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Re: [Phys-L] unification or not .... was: standard DC circuits



I've been thinking some more about this.

The smart way to handle introductory circuits goes
like this:

The hookup wire is a good conductor. In the DC
limit, if you tried to establish a voltage difference
between one end of the wire and the other, the
electrons in the wire would re-arrange themselves
so as to cancel the voltage difference. For present
purposes (and a *lot* of other purposes besides) we
do not care about the details of how the charges
re-arrange themselves.

This is both traditional and sensible.

Also, it is entirely consistent with how we handle
other physics topics. For example, in introductory
mechanics, when there is an elastic collision between
two billiard balls, we "could" ask for details on the
force profile
-- is there a small force for a long time?
-- is there a large force for a short time?

That is a perfectly reasonable question, and sometimes
students do ask it, but for present purposes (and a
lot of other purposes besides) we do not need to know
the answer.

For an inelastic collision, where the balls collide
and stick, the details of how they stick are even
more complicated.

A student who is curious about such things should be
encouraged to stay curious, but there is such a thing
as delayed gratification. As we have discussed before,
a big part of teaching involves knowing when to keep
your mouth shut, to /not/ say everything you know.

Part of the charm of physics is that we imagine we
could explain everything in detail, 100% reductionist
detail. Meanwhile, however, another part of the charm
of physics is that very often we can obtain the answers
to important and interesting problems /without/ having
to spell out every detail.

In high-school geometry, the game is to start with a
handful of basic axioms and then derive everything
else. However, as Feynman and others have emphasized,
physics is not like that. In the introductory course,
it is entirely OK to use the ideal gas law without
bothering to derive it from quantum-mechanical first
principles. There is such a thing as the spiral
approach. There will be plenty of time to spiral
back and derive the gas laws from first principles
in the upper-division thermodynamics course. Ditto
for the steering charges in electrical circuits.

To every thing there is a season, and a time to every
purpose under heaven. -- Ecclesiastes 3:1

In the non-introductory course, I am 100% in favor
of discussing the equilibrium charge distribution.
Indeed, I am support teaching a simplified version
of methods for calculating the actual charge
distribution.
http://www.av8n.com/physics/laplace.htm

This stands in contrast to the "artist's conception"
distributions that one finds in certain books, which
have some inaccuracies. The fact that nobody seems
to mind -- or even notice -- tells me that the details
of the charge distribution are not really important.