Suppose that magnetic wire with resistivity similar to copper but with non-negligible permeability existed. What effect would magnetic wire have on the coil inductance versus a copper coil of the same size/construction?
This is of course a purely academic exercise, since such a material does not exist, though it could perhaps exist for plated wire at high frequencies, due to the skin effect.
I guess it's not entirely academic. isdi pointed out that "high permeability wire" actually exists.
According to this:
Mu Metal Wire is used in the production of inductors and electrical transformers. It has one of the highest magnetic permeability ratings of any metal or alloy, making it an industry standard in applications where metals with high magnetic permeability are needed.