Force at high current density

[jim271@xxxxxxxxxxx]

I have a question about the force on a solenoid plunger when the 
metal is saturated.

Using FEMM, I've noticed at low current density the force is 
proportional to the current density squared, as expected for a linear 
material. As the material becomes saturated (using the non-linear BH 
curve, mu->mu_0 ), the force seems to become directly proportional to 
the current density (doubling J doubles the force). Is this the 
general limiting relationship between force and current at high field 
intensities? 

TIA

-- Jim