Re: volume polarization vs. surface charge

["Donald E. Simanek" <dsimanek@EAGLE.LHUP.EDU>]

On Fri, 5 Mar 1999, John S. Denker wrote:

> At 10:23 AM 3/5/99 -0500, Donald E. Simanek wrote that the "sticking" point
> is this:
> > The surface charge due to polarization of a dielectric is, whether you
> > consider it "real" or "virtual", not capable of constituting the charge
> > which makes the spark when the capacitor discharges. It isn't
> > macroscopically mobile.
>
> Hmmm.  If I understand correctly, the topic of conversation can be boiled
> down to two questions:
>
> 1) Given that charged particles are moving in one part of the circuit (the
> dielectric) and also in another part of the circuit (the spark gap), are
> these the *same* charged particles, having traveled from one place to the
> other?

Of course not, as you restate this in so general a manner. The issue was,
I thought, "Where do the charges in the spark come from. That is, where
did they reside in the capacitor. We established that before the spark,
the charges were not on the metal cups (we checked that by disassembly of
the device and nesting the cups directly to each other, ensuring they were
at the same potential, and also discharging them if you wish. On
reassembly, we see the spark. No one doubts the electrons through the
spark must have come through the metal cans. But they had no excess charge
before the spark, and we can check they they have negligible charge after.
So the electrons in the spark must have come from the dielectric. We can
do the experiment again, and this time after disassembly, put a hand
inside or outside the insulating cup and feel the mobile charges transfer
to or from our hand. Let them discharge through an electrometer if you
like.

> 2) Does the answer to question (1) tell us anything interesting about the
> nature of this circuit in general or capacitors in particular?

I didn't see anyone here claim that this demo was supposed to explain, or
tell us anything interesting about capacitors. I certainly didn't claim
that. Nor have I seen any print version of this demo make that claim, but
it wouldn't surprise me if one did. If the demo has any value at all, it
tells us something interesting and valuable about how you test hypotheses
relating to charged bodies and charging of bodies in an unfamiliar and
surprising context. If we only ask questions of students about things
they've already studied in the textbook or class, we never know whether
their book-learning of physics transfers to new and unfamiliar situations.
There's no value in just showing students this (or any other demo) but
there may be value in the interactive dialogue and thinking about the
physics of it, before, during, and after the demo.

I'd compare it to the venerable "Atwood's machine" of mechanics -- two
unequal weights connected by a string over a stationary pulley. Clearly it
is not a useful device, with no application I know of in industry or
technology. Yet in the introductory lab (and even the advanced lab) it has
great value in reinforcing ideas of free-body diagrams, acceleration and F
= ma, or if you wish, center of mass, and conservation of momentum and
energy. And you can test that understanding by asking students the
question: "If an Atwood machine were placed on a bathroom scale, would the
scale reading change as the weights are in motion, compared to its reading
when they were at rest? If not, then why not? If so, does the scale
reading increase or decrease?"  Try those questions in a
conceptual-physics class. And after they've answered, of course you must
test the answers with a demo.

> Consider an ordinary extension cord: 16-gauge copper wire, six feet long,
> carrying 1 amp at 60 Hz.  Some electrons go in at one end, and some
> electrons come out the other end.  Are these the same electrons?  No.
> According to my calculations, all of the electrons involved move only
> submicroscopic distances.  It's an easy calculation.

Of course, what you've said above is correct. But it's irrelevant to the
dissectable capacitor demo. The question there was something like this: We
put excess charge onto the device. Then we tested the metal cans and found
no excess. The spark was due to an *amount* of charge equivalent to the
excess we stored in the "charged" device." We don't care whether the
stored charge was made up of the *same* electrons which went through the
spark, we were trying to account for the *amount* of charge through the
spark, and where that *amount* of charge was in the "charged" device.
Here's the value of the demo. It forces students, and us, to think about
this different situation.

Since, as you noted, we've sometimes been careless with terminology, it
could be that we said something like "The charge going through the spark
was the same as was stored on the insulator." Perhaps we should have said,
The *amount* of charge going through the spark was the same as was stored
on the insulator. I fully agree with you that we ought to be more careful
about such language.

> Therefore when it is pointed out that for capacitors containing *unfree*
> carriers, the input-carriers are not the same as the output-carriers, it is
> hard to see why this is interesting or relevant.  It is hard to see why
> this tells us anything about the nature of capacitors.

If that's all you say about the demo, then I agree that it is trivial,
and, as I noted, we never claimed it was intended to tell us anything
useful specifically about capacitors.

> Or have I completely misunderstood what is the topic of conversation?

That's easy enough for any of us to do, as much interesting wandering from
the topic goes on in any worthwhile discussion. I often scratch my head and
wonder "What *was* the original question?" But in physics, every answer
leads to another question.

Actually, I thought this issue of the demo was "settled" several days ago
and was hoping it would wander to a more fundamental (and important)
question:

In any capacitor (forget the dielectric) why does the mere act of
connecting wires to its plates and bringing them together cause *any*
electrons to take the long route around the wires to discharge the
capacitor? The field in the vicinity of the electrons must change, and
throughout the wire, just from the act of connecting the wire. Why? What
are the *details*? What's going on within the wires?

Students actually ask, and are troubled by this question. Few books even
address it. Most physics teachers (and I have tested this) are speechless
when asked this question "cold". Or they mumble some totally insufficient
"answer".

        -- Donald

.....................................................................
Donald E. Simanek
dsimanek@eagle.lhup.edu                 http://www.lhup.edu/~dsimanek
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