# Superposition of Magnetic Fields

Two part question:

1. If I have two coils of wire facing each other with all parameters for both being equal: Current, radius, # of turns, current traveling in same direction, etc. and there is a space between the two of them (fig 1), is the magnetic field geometry always going to just be a superposition of the dipole fields generated by each one? Or do the field lines merge into a single dipole field and thus make them equivalent to fig 2. If they do approximate to fig 2, is this determined by some limit for each parameter mentioned earlier? If so, how would that be determined mathematically? I know from electrodynamics that we can solve for electric fields of discrete charge density distributions using Greene's function. but I never applied it for B-fields and am pretty sure that doesn't work. If fig 1 does approximate to fig 2, what mathematical tools can we use to try to solve for that geometry similarly to the Greene's function for charges?

1. If I have an even more complicated system now (fig 3), where I have two pairs of coils facing each other and each pair is perpendicular wrt each other, will those field lines merge and combine into some uniform, single continuous geometry, or will it still be a superposition of now, 4 dipoles?