Ouch, so I seem to have missed the fact that I need some boundary conditions, which would indeed "center" my solution onto the z-axis. It seems like I just took a look at the differential equations and thought to myself "Oh golly, I will just use that fancy thing I read about in my textbook."...
I suppose that my main question is how to find the induced electric field given a time-dependent magnetic field, but i will demonstrate my question with an example:
I constructed a simple magnetic field B = b*tz , permeating the whole space. The induced electric field will lie in the xy...