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Re: funny capacitor (EUREKA ?)



Two days ago I wrote:

So why was I confused? Because I accepted John's
potentials. They are not physical concepts defined
in terms of work per unit charge.

John objected:

I wouldn't have said that.
1) What I call the potential most certainly is work per unit charge.
2) It is a potential in the mathematical sense.
3) It is agrees completely with what Feynman calls "the electric
potential" in section 4-3 of Volume II. He says (at the end of the
section) that it is measured relative to "some reference point".

How can work be defined without a reference point from which
the probe charge is delivered to a point of interest? Once a reference
point is declared the potential becomes a difference of potentials
between two points. That is why I still think that distinguishing a
"potential per se" from a "difference of potentials" is a significant
departure from traditional physics terminology. Feynman does
not make such distinction; his reference point, in section 4-3 is
the "infinity".

I use delta_V to represent potential differences. Some of the
things I say about potential differences are not true about
absolute potentials (which I represent by V).

That what confused me. The standard notation is symbol V
(or the corresponding Greek symbol used by Feynman) for
a difference of potential. I would probably not be confused
if another symbol, such as A or B, was used for the "absolute
potential".

Any speck of dust can be a reference to which you would
attach the black lead of a voltmeter; I am more comfortable
with a grounded chassis or with "infinity". The "infinity"
is not the best term, I prefer to say "a conductive enclosure."
The far-away enclosure has an advantage that its shape and
size are not significant. That is what the word infinity stand
for, in my mind.

What is the evidence that my usage is less than 100%
traditional? I didn't invent gauge invariance!

A traditional model, on the other hand, does not
allow small objects to be references.

Says who?

For example, a technical assistant.

(A traditional reference must be very very large to keep its
potential constant when its net charge is changing.

Hogwash. Anything you choose as a reference will be constant
by construction, by exercise of gauge freedom, no matter what
its size or location.

Remember this started with numerical Laplace-equation solvers.
The program is perfectly happy to find Q as a function of the _
four _absolute_potentials V (not delta_V). ...

That why, in my opinion, a potential per se belongs to mathematics
while a potential with respect to a reference object belongs to physics.
Traditional reference objects (earth or infinity) are very large and
that is why we say V=const, no matter how large Q they receive or
loose. In my opinion this is very different from saying that V=const
"by construction". I am trying to explain my confusion, not to argue
about a powerful new concept of gauge. I would like to know what
other teachers think about that concept. I was not familiar with it;
would this concept be useful in an introductory physics course?

Gauge theories are central to modern physics. The gauge of
electrostatics is just the teeniest tip of the iceberg.

http://www.nobel.se/physics/laureates/1999/press.html

http://www.nobel.se/physics/laureates/1982/wilson-autobio.html

http://www.nobel.se/physics/laureates/1979/press.html