vaso@mips.COM (Vaso Bovan) (06/07/89)
I am the original net poster of the "Capacitor Paradox". As several writers have commented, this puzzle is not new. The two standard explanations are: A) The "lost" energy is dissipated in circuit resistance ; B) The energy is radiated away. My purpose in posting was was to get a clarification of the two answers. In printed derivations of answer A, the statement is generally made that energy is dissipated in circuit resistance "independent of the value of resistance." Such derivations show a solution with resistance in the denominator of some equation. This explanation is intuitively incomplete, because of the behavior of the solution equation as resistance goes to zero. Re answer B, I've never seen a complete derivation from Maxwell's equations. I was hoping someone on the net would post or E-mail such a derivation. All the answers I've seen here on the net and elsewhere based on answer B have been armwaving exercises. 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.
myers@hpfcdj.HP.COM (Bob Myers) (06/09/89)
>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.