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1) In old days, Coulomb's law was used for two purposes,
(a) to express the observed proportionality between F and
Q1*Q2/r^2 and (b) to define the unit of electric charge.
After writing F=Q1*Q2/r^2 a teacher would say:
Two charges of equal magnitude interact with a force of
one unit from a distance of one unit. What can be more
simple and more natural to somebody who is just starting
to learn electricity?
(a) Pedagogically, it is not wise to tell students "accept
Coulomb's law as written; the advantage of the 4*Pi will
become clear later". The old advice "do not accept anything
without understanding" is still worth giving.
b) A situation in which the writing of a formula depends on
the system of units is not desirable.
Note that F=m*a, or any other formula in mechanics, does not change when
we decide to use feet and pounds instead of meters and newtons.
It all depends on *which version* (the local differential versions or the
integrated bulk versions) of the laws of electromagnetism whose
appearance you are most interested in simplifying.
4) Let me add that the incorporation of the dimensional
constant, epsilon_zero, into Coulomb's law, multiplied
pedagogical difficulties by one million times,
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.