DC MMF and flux density variation in space
MMF or magneto motive force is quite simply amps x turns. If turns remain constant and current is DC then clearly MMF is constant.

In magnetics, MMF is the driving force behind flux and certainly the flux produced by a DC current is going to tail away to insignificance at some arbitrary distance.

MMF is similar to voltage in a dc circuit with a resistor; the current taken by the resistor is equivalent to flux (not flux density) and resistance is equivalent to what we call reluctance in magnetics.  

This wiki article seems to explain the concepts adequately.