I was looking at a problem regarding solenoid with an iron core inside. the iron core has an air gap . once the MMF was turned on, a constant flux will flow thru the core and air gap (ignore fringing), so B's are the same for air gap and core but H's are different. I am guessing some similar situations would apply for E and D as well. D will remain the same thru out different materials but E actually varies. My conclusion is that MMF or EMF are the "fundamental driving forces". whenever new materials/objects are added for MMF to drive thru, B and H will all change everywhere. just like voltage as the fundamental driving force in a circuit, with Rs being the different materials and I and J as flux and B. E as H.