I have a theoretical question involving the properties of inductors, I hope someone is able to help! I know that the voltage across an inductor is proportional to the time rate of change of the current through the inductor, and that if the current is changed the inductor will generate a "back-emf" proportional to the rate of change of current through the inductor in an attempt to keep the current constant. Of course, the back-emf can't stay constant forever, because if it did there would be no change in current to produce the back-emf! So the changing current eventually "wins" over the back emf and the voltage spike generated decays away as the current rises or falls to its new value. My question relates to the following situation: In a circuit like a relay, or a vacuum cleaner motor which is suddenly unplugged, as I think about it it seems the current is changed from whatever it was before to zero in "infinitesimal" time, i.e. there's a moment where the circuit is connected, and then there's a moment an infinitesimal amount of time later when it's not. Perhaps that's not an accurate way to look at it from a quantum-mechanical point of view as there may be a more broad interval when the wavefunctions of the electrons in the contacts of the circuits are still interacting. In any case, in the real world the potential across the inductor doesn't rise to infinity if the contacts are switched in "zero" time, what happens is, in the running vacuum cleaner motor for example, the potential exceeds the breakdown voltage of the air and current continues to flow through a spark from the plug to the outlet. What would happen, though, if you had a circuit in vacuum with no other conductors except the wire completing the inductor circuit (in the thought experiment universe) and were able to take some kind of material with a large dielectric constant, make it ridiculously thick (say 100 miles) and break the connection between the inductor and the wire? What would the back-emf of the inductor do, if the current suddenly dropped to zero like that but there was just no way for the back-emf to keep current flowing? My intuition doesn't seem to be much help here so any ideas would be appreciated!