Creating an external Magnetic Field

Hi,
I am trying to model a superconducting wire under magnetic field. Since the design of a SC wire includes a circular variable dependency of the conductivity and the current density, I have to use PDE general form to model it. The model works nicely in 3D (attached) without the magnetic field. (Note: this file is without the solution so it is uploadable - the mesh is extremely fine so change it if you run it).

I have been trying for over a month now to apply that magnetic field. An external magnetic field seems like something impossible for COMSOL to comprehend; even when I try adding MF and current in Helmholtz coils nearby to create the field on the wire, it seems that the coupling of the H field in the MF physics and the H solution for the PDE are just not cooperating - they are not the same, and the solution, if it solves, is incorrect.

Please help me!
I need to create a A*cos(21*pi*t[1/s]) magnetic field on the wire while the current flows in it, how can I do that?

thank you very much for your time,
Shoval