[jacquesm]

> essentially it allows you to decompose the 'A' and 'B' fields of a system of wires, for instance a current carrying loop and a load.

Too late to edit 'A' should of course have been 'E'. (E -> electrical field, B -> magnetic field).

I think a big part of the confusion stems from separating the wires from the load: they are all the same thing, wires are load too and there is no 'privileged' reference frame for any particular chunk of wire (or load, or internal resistance in the battery) that deserves special consideration or that needs to be paired with something else to make it work, as long as the circuit is whole current will flow and the moving electromagnetic field is sufficient to explain all of the observed phenomena. The only part where the electric field figures in is as the accelerating force for the free electrons in the circuit, the higher the voltage the more of those electrons that will partake in the movement (which is effectively how you can derive Ohms law).