I am always unhappy in justifying the 4*PI*epsilon
factor while introducing the Coulomb's law. As stated
yesterday, the dimensionless 4*Pi factor is much less
troublesome than the epsilon_zero. whose dimension, in
terms of four basic SI units, is (A^2*s^4)/(kg*m^3).
What is epsilon_zero? Why is it called permittivity?
What kind of experiments had to be performed to find
out that epsilon_zero happens to be equal to 8.85*10^-12
SI units? Most students taking an introductory physics
course, either in a high school or a college, never learn
how to answer such questions. As far as they are
concerned physics is dogmatic; it asks them to accepts
things without understanding.
Most textbooks introduce A as C/s, and redefine it later
in terms of magnetic interactions. Does this bring some
clarity? Not much. The magnetically defined A introduces
a new mysterious parameter, mu_zero? Why is it called
permeability? Is this also an experimental value, like
epsilon_zero or is it simply 4*Pi*10^-7 by definition?
These questions are usually not answered.
Conceptual difficulties of that kind are purely artificial,
they did not exist when I was learning physics for the
first time. The SI made physics more complicated than
it should be at the introductory level; it forced us to
teach physics dogmatically. I am not trying to glorify the
situation which existed before 1960; the introduction of
SI helped to eliminate some undesirable things.
The most important, in my opinion, was the elimination of
two cgs systems, CGSE and CGSM. Why did physicist use
two systems when one would be sufficient? Because they
wanted to preserve practical units (volts, ampere, ohm, etc.)
used by technologists. Units which were either too small or
too large were not desirable from the point of view of
"computational efficiency". The SI people said "our one
system does include practical units" and they were successful
in making this system "official" in physics.
In my opinion the benefits (avoidance of very large or very
small multiplication factors in household computations) were
not worth the intellectual costs. The hidden epsilon_zero
(experimentally measured) and mu_zero (artificially imposed)
made physics more difficult than it ought to be. And they are
totally inconsistent with the traditional order of teaching
topics one after another.
So what is the remedy? Perhaps a totally new sequence of
teaching electromagnetic topics can be invented to match
the SI system. I do not think that the SI will go away very
soon and new sequences are worth trying. Another approach
is to invent a better system of units for our traditional
sequence (which begins with electrostatics). Am I the only
one who is bothered by dogmatization of elementary
physics imposed on us by SI?
Ludwik Kowalski