We studied electric fields due to point charges. The magnitude of these fields decreases with the square of the distance from the point charge.
It seems to me that we could treat the positive terminal of a battery as a point charge. So, I would conclude that the magnitude of the electric field set up by the positive terminal inside a wire in a circuit should fall off with the square of the distance from the end of the battery.
However, this does not happen. Instead, the electric field inside a wire in a circuit is constant. Why is this? Is it that the positive terminal can't be modeled as a point charge? Or is it perhaps some special property of the wire, or the fact that there is moving charge in the system?