Let's say I am trying to find out the effect that an iron ring has on the Earth's magnetic field (approximated to a uniform field at infinity). Can I solve it in 4 steps:
Find the magnetic field due to a hole of radius R in a flat sheet of iron
Find the magnetic field due to a hole of radius r (where r - R = thickness of ring)
Find the magnetic field due to a plane sheet of metal
Then the field due to the ring is F1 - F2 - F3
I am thinking this will yield the right answer due to the principle of superposition.