Re: The conceptual change process (long)

[William Beaty <billb@eskimo.com>]

On Sun, 15 Feb 1998, Bob Sciamanda wrote:

> Bill,
> Had you been my student, you would have examined the details.  You were
> taught (or at least learned) words, not physical phenomena.

Bob,

The trouble is, I DID examine details.  As I student I used H&R, and as
part of electronics classes I did lots of capacitor experiments.  But the
particular way that my mind "pigeonholed" the information was the cause of
the problem.  I see that all this happened on a conceptual level, not a
level of words.  My concepts were fine, it was my "concept net" that was a
horrible mess.  Things didn't connect.  My analogy for a capacitor was
that of a charge-filled bucket, when it should have been that of a
stretched rubber band, or of a membrane between two water-filled chambers. 
The bucket-metaphor made me misinterpret everything.

> I sympathize
> with your indictment of poor teaching; I just think that the problem is not
> in (or cured by changing) the words, it is in the ideas.

Exactly.  In hindsight, I see that my long-held capacitor misconceptions
centered around a particular misconception which caused all "correct" 
concepts to become distorted even as I encountered and internalized them. 
When all was said and done, my understanding of capacitors was dominated
by a tyrannical misconception: the idea that capacitors are basically
devices for storing charge.  Now I know better, and I have reassembled my
concepts into a somewhat coherent whole.  Yet I still recall my earlier
unfortunate state, and I'm pretty sure that I understand what caused it.

I admit that I got off-track with the "charging" and "discharging" thing. 
I am leery of those terms, but as long as an educator takes pains not to
let the "capacitors store charge" misconception take hold of their
students, then those terms serve.  Cannons are charged and discharged with
gunpowder.  Springs are charged and discharged when they are compressed
and released, sort of.  As long as students realize that "charged" and
"discharged" refers to energy or "charge configuration" and not to
electric charge itself, then the terms are OK.  But the terms do lend
themselves to being misused, like this:

   "when a capacitor is charged, a flow of charge is directed into the
   capacitor and is stored there".

That statement IS the misconception.  It's like saying "when a rubber band
is stretched, a flow of rubber is directed into the band and is stored
there." 

>  Don't rely on
> words (or mathematics) alone to convey or express the physics; they must be
> chewed, ruminated, digested, purged of waste materials, and only then
> assimilated into our being.  Whatever word choices we make, they too are
> faltering, incomplete (linguistic) models for ideas (which themselves are
> models of reality).

My arguments center around my recent activities in journeying back into my
earlier physics learning experiences and their results, and my discovery
of a major distorting concept in myself.  I had originally failed to chew
and digest old concepts.  I could use the concepts, but realized that
something was seriously wrong.  When I went back and sorted things out
(with the benefits of having worked on K-6 misconceptions), I extracted a
single large monkey wrench that had been lodged in my "concept digestion
mechanism." Then later I discovered that many other people suffered under
(apparently) the same distortion as I.  If this misconception had been
limited to myself, I wouldn't be spending so much time with it on phys-L. 
I'm extremely passionate about it (obviously), and anyone who tries to
paint it as silly or trivial is going to attract a bunch of screenfuls of
debate from me, because I think I've seen evidence that it's neither. 
Perhaps in physics and other sciences it is tolerable, but for electronics
people it is a mental disease which causes incompetence. 

> Can a piece of amber store charge?  Can two objects store equal and opposite
> charges?

Yes.  And if two equal and opposite charges are put into a single
container, has electric charge been put into the container, or did the
first charge cancel out the second?  If I shoot a proton and an electron
at you, have you aquired an electric charge, or do you now have an extra
(neutral) hydrogen atom?  If you pull an electron and a positron out of
the vacuum, did you create any charge?  These questions all have definite
answers, and the 2-plate capacitor should not be treated as a special
case where the answer is non-standard.

