Because woks are domed on the bottom, they don't jive well with a flat stovetop. For that reason, there exist wok-specific induction stoves, both standalone and drop-in, where the heating element is concave:
The problem is that if you cook with both woks and conventional flat-bottomed pots and pans, you give up a measure of flexibility by committing to either type of stovetop. Thus Seoul-based industrial designer Myung-Nyun Kim designed this Amphi concept for a stovetop with a morphing heating element:
The idea is that each concentric circle of the rightmost heating element would be able to move:
"Each of the circular parts stay in plane when heating a [flat-bottomed] pan," Kim writes. "When heating a wok, the heating elements extend downwards to fit the wok like an amphitheater." Hence the concept name.
In the image below, you can see a metallic strip on part of the circumference. "During the use of the wok, in order to mix ingredients, people move the wok intensely," Kim writes. "Therefore this particular part was designed with a metallic cover for protection, [at the spot] where the wok would continuously hit."
Interestingly, Kim envisions the knob that controls the temperature as being magnetic and removable, as per user preference. Users would still be able to control the temperature without the knob as the surface below it would be a touch-sensitive dial.
And while there's no word on what type of mechanical magic would be required to get this to work, Kim does address one glaring issue: "The drawback of movable, sliced heating elements is that ingredients would fall through the spaces in between," he writes. "For a solution, heat