Basically magnetic field and electric field is like the two sides of a coin they come hand in hand hence the name "electromagnetic field".
Em field can be explained both in classical terms based on the real life phenomenon which it exerts on conductors, transformers etc. and in quantum terms, you have to choose based on your level of knowledge which explanation suits you best.
If by the "material " you mean a transformer core then yes the core itself isn't electrically charged as it is a loop of metal that lets the magnetic field lines to be distributed upon, but if you measure the secondary winding at any given place you will notice a potential difference which you will recognize as voltage, place a wire along a live wire connected to your mains and even in that wire there will be a small amount of voltage as the live wire carrying the ac mains makes an em field around it which then induces another em field in that not connected wire that will run parallel to the live one and you will see potential difference on that one, a small one but still.
By constant potential difference, that depends whether the magnetic field which in turn is induced by electric one will be constant as if the potential difference will minimize in the first wire also you will notice the same thing in other placed near to the first.
But to answer your question yes we have a constant potential difference and if it wouldn't be possible no AC mains distribution system would be possible either.
P.S. if you would place a really long wire in a straight line across miles of land you would see a potential difference too as the earths magnetic field would induce electric current in that wire.