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Re: Conserving Q ?



Date: Fri, 20 Nov 1998 10:52:31 +0100
From: Ludwik Kowalski <kowalskiL@MAIL.MONTCLAIR.EDU>
Subject: Conserving Q ?
To: PHYS-L@LISTS.NAU.EDU
Reply-to: kowalskiL@mail.montclair.edu
Organization: Montclair State University, New Jersey

More "teasers" for physics students? Suppose an electric
circuit (very complicated or very simple) is connected to a
battery via two wires, #1 and #2. We often say that in any
short time interval the current in wire #1 is equal to the
current in wire #2. And some add "because charges must be
conserved". Here are some questions.

An experiment was performed showing that I1 is largerthan
I2. And integrals of currents (when I1>0 and I2>0) differ in
the same way. For example, I1=5*I2 and Q1=5*Q2. Would such
data be in conflict with the law of conservation of electric
charges? I do not think so. By the way, the description of a
real experiment of that kind is going to be posted
separately.

Suppose a circuit is very simple, only one branch, a vacuum
capacitor C (parallel plates very close to each other) in
series with R. Plus two ammeters, one inserted into the wire
#1 and another inserted into the wire #2; the R*C is
conveniently long. An experiment shows that I1=I2, at any
moment. How can it be if there is no motion of charges in
the vacuum? The displacement current through C was invented
by Maxwell; is it real or imaginary? These two adjectives
are NOT used in the context of complex numbers. An old
question for each generation of physicists and engineers.

Some say the displacement current is a mathematical
abstraction (extremely useful); it is not a real current.
What makes it less real than other abstractions, such as
"ohmic current" in a wire, or "water current" in a tube?

Ludwik Kowalski

Ludwik,
Your questions always seem to get me in over my head!
But here goes anyway. I don't think that the displacement
current is any less real than an "ohmic current". Among
other things it serves the function of preserving charge
conservation in the following sense. It preserves the
nature of current that there are no true sources or sinks
for electric current. Between the plates of a charging
capacitor the current exists and flows along so that if you
integrate the source/sink density over some volume,
including the space between the plates, you always find
that the same amount of current is flowing into the volume
as is flowing out. W. B. Newbolt
Barlow Newbolt
Department of Physics and Engineering
Washington and Lee University
Lexington, VA 24450

There is something fascinating about science. One
gets such wholesale returns of conjecture out of
such trifling investments of fact.
Mark Twain
Telephone and Phone Mail: 540-463-8881
Fax: 540-463-8884
e-mail: NewboltW@madison.acad.wlu.edu