I think that analogies illustrate the flaw more clearly.  If I stake down
the ends of a rubber band, then grasp the center of the rubberband between
thumb and forefinger and move it towards one of the ends, have I "stored
rubber"?  No, because every bit of rubber that was removed from one side,
was placed into the other side.  Considered individually, one side of my
rubber band has less, and the other side has more, but no rubber has been
created, destroyed, or added.  If I boost an atom's electron from a lower
shell to a higher, have I injected charge into the atom?  Is the atom a
device for storing charge, or does it have constant (but energetically
reconfigurable) charge?  Is my rubberband a device for storing rubber, or
does it have constant (but energetically reconfigurable) quantity of
rubber?  Do we usually reconfigure the charges in a capacitor
energetically, while simultaneously leaving the capacitor neutral before
and after?  I'd say yes. 

> A capacitor is a thing;  in the most common use of the word it is
> a system of two conductors, electrically insulated from each other.  Many
> things can be done to/with this thing;  the two conductors can each be
> electrically charged in a wide variety of ways.  Such a physical discussion
> should be engaged (and played with in electrostatic experimentation - real
> and/or gedanken) long before the concept of "capacitance" as a definable
> property of a properly designed system subjected to a definite procedure is
> created.

True, and the bulk of my comments are regarding a 2-plate capacitor.  This
is different than the "3 metal sphere capacitor."  In the 2-plate
capacitor, the inherent 3rd plate at infinity creates two more capacitors
usually having capacitance that is MANY ORDERS OF MAGNITUDE less than the
capacitance caused by the two plates.  With this type of device, I
obviously can place +1000uC charge on one plate and -2000uC charge on the
other, but the result might be a capacitor with ten volts between its
leads, and 1 billion volts negative on the capacitor with respect to
ground (or infinity.)  So, for this type of capacitor on the lab bench, I
CANNOT put two different charges on the plates.  Yes, this does not apply
to a 3-sphere capacitor. But a 2-plate capacitor (say 1000uF) is a
different animal because its capacitance to infinity might be 3pf.  In
this sort of capacitor, more general concepts get split into two separate
concepts: 

  "charge difference inside the capacitor"  (Important)

  "electrostatic charge on the device with respect to ground."  (Tiny
   enough to be ignored) 

If I take a long view regarding these messages, I note that what I'm doing
is to insist that all explanations of capacitors stringently stay
consistent with the conservation law.  If we place equal (+) and (-) 
charges into any device, then we damn well better NOT say that we have
injected any charge into that device.  Putting in the (+) may increase the
charge, but putting in the (-) decreases the charge again. 

I would even extend this into the single-proton-universe stuff: keep the
universe neutral, and when we inject (+) and (-) into the plates of our
capacitor, WE SHOULD NOT IGNORE WHERE WE GOT THOSE CHARGES.  Charge cannot
be created.  Opposite charges must arise together.  Maybe the universe
isn't neutral, and there are unmatched protons laying around somewhere. 
But wouldn't it be simpler to assume a neutral lab-bench, to avoid the
extra complexity?  Then, when we "charge" a capacitor, we have to find a
blob of neutral matter, extract equal amounts of (+) and (-), then place
them on the capacitor plates.  Or, we can note that the capacitor plates
themselves are matter, and we can steal some (-) from one plate, which
leaves (+) behind.  This adds complexity to an explanation, but it also
knits the explanation into the rest of physics in a way which "capacitors
store charge" definitely does not. 

> I agree with your complaints (I had some terrible teachers, too).   But my
> biggest complaints are with semantic arguments over non-problems and with
> semantic cures for real problems.

I see your point.  I do agree that a ban on the words "charged" and
"discharged" leans too much towards the behavior of a Grammar-nazi.  But
it still gives me the creeps to use them, knowing how I was misled myself,
and gradually discovering more and more others who have this same
"infection."  I'm not trying to force terminology on people in order to
satisfy a pendantic streak in myself.  I'm trying to get them to stop
teaching a misconception.


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