Re: Conserving Q/Faraday

["John S. Denker" <jsd@MONMOUTH.COM>]

Hi --

At 12:17 AM 1/28/99 +0100, Ludwik Kowalski wrote:
> Did [the net Q] enter when the slab was in the E field or
> when we were removing it from Al electrodes?
> Than is the questions for which we have no answer so far.

Earlier, at 10:30 AM 1/26/99 +0100, Ludwik Kowalski wrote:
> In this particular case the net Q was observed first
> and the "why" question was postponed. We just want a clear answer
> about the reality of the net Q.  Is it really there or was
> it introduced by a poorly designed experiment.
> Haw can this question be answered by performing
> a better experiment? The was
> the nature of our call for help.

OK, now I understand the questions.  Those are reasonable questions.  Clear
answers are available.

First, let's replace the insulating dielectric by a conducting dielectric;
that is, we build a three-plate capacitor as follows:


       P1  P2  P3
       P1  P2  P3
       P1  P2  P3
wwwwwwwP1  P2  P3wwwwww
       P1  P2  P3
       P1  P2  P3
       P1  P2  P3

where "w" indicates a wire, and P2 is the "dielectric" plate.  The
advantage of this scheme is that we can unambiguously talk about the
voltage on P2.

Metal has effectively an infinite dielectric constant, but as long as P2 is
separated from P1 and P3 by an air gap (or other insulator), the
combination of insulator plus P2 makes a fine dielectric, increasing the
capacitance of the P1/P3 capacitor.

1.1) The first thing to notice is that even if there were a huge net Q on
P2, it would have no effect on the operation of the P1/P2 capacitor, which
could still be treated as a two-terminal device, with no change in
capacitance.

1.2) There are physical processes whereby P2, even if initially neutral,
could acquire a net Q while in the capacitor.  In particular, suppose the
P1 and P3 plates is made of something with a really high work function e.g.
tungsten, while P2 is made out of something with a really small work
function, e.g. cesium.  Then in equilibrium, P2 would be at a different
voltage than P1/P3.  That's how batteries work.  If you leave P2 in there
long enough to come to equilibrium, and then take it out quickly, you will
be able to carry away a measureable net charge, indeed possibly a rather
large net charge.  But once again, this has nothing to do with the normal
operation of the capacitor.

1.3) There are many ways that additional net charge could be introduced
during disassembly.  Again, this has nothing to do with the normal
operation of the capacitor.

> who knows,
> something useful can always be discovered. Students should be
> presented laboratory puzzles, when possible.

2.0) Well, I'm not sure about that.  A big part of being a physicist in the
real world is having good judgement about what experiments are *not* worth
doing.

I'm sure I could design an experiment to measure the net charge on the
dielectric _in situ_, perhaps by dangling a test charge inside the
capacitor without disassembling it.  But I wouldn't do it.  That's because
I have too many better things to do with my time and other resources, such as:

2.1) If I wanted to study work functions, there are ways to do that.  A
Kelvin bridge would make a fine classroom demo (for students at the
appropriate level).

2.2) If I wanted to explore the limitations of Kirckhoff's laws, there are
other places I would look.  The experiment in question is not well designed
for this purpose.  It offers too many ways whereby poorly-controlled
combinations of known laws can affect the results, leaving little chance of
a reliable observation of any new phenomena.

2.3) If I wanted to study the disassembly effects, I would play with an
electrophorus or perhaps a condenser-type microphone -- but I would be
careful to do it long after the students understood how a normal capacitor
works, and I would be careful to point out that normal capacitors are
designed so that these effects do not normally occur.

2.*) Concerning my philosophy of pedagogy:  Any net Q on P2 is either
irrelevant to, or a violation of, the usual laws of capacitance.  I would
make sure that the students understand the basic, normal laws.  Only after
that knowledge was well consolidated would I delve into deviations.

Cheers --- jsd