# Current across two points in space and zero electric field

I was wondering what would happen in the following case:

There's an electric field and points A and B nearby the field. As you can see, the's no electric field at those points. Will there be a current flow from point A to B once I connect them with a wire?

According to the definition of voltage, it's a line integral of the electric field over the path from A to B, so in this case the voltage across A and B won't be zero. But I think that only electrons in the area of non-zero electric field will move and because A is not in a non-zero electric field, no electrons will flow from that point towards B.

If I'm wrong, then is it because the electrons located in the middle part of the wire will move towards B, and that will create a shortage of electrons "on the left edge of the non-zero electric field" (looking at the image) and the electrons will be pulled from the area near A?

• You cannot have electric field lines starting and finishing in space as you must have charges present. So how is it that the electric field at $A$ and $B$ is zero? – Farcher Mar 2 '17 at 21:16