The way that I introduce the constant in Coulomb's law is as
follows (1) I point out that the size of the basic unit of charge (like
all other basic units) is arbitrary - we are free to select any size unit
that is convenient, (2) I remind students that the force unit (the Newton)
already has been established by our work in mechanics, and that the result
of Coulomb's law must be expressed in terms of force units, (3) that the
most CONVENIENT value for the constant obviously would by unity, i.e. when
we have two one unit charges one meter apart there should be a 1 N force
on each, (4) I then bring in a little history and tell them that in some
earlier systems of units that is exactly what was done, (5) then I point
out that when you do it this way you are relying on an ELECTROSTATIC
experiment to maintain the basic unit of charge and supply a few reasons
why that may not be the most practical way to maintain a basic unit if you
are in the business of running a standards lab, (6) then - and only then -
do I tell them that it is much easier to maintain a unit of current than
charge so in the SI system the Ampere is the basic unit etc. etc....
While this may not square with someone's "ideal" for teaching, it
happens to be the ugly truth, and since physics is an experimental science
they might as well get a feel for how one maintains the basic units
experimentally.
Dr. Mark H. Shapiro
Physics Department
California State University, Fullerton
P.O. Box 6866
Fullerton, California 92834-6866