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Units

When Physicists are working out problems "formally" (that is, trying to understand "how things behave") they are usually only concerned with deriving a formula which describes the behaviour, not so much with getting "numbers" out of the formula. This is why we can tolerate so much confusion in the details of the alternate electromagnetic unit systems. We never actually calculate any "answers" that an engineer could use to build devices with; we simply derive a formula for such calculations, preferably in a form as free of specific units as possible, and leave the practical details up to the engineer (who may be us, later).

So I have left the unspecified "coupling constants" k_E and k_M undefined while we talked about the qualitative behaviour of electric and magnetic fields. Now we finally have to assign some units to all these weird quantities.

The history of units in ${\cal E}$&${\cal M}$ is a long horror story. It isn't even very entertaining, at least to my taste. Numerous textbooks provide excellent summaries of the different systems of units used in ${\cal E}$&${\cal M}$ [there are at least three!] but even when one understands perfectly there is not much satisfaction in it. Therefore I will provide only enough information on ${\cal E}$&${\cal M}$ units to define the unavoidable units one encounters in everyday modern life and to allow me to go on to the next subject.

As long as electric and magnetic fields are not both involved in the same problem, one can usually stick to familiar units expressed in a reasonably clear fashion. Let's discuss them one at a time.