...When it comes to real materials the relative permeability is not a constant, it depends on the H history leading to hysteresis. So what µ should we use in that formula? For square-loop material that has been magnetized (a permanent magnet) what µ would you use? We're talking about µ at the moment we apply the calculation. The relationships between B(t) and µ(t) are true at every instant, including that of magnetic energy density. When µ varies, it's because the energy is distributed differently. For example, some of it may be lost through its work on realigning the magnetic domains at the same time as µ is reduced. Whether the variation is in time or in space (e.g. a ferrite used as a transmission line), the equations apply step by step, in time or in space. If we remain on a macroscopic scale and see only the whole, we can't draw any conclusions. If µ varies, we need to look step by step in time and space to see where the energy is going and in what form. In an AC transformer we have the core being demagnetized over part of a cycle inducing voltage ino a coil driving current into a load resistor yielding energy far in excess of that supplied for the magnetization. In that case the "something" supplying that energy is the voltage.current in the primary coil. I don't agree with this way of presenting the facts. That the magnetic energy of a transformer is constantly fed by the primary current and constantly consumed by the secondary current is nothing new. The quasi-concomitance of the two gives the illusion that the transformer doesn't store the energy passed from one to the other, but this is not true. There is a delay during which the energy is stored in magnetic form in the transformer core, during this very short transfer time. The principle is the same as if energy were passed through a capacitor alternately switched from input to output. For the system being discussed in this thread the "something" is the thermal input KT (K is Boltzmann's constant and T is absolute temperature) that appears in the Neel formula for the remanent magnetism relaxation time (decay time constant). When we use that non-electrically-driven decay we are not extracting the so-called magnetic energy stored in the core, we are extracting it from the effects of the thermal agitation. Yes the loss of magnetic energy needs replenishing and that is taken into consideration. We have to resupply that energy including losses just as we do in the normal transformer.
Smudge
Heat is one of the forms in which magnetic energy can transform when µ or any other parameter changes, and it's one of the changes of form I mentioned in paragraph 1. I fully agree that this transformation can be achieved by supplying energy. But if you agree that "the loss of magnetic energy needs replenishing", that's the crucial point. If you can't replenish this energy at a lower cost, the device remains completely conventional, and I can't see any reason why it shouldn't be.
---------------------------
"Open your mind, but not like a trash bin"
|