PDETool Magnetostatics - homogeneous boundary condition

Hey to you all,

pleas be so kind to answer one question in order to understand the boundary conditions better. Does a homogeneous Neumann boundary condition in magnetostatics PDE mean that g is zero or rather q is zero?

The background is that I would like to build a model as shown below with two opposed coils in an outer field as shown below with an outer field applied. Unfortunately I haven't come around van Neumann recently. Unfortunately the single literature I have for a model as shown is only referring to a so called homogeneous Neumann solution. If you'd like, please feel free to give a Dirichlet workaround as well.

So, if you could help me out with all the g's and the q's I would be definitely grateful