For a different project I was reading about developments in induction heating technologies and realized I had a small misunderstanding about how induction stoves work.
So, the classic misunderstanding is in why steel works on an induction hob but aluminium doesn't. Most people assume this is because you need a magnetic material in order to induce a current, but if you know your physics you know this isn't true. You can induce a current in any conductor, and indeed inducing currents in aluminium is something that happens in industry all the time.
So then you get to my understanding of why you can't use aluminium and copper, which is that they're too good at conducting electricity. Induction generates a voltage that pushes a current through the material. Aluminium and copper are much better conductors than steel, so the generated potential is lower and the overall current is lower as a result of material interactions with the field, so you don't get nearly as much heat out of induction on aluminium as on steel. This was what I thought. This is also wrong, although it's closer.
The actual answer is one step deeper. Induction hobs have to operate at pretty high frequencies, usually 24-ish kHz, both for audible noise reasons and, crucially, because they rely heavily on the skin effect. Interestingly this makes that first wrong explanation kind of more correct, I'll get to that in a moment.
The skin effect is a thing that happens when you have an alternating current in a bulk material; the AC signal sets up magnetic fields that force current to flow in a thin layer closer to the surface of the solid rather than flowing evenly throughout the material. This increases the effectivene resistance of the material, since you end up with a reduced effective surface area through which current can flow. The skin effect gets more pronounced at higher frequencies, and it's part of why you'll see bundles of smaller cables used to conduct high power AC: each cable has its own skin that can carry more current than the same quantity of material in one bulk cable.
In the right kinds of steel and iron, 24kHz is enough to generate a current carrying skin only a few tenths of a millimeter thick, which has a high enough resistance to generate the heat needed for cooking. Ferromagnetic materials have very high magnetic permeability, which causes them to experience much stronger skin effects. Copper and aluminium, between their high conductivity and lower magnetic permeability, have much weaker skin effects, their skins at 24kHz are much thicker, and so you just can't kick up enough resistance to the current to generate heat, it just spins around in there getting kind of warm but you'd have a hard time actually cooking with it. Indeed, non-magnetic stainless steel also won't work on induction hobs, because it also has a much thicker skin effect.
So you have the "real answer" being a fun hybrid of the two incorrect explanations.
The main side effects I take away from this are twofold.
1) you can absolutely make an induction hob that will heat copper and aluminum and non-magnetic stainless steels, you just need a high enough frequency to generate a strong enough skin effect to generate heat. Panasonic makes one that uses 60+kHz induction under the brand "Met-all".
2) if you physically constrain the current by having a really thin piece of metal, you can induction heat it anyway. When I read this, I stopped, took out a piece of aluminium foil, and stuck it on my induction cooktop. It almost immediately got incredibly hot and I pulled it away before anything bad happened. Turns out you could definitely melt and maybe even vaporize aluminium this way. So don't do that. Apparently people do this with lightweight titanium cookware too, which would not be able to sustain the necessary currents in a large bulk solid but can if you thin the base of the pan out enough.
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