So I understand what the B field is in magnetism. This is the fundamental field. We can also define a H field, H = B/u - M, to take into account that we cannot actually measure magnetization currents (cf. solenoid). Now, if we have a B field applied to a material, call it Ba, the field inside is given by B = u(Hi + M), where Hi is the internal H field, defined as Hi = Ha - NM. Its this last part that confuses me. What is this demagnetizing field, NM???
Most writers state that the magnetism in a ferromagnetic object is induced by an external H (not B) field. To visualize the demagnetizing field, imagine an iron cylinder with its axis parallel to a field H_0. Boundary condition equations allow one to replace the induced M by an effective (and fictitious) magnetic charge density on the face of each end. The field outside the rod is that from the two charged surfaces (this field appears dipolar at sufficient distances) added to H_0. Note that inside the rod the charges produce a field that opposes the external field, tending to reduce M. This is the demagnetizing field.