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Re: Capacitor Charged, Right term



David, Thanks for the comments regarding how the global topological
properties affect my statements. I was being rather intellectually lazy and
was only thinking of open universes, which of course have no logical
necessity.

Joel Rauber, being dissatisfied with the idea of charges at infinity,
wrote:
I have never been happy with the statement that the field lines on the +Q
charge must continue to -Q's at infinity. . . . .

I probably overstated my point, I'm not so much dissatisfied as much as I
felt the logical necessity wasn't there. I admit to appealing to the
construct all the time in class; but it is simply to make my life easier.

Whether or not the idea of a universe with a net electric charge is a
necessity or just a convenience depends on the asymptotic topological
structure of the spatial sections of the spacetime of the universe. If the
universe is spatially infinite then the idea of neutralizing charges at
infinity is a convenience. If the universe is topologically compact, (i.e.
closed and bounded in extent) then the universe *must* be charge-neutral.
. . .

If one writes the Poisson equation for the potential on a compact space
with
a net nonzero source charge (i.e. integral of the charge density over the
entire space) the equation will admit no solution. If the whole compact
space is charge-neutral, however, the solution is unique up to an arbitrary
additive constant.

I intuitively understand what you are saying, regarding the Poisson
equation, based on you're wonderful example above that I snipped. Can you
quote any theorems or direct me to any references? This is a quite
interesting topic of how global topological properties affect uniqueness and
existence of solutions and is something not addressed in the usual advanced
physics E&M texts.

BTW, I don't mind at all saying that a capacitor is charged and discharged.
I *do* believe, however, that before ever using the word 'charge' as a verb
in connection with a capacitor, that the instructor very carefully define
the meaning of that verb in terms of a process where net positive charge
accumulates on one electrode 'plate' via conduction from a connection to an
external circuit *and* a compensating net negative charge accumulates on
the
other electrode 'plate' via conduction to the other side of the external
circuit in such a way that the total net charge on both electrode plates
together remains effectively zero.

This is exactly how I approach the topic in class, including the careful
definition of the verb in terms of the process of accumalation of net charge
on the positive plate, etc etc.

Joel