2D, Magnetic and electric field module

Hi everyone,

I'm trying to model a very basic problem.
I have a conductive current carrying wire (an extremely thin wire actually) and I would like to obtain the spatial distribution of the magnetic field created by the current flow.

I'm using the "magnetic and electric fields module".

The first question is,:
Is there an easy way to define a thin wire in order to eliminate all the meshing/memory issues?

The second problem is that, in addition to the difficulties in meshing a thin geometry (I kinda solved it by using a "swept" mesh) , in 3D everything works fine: I set an electric potential across the wire and, and I get a current and magnetic field as a result. On the other hand, in 2D if I set the the electric potential on the bounds of the wire, I ONLY get the current as a result (the magnetic field is '0' everywhere, and so is the magnetic energy).

Any ideas on how to solve these two problems?

Thank you in advance!