220209-2341 EST
wwhitney:
"OK, so to expand on that, what is the key detail that forces them to be in phase? Is it that the coils are interwound and the spatial extent of each coil (along the central axis) is the same? I.e. if you had a single iron core, but some coils are wound only around half its length, and other coils are wound around the other half of its length, would that allow the second diagram I drew?"
If you have multiple coils on a common high permeability core with negligible leakage flux, then all coils see essentially the same changing flux, and there is low leakage inductance.
If you take an EI transformer core structure, and put all the windings on one leg, then you get essentially all flux coupling all coils. But, if instead you put one coil on one outer core leg, another coil on the opposite leg, and nothing on the center leg, then magnetically the center core leg shunts magnetically some of the flux. Thus, incomplete coupling between the two coils, and effectively high leakage inductance between the two coils.
.