select the appropriate equations in the desired set of units, and from them derive the formulas we need to know. Although this process gets the job done, it usually requires a lot of work. To avoid the unpleasant prospect of deriving all of our formulas and equations from Maxwell's equations and the Lorentz force law, we construct instead a long list of basic electromagnetic equations that contains everything (including Maxwell's equations and the Lorentz force law) likely to be useful. Instead of providing six long lists—one for every electromagnetic system—we use the four free parameters ε̃, μ̃, k₀, and ∏ FT shown in Table 4.2 to reduce the six lists to one.