vanhees71 said:
Dotini, there is no contradiction between the quote you give and the fact that magnetic fields don't do work. Of course, if you compare the final state (paper clip attached to the magnet) with the initial state (paper clip separated from the magnet), you of course find that the change in magnetic-field energy is given by the work necessary to pick up the paper clip, attaching it to magnet.
This is precisely the content of Poynting's theorem, nicely explained at DaleSpam's link. This epxlains the the work is done by induced currents and electric fields during the transient (i.e., time-dependent!) situation when picking up the paper clip!
Missed responding to this before but address now - given your weight here as currently the thread's only expert/authority figure. If your claim that -d
A/dt
E fields acting on induced currents explains the above, I invite you, as someone familiar with both classical and QM regimes to apply that to what I brought up in #10. Do you disagree with my observation there that flux quantization in wholly superconducting circuits directly implies the failure of dW =
E.j dv over an interval of magnetic interaction where supercurrent I
s is forced constant, despite a changed increment of enclosed flux and thus a changed
A.Is dl, where dl is an incremental length along the thin supercurrent? This despite that *on average* that quantity is invariant in a superconducting circuit - i.e. *on average* enclosed flux is an invariant? Moreover that as the superconducting circuit is shrunk smaller, so the interval of applied external
B field variation over which I
s = constant grows in inverse proportion to enclosed area? Do you further agree or not with my observation that an electron is in a sense the ultimate endpoint of shrinking, not a classical, but a superconducting, loop current re it's magnetic interactions? And that in that case there are precisely zero conditions in which
E.j is relevant to electron-as-magnetic-dipole? And that a permanent magnet is an ensemble of such fundamental dipoles - notwithstanding that *quantized* electron orbital motion contributes to magnetization here, though generally to a minor degree? (Earlier I had specified fully magnetized when referring to interactions involving permanent magnets owing to it simplifying things, but that restriction can be dropped with no consequences for the argument here.) And that induced eddy currents - which may be treated as behaving entirely classically, are in general a very minor consideration - especially for slow relative motions and for certain materials such as 'hard' ferrites? I shall be interested to see how or whether you choose to deal with hopefully all of the above questions.