If I got this right, the H-field does not depend on the material it is applied on and is only determined by its sources (free currents).

So, suppose that we have a toroidal coil and some undefined core. As far as the H-filed is concerned, it would not make a difference if that core was air, a ferromagnetic material or some combination of those two. The H-field would remain the same.

However, if we apply Ampere's Law to a simple magnetic circuit, consisting of a ferromagnetic coil toroid having a small air gap, the result would be (taken from theory):

HfLf + HgLg = NI, where f, g refer to ferromagnetic material and air gap respectively.

Obviously here Hg is much greater than Hf

Now I'm confused! I know that the magnetic flux must remain constant throughout the circuit, but still I can't grasp how Hg and Hf could be different (the distribution of free currents did not change)!

Any help much appreciated!

 

The field is affected by the magnetic permeability of the core material.

so flux is used up crossing the gap.

(Like a high value resistor will drop the majority of the voltage across itself, leaving little for the rest of the circuit.)

The air gap behaves like a high value resistor to the (MMF)flux.