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From: myers@hpfcdj.HP.COM (Bob Myers)
Newsgroups: sci.electronics
Subject: Re: Capacitor-Lost Joules
Message-ID: <11170014@hpfcdj.HP.COM>
Date: 8 Jun 89 18:00:24 GMT
References: <21145@quacky.mips.COM>
Organization: Hewlett Packard -- Fort Collins, CO
Lines: 38

>The puzzle was stated in terms of ideal components. As many writers have
>noted, real circuits have both resistance and inductance.

>Perhaps it's time now to end further net postings on this topic. If anyone
>can cite detailed and complete solutions to this puzzle, especially solutions
>based on Maxwell's equations, I would like to receive them by E-mail.

A numerical solution to the puzzle "based on Maxwell's equations" (actually,
likely based on other well-known equations in EM field theory which are
themselves based upon Maxwell's) is not possible without some details on
the physical construction of the circuit in question.  Clearly, when the
circuit goes into "oscillation" (as it must, since the MUST be some inductance
in the conductors connecting the capacitors, even if they have exactly zero
resistance), the conditions are right for EM radiation.  Some questions remain
to be answered, though, before we can tell how this radiation behaves:

1. What is the length of the conductors between the capacitors (to find the
   inductance, and therefore the resonant frequency of the system, for one 
   thing.)

2. What is the loop area formed when the circuit is closed?

3. How are the capacitors oriented with respect to one another?

For simplicity's sake, I think that we could still assume some other "ideal"
properties - that the circuit is in free space, an "infinite" distance from
any other conductors, and that there is nothing particularly odd about the
way the conductors are run from one cap to the other, or their permeability,
etc..

Given the above, I'll now once again recommend what I consider to be one of
the best introductory texts in field theory:  "Engineering Electromagnetics",
by William H. Hayt, Jr..  You take it from there.


Bob Myers  KC0EW   HP Graphics Tech. Div.|  Opinions expressed here are not
                   Ft. Collins, Colorado |  those of my employer or any other
myers%hpfcla@hplabs.hp.com               |  sentient life-form on this planet.