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339:: if you create a field using the primary coil and then leave the secondary coil open-circuit, you observe an emf even though the B field that 'touches' the wires of the secondary coil is negligible. So when the Rousseaux article says "the effect can be understood using the vector potential while it cannot using only the fields", it effectively sounds like they are saying that you can't understand transformers using electromagnetic fields!
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Saying "the magnetic field is practically static inside" seems misleading since the rate of change of the magnetic field (likewise rate of change of vector potential) is absolutely the point of focus here. In fact we might decide to take a snapshot at the instant in time when the current passes right
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Mathematically is perfectly clear you reasoning but physically I see a current where B is almost zero (see note 4) and A is not. I don't know if A is real or not, if A originate B or viceversa or what else. I just see a place in space where there is an action on electrons and there the field A is not
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User 151.20.154.132 derived e.m.f. without the use of vector A, thinking in this way that is possible to get rid of it. But the fact that B is null (with good aproximation) where the e.m.f. is recored remains. So who generates the e.m.f. in that point of space? There, just A is not null and
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through zero (and so vector potential and magnetic field are zero everywhere, for an instant), and we would see the nonzero induced electric field even at this time instant when the relative change in magnetic field is so large. --
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I think their article fails to show inadequacy of
Maxwell equations. But that doesn't mean that A potential is not real, nor does it mean it's wrong to use A (I happen to like A field very much even in classical electromagnetism).
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As for the question about what generates the E field, we can just as well ask what generates the A field? Both are located away from the current distribution. In fact, the two equations
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My understanding is that the common explanation of why E is nonzero (where B is zero) is simply what we call
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are so very similar, so if you can answer "what generates the A field" then that seems to answer both.
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388:{\displaystyle \nabla \times \mathbf {E} =-\partial \mathbf {B} /\partial t}
328:{\displaystyle \nabla \times \mathbf {E} =-\partial \mathbf {B} /\partial t}
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424:{\displaystyle \nabla \times \mathbf {A} =\mathbf {B} }
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