Consider two simple magnetic circuits shown below. Both are made of ferromagnetic material but the right one has also an air gap. enter image description here

If we close the switch $S$ and we wait long enough, the magnetic field $B$ will set up in both circuit. If we use Ampère's law $$\oint \vec{H} \,d\vec{l}$$

we can easily find $B$ and see that it is smaller in the second circuit with air gap.

Question : Without talking about reluctance or making any electric circuits analogy, can someone explain why it is the case? What happens as soon as we close the switch that makes $B$ not able to grow as much in the presence of the air gap?


Let's separate the systems into 3 parts: the magnetic material under the coil (1), that not under the coil (2), and the part with/without the gap (3). As current is fed through the coil, (1) magnetizes by forming domains (the electrons start lining up with the field.) Progressively onwards (2) starts magnetizing towards (3). Now, at (3) the gap free section goes about normally. However, the gap version doesn't have a rigid material to magnetize, so the field is weaker.

The fields measured are those standard and induced (pardon my inaccurate terminology.) the standard are from anything but magnetization. Rather than remove the whole chunk, let's just compare two loops of the same ferromagnetic material, but finely carve out half of one to make it half as dense. Throwing a field over them makes the dipoles in both line up. There's only about half as many in one though, so it's induced field will only be about half as strong. The total field is the external plus this.

  • $\begingroup$ Ok so you are making a local argument here about the field being 2 times smaller in that part of the material. But what mechanism causes the whole field everywhere else to be smaller? Is there a feedback mechanism that makes the field in the denser part become smaller? $\endgroup$ – Dory May 21 '18 at 10:16
  • $\begingroup$ If there's no field induced in the gap, that's less field overall. This is less field to align even more dipoles in the neighboring materials. Think of the loop of ferromagnetic material as instead being a track of many pinned down (in the center) magnets with varying levels of rotational friction. Flipping a few will create a domino effect to line numerous up. If you remove some (the gap,) you snuff the domino effect a tad, as now there's a lesser induced field meaning some of the high friction pinnings won't turn. $\endgroup$ – Captain Morgan May 21 '18 at 10:24

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