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Re: Capacitance problem



29 Mar 1997; I am responding to Mark's message (see below)

Here is my interpretation of what you are saying; is it correct? I will use
identical plates whose shapes are square. They are in a vacuum and nearly
touch each other. One pair is charged the other is not. All is static. You
tilt the base ("closing the switch") and plates are connected at once. One
pair of plates is discharging (a wide upward displacement current) while the
other pair is charging (an equally wide displacement current downward).
Current loop loops are created and they produce changing magnetic field.
I agree. Note, however, that loops have two horizontal segments; real
currents through metallic plates.

What is the condition for oscillations? The effective R of loops must not
be too large. If R is too large we will have an "overdamped", transition
from one equilibrated system to another. I suspect that this condition
prevails because charges flowing through the metal are bound to inner
surfaces of plates. Remember |Q1|=|Q2| and plates are wide in comparison
with their separation. No matter how thick the plates are the effective
cross sections of the currents through them are very small. I do not know
how to estimate R but I suspect it is sufficiently high to prevent
oscillations.

Yes, it is only an intuitive guess. One way to verify it perform the
experiment and then quickly drop the plates into a calorimeter. Will the
heat added to water be about one half of the energy originally stored in
the electic field? An experiment of that kind may be easier to perform
than trying to measure the time-integrated radiant flux in a broad range
of frequencies.

Yes, I am improvising. I did not even estimate anything numerically. Let
me try this, as I am typing. Suppose each C=20 microF and can hold 300 V.
(An old radio set in my basement has two such capacitors); they are quite
large. At 100 volts the energy is 0.1 J but at 300 volts it is already
nine times larger. A much smaller supercap will hold 62.5 J (5 F, 5 V);
this is about 15 calories. The experiment seems to be feasible. Can
somebody perform it and share the findings?

Now suppose R is not very large and an oscillation of charges does take
place during the transitory period. Some energy will escape in the form
of e.m. waves. How much? How is it going to be distributed? I do not know.
But my intuition tells me that it will not be too much for very large
plate surfaces. I do not have enough self-confidence to explore this with
Maxwell equations.
...................................................................
: Gedanken-ing is not enough; physics is an experimental science! :
: Inspired by thinking about phys-L messages on capacitors :
: Ludwik Kowalski :
...................................................................
kowalskiL@alpha.montclair.edu http://www.csam.montclair.edu/~kowalski
----------------------------- ---------------------------------------

From: Mark Shapiro <mshapiro@sputter2.fullerton.edu>

Basically, the question that you are asking is if Maxwell's Equations are
a correct description of the way electromagnetic fields behave. If you
agree that you have a time-varying electric field between the plates, and
you agree that Maxwell's Equations give a correct description of the fields,
then you reach the conclusion that you have to generate a magnetic field
that also is time-varying. If you are willing to do the calculation for a
simple case (a parallel plate capacitor with circular plates) it is not
hard to show that you generate lines of the B-field that are circular,
and that the amplitude of the B-field decreases linearly with distance
from the axis of the capacitor at any instant of time. That's the condition
you need for radiation!