When does an iron core solenoid's magnetic field behavior change with coil proportions?

[mapache]

Hi, I've been trying to learn about iron core solenoids and I'm having trouble finding information on a concept (probably obvious but I'm new to this). I've been looking at the equations for iron core solenoids online, and it's alluded to that these equations only hold true when the proportion of the solenoid coil width isn't greater than the iron core diameter or something like that? Is this correct? Is there some "drastic shift" in the magnetic field properties that is going on when these proportions are exceeded? I'm hoping someone can enlighten me and point me in the right direction for further study.
Thanks

 

[anorlunda]

Yes, it is called magnetic saturation.