Magnetic Saturation in Solenoids: Core Size & Shape Impact?

[celeramo]

Magnetic Saturation??

In a solenoid, does the magnetic field strength at which a core, in this case iron, begins to saturate change relative to the core's size or shape? Or is it constant for the material of the core, regardless of other factors? in other words will the core begin to saturate at so many gauss/tesla regardless of the core's size or shape? Please and Thank You

 

[Meir Achuz]

The saturation actually depends on M.
For a long or toroidal core, B~4pi M (in Gaussian units), so the saturation would seem to depend on the same B.
However for other shapes, like a sphere or a disk, B<4pi M for much of the material, and saturation would occur at a lower B.