  We derive an equation of motion for the the dynamics of a ferromagnetic
domain wall driven by an external magnetic field through a disordered medium
and we study the associated depinning transition. The long-range dipolar
interactions set the upper critical dimension to be $d_c=3$, so we suggest that
mean-field exponents describe the Barkhausen effect for three-dimensional soft
ferromagnetic materials. We analyze the scaling of the Barkhausen jumps as a
function of the field driving rate and the intensity of the demagnetizing
field, and find results in quantitative agreement with experiments on
crystalline and amorphous soft ferromagnetic alloys.
