I have a pile of textbooks here but I'm still having trouble wrapping my brain around this.

(here A is magnetic vector potential, a is area, J is current density, i is current, M is mutual inductance)

I'm modeling loops of wire in FEMM and trying to calculate self- and mutual inductance (because I can look these up.. I have a more complex model to work on next). I have it pretty much down but I am confused by the instructions for calculating mutual inductance, and I am also unsure of how it all comes into play.

The instructions for FEMM say that you can calculate the mutual inductance in a structure by integrating A over the cross-section of a conductor "with only one coil turned on." However, the authors make no effort to explain what "turned on" means. I can leave the secondary out of circuit, which produces a completely unreasonable value for M. I can also make the secondary out of air, or put it in its own circuit with i=0. These approaches come much closer to theoretical values, but I don't know which is correct, and I am sure there is a big difference at some point, because the field lines differ in these cases.

I've googled around for a better explanation but most forum posts seem to be pretty specific to one problem or another. Can someone else offer a source, or pen an explanation, of calculating/modeling self- and mutual inductance in a more generic sense? Even some hints would help.