... Sadly, this confirms to me that the vector potential does not offer an induction effect when charge is moving through a "static" vector potential changing only due to the movement of the charge.
On a closed circuit and static A, one cannot expect an EMF because a force deriving from a potential is conservative. But I think that a variation of A in time is well accompanied by a gradient in space seen from a moving charge and vice versa. To do the integral over a circuit in a A gradient, with the variation of A in time seen from the charge, as if it were a real ∂A/∂t seen from an observer at rest with respect to the circuit, is to mix values seen from different reference frames, it can only lead to false results. If the integral over a circuit is done in the reference frame of the charge moving in a A gradient, then the charge sees ∂A/∂t BUT also a moving circuit, so the calculation cannot be done as in the case of the circuit at rest with respect to the observer.

"Open your mind, but not like a trash bin"
