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[Phys-l] dimensionful permittivity



Hi --

1) Happy solstice everybody.

Now that the days are getting longer (in the northern hemisphere) maybe
we ought to have a big celebration. Oh, wait, never mind.


2) I revised my web pages on electromagnetism including
http://www.av8n.com/physics/maxwell-ga.htm and
http://www.av8n.com/physics/straight-wire.htm
so that both c and ε appear explicitly.

This makes the equations valid in /any/ system of units, including
SI among others.

In contrast, in /some/ systems of units, it would have been
possible to write less-general but more-compact formulations,
perhaps by choosing units such that c=1 and/or 4πε=1.

My rationale goes something like this:

1) I like elegance as much as the next guy, but given the choice between
a small amount of elegance and a large amount of practicality, I choose
practicality.

You can walk into Home Depot and buy a voltmeter, but not a statvoltmeter.

2) Students are even less fond of statvolts than I am.

3) There are ways of re-arranging the equations very slightly, so as
to keep most of the symmetry without sacrificing any of the generality
or practicality.

4) Converting from the more-general form to some less-general form is
easier than the other way around.

On the other side of the argument, cgs/esu is not dead. Theorists use
it. The more theoretical they are, the more likely they are to use it.
AFAICT practically everything heretofore published on the Geometric Algebra
approach to electromagnetism has set 4πε=1.

*** If anybody has good arguments pro-or-con this-or-that forumlation,
I'd like to hear them. I kept the old cgs/esu version around just in
case.

I thought about writing something about converting to other systems of
units but I decided not to bother, on the grounds that few people are
interested, and the ones who are interested are the ones who do E&M for
a living, and they already know how to do the conversions. For details
see the wikipedia "cgs" article, or the Baylis & Drake article cited in
http://www.av8n.com/physics/maxwell-ga.htm

==============

I added a section to
http://www.av8n.com/physics/straight-wire.htm
wherein I mention Stokes’s Theorem and Ampère’s Law ... and apply them
to the case of a solenoid. Nothing earth-shaking.