My original interest in this subject was insprired by the case where no current flows, like the open terminals of a generator or the the unused electrical outlet in your home. There is NO current flowing, BUT there IS an alternating electrical field in those wires, right? If so, I wanted to know if this, in itself, could generate electromagnetic waves.If you want to associate EMF with a field then where do you want this field to be? Is it between the battery terminals is it between the terminals on the motor or heating element? Field is measured in Volts per Metre and, if you want to discuss fields in a circuit, you would need to consider the size of the battery, for instance. The field across an AA cell would be different from the field across a D cell.
You could insist that it's fields that cause individual electrons to move about but each electron is subjected to a different field. True in principle but do you really think it helps to analyse what goes on in a circuit by considering every microscopic bit of every piece of material it's made of? Potential Difference deals so nicely with it all so why not use it?
Why should you want to? It's just a matter of chicken and egg. The two go together. Neither is the 'cause' and neither is the 'effect'.
To extend this, when you touch the ground, do you have an alternating electric field in your body at 60 Hz because you are in synch with the alternating field in the ground produced by the power company? To me, that makes sense and explains why current would flow through you in response to touching a "hot" wire, which has an out of phase alternating field.
This article was very helpful and interesting. Thanks.