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DrZoidberg, could you expand on this a little bit please? I'm struggling to understanding why the field needs to be zero.

Yes indeed, in water it is the impurities that conduct electricity. I'm hoping to grasp what an ideal conducting medium might act like in this model, so I suppose 'ideal' needs some clarification. To my beginner's mind this might mean that the electrons are free to move in any direction, so that...

I do not have enough knowledge to define such a substance, so perhaps I can ask it in a different way, starting with a first step. As a thought experiment, is it theoretically conceivable that a substance could exist with the properties that it could surround a battery allowing current to flow...

If an AA battery were placed in some kind of ideal conducting 'ether': 1) Would current flow, and if so, what would the flow of electrons look like? 2) How would the magnetic field look? (I imagine that if there was an electric current flowing, that the magnetic field would look a little like...