I agree with all the interesting comments below, both Stephen's and yours, relative to the unavoidable antenna aspect of a coil, which makes it non purely inductive to some extent when current varies with time.
However, may I remind you that my initial statement, which you deemed 100% incorrect, simply said that "keeping the current going" in an isolated non-resistive current loop would not consume energy. In which case i is constant in time, so the frequency f of the signal is zero, so the wavelength lambda = c/f is infinite, so the radiation resistance: Rr= 31171 * A^2/lambda^2 (with A the area of the circular loop) is zero. So the power Rr*i^2 consumed in Rr is zero too. This still doesn't make my loop consume energy. However this discussion on radiation makes me think there is indeed one thing I have overlooked and which will make my constant-current loop consume energy, it's synchrotron radiation. You know, that thing which should make electrons lose energy while orbiting their nucleus. I doubt it can be significant at the low speed of electrons in wires though. All this goes to show that there is more than meets the eye in a "simple" current loop. BTW, wrt your initial problem with the energy balance of aligning magnetic dipoles, title of this thread, if you object to the use of magnetic potential energy you could, equivalently, consider the work of the magnetic torque as your source of energy. It should be equal to the increase in kinetic energy plus any radiated energy to verify coe. Michel ----- Original Message ----- From: "Paul" <[EMAIL PROTECTED]> To: <vortex-l@eskimo.com> Sent: Sunday, January 28, 2007 6:29 PM Subject: Re: [Vo]: Energy *Violations* using *standard* physics > Stephen A. Lawrence wrote: > [snip] > > However, there's something here that bugs > > me whenever I think about this stuff. > > > > Michel Jullian wrote: > > > >> Energy stored in a pure inductor is fully > recoverable actually > > > > Yes, of course, v = -L dI/dt and what goes in must > come out. > > > > But as someone mentioned, when you turn on the > power an EM wave travels > > out from the inductor at C, carrying energy. How's > that energy get back > > to the inductor again when we open the circuit? If > it doesn't, then > > that formula, v = -L dI/dt, must not be quite > correct. > > > The fundamental equation appears correct. What is > commonly misunderstood is that > electro-magnets cannot be purely inductive due to > radiation resistance. There's wire > resistance, and there's radiation resistance. > > > > > > Related issue: If the inductor is part of a > transformer the "other > > coil" absorbs energy and that doesn't come back out > (or, rather, it > > comes out the "other side" of the transformer). > But if we separate the > > primary and the secondary coils by significant > distance, the primary > > doesn't know for a long time that the secondary > absorbed some of the > > energy -- so how does it know it shouldn't give > back the full complement > > of energy to the power supply during the second > half of the cycle? > > > In such a case energy from the primary is radiated. > This causes radiation resistance on > the primary coil. It would be the goal of the > secondary to capture as much radiation as > possible. > > > > > > > This is particular interesting with regard to an > antenna, which seems > > like it's just a transformer with a lot of distance > between primary and > > secondary. An antenna is basically just an ideal > inductor, yet it > > radiates away power that doesn't come back out at > the terminals. > > > Radiation resistance. > > > > > > What's the difference between an antenna and a > simple coil, _aside_ from > > the fact that we "think about" an antenna as > broadcast device and a coil > > as an energy storage device? > > > As you know, coil designers try to eliminate as much > radiation resistance as possible. > Antennas are designed to do the opposite. Both have > inductance and radiation resistance. > > > > > Regards, > Paul Lowrance > > > > ____________________________________________________________________________________ > Bored stiff? Loosen up... > Download and play hundreds of games for free on Yahoo! Games. > http://games.yahoo.com/games/front >
