Re: EPSILON_ZERO, OK ?

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Hi Dan:
What bothers me most is that they (designers of SI) forced us
to introduce epsilon_zero at the stage at which students are not
ready to understand it. I agree with you, if I had time I would
eventually come to the sqr(esp*mu) and all that. I hate to say
the "justification will be clear later", especially if I can not be
sure that this will really happen. Borrowing from future is not
an acceptable way to teach physics, in my opinion. I wrote a
note about SI in The Physics Teacher (February 1986, p 97).

Pedagogy was obviously not one of the concerns when SI was
introduced; the main point was to be correct in overcoming
limitations of old systems. By the way, I agree with Michael
that Gauss law would not be less clear if it were expressed
in terms k instead of epsilon. (In fact that is how I learned
it, except that k was dimensionless and equal to one).

"Daniel L. MacIsaac" wrote:

> > Let us invent our own unit of Q and call it S (after Satan). The
> > immediate consequence of this is that the unit of k must be
> > N*m^2/S^2. What is the numeric value of k? It depends on
> > how large is one S. If S is large then k is small, and vice versa.
>
> HA ha ha :^).
>
> > Please verify that the above definition of Coulomb implies that
> > k=8.99*10^9 N*m^2/C^2. It turns out that 4*Pi can be eliminated
> > from some derived formulas if k is written 1/(4*Pi*epsilon_zero),
> > where epsilon_zero is 8.8542*10^-12 C^2/(N*m^2). The name
> > given to epsilon_zero, "permittivity of free space", can not be
> > appreciated in this introductory physics course.
> > Ludwik Kowalski
>
> Ahhh, but you can relate epsilon_zero to something: mu_zero.  You will
> have to explain mu_zero later in your same course.  After that you will
> have to discuss the relationship between mu_zero and epsilon_zero and
> the speed of light c as was (perhaps I am wrong here) discovered by
> Maxwell while playing with the units of epsilon_zero and mu_zero
> and trying to make a constant with units of velocity.  So you have
> a complete and coherent story line for epsilon_zero across three
> chapters.  This puts you ahead of most intro physics texts, which
> have problems maintaining notation (let alone a conceptual story line)
> across chapters.
>
> I'd encourage you to do a little hand-waving on Gauss' law, which ties
> epsilon_zero to k and starts the chain.  And definitely keep the
> Satan system; I'll have to try that myself :^).
>
> Dan, who has no real intention of going to Law School although he
> is often encouraged to develop precision in language in a lawyerly
> fashion.
>
> Dan MacIsaac, Assistant Professor of Physics and Astronomy, Northern AZ Univ
> danmac@nau.edu         http://purcell.phy.nau.edu         PHYS-L list owner