Sorry, but I'm going to have to stick with what I said on this one. I tried to look up some simple references to cite here but the textbooks that deal with fields are pretty hard to digest in a paragraph or two. One confusing part of this is you can talk about the total MMF -- apmpere-turns -- for the whole device, but you can also talk about the H-field intensity -- ampere turns per inch -- of a differential element within the flux field. It's easy to get a headache trying to keep all this straight.
DK, the analogy between electrical current flowing in an electrical circuit with resistance and a magnetic field "flowing" in a magnetic circuit with reluctance is technically accurate, but most every text book fails by
not talking about these equivalences:
conductance()............permeability() --- reciprocal of resistance/reluctance
these equivalences are really simple, take the time to get acquainted with them,
especially the difference between flux (total-over-entire-cross-section-area) and
field (per-unit-cross-section-area), there's no headache here !!!
then, the notion that 1/2 the energy is stored in the gap doesn't fly because it utterly
fails when you try to make the analogy with electrical current, the gap is a magnetic
resistance, IE reluctance, and resistors just don't store energy.
PS, the Oersted, amp-turns-per-inch, is for a long solenoid, the longer the solenoid
the more amp-turns you have, but also the longer the field lines have to travel through
the reluctance of air, so the field strength is independent of the coil-plus-core length,
its a very confusing unit because it combines two concepts, the strength of the coil
(ampere-turns) with the reluctance of the medium in the coil, with the implicit assumption
that the length of both varies identically. Or at least for me its confusing and distracting
because there's no good analogy in electrical circuits. OK, here's one, if you stack up
batteries in series you can measure volts-per-meter(of battery stack), and ask what is
the current if you short them out, which because the batteries all also have the same
resistance and hence resistance-per-meter, turns out to be a constant, same current
no matter how many meters of batteries you have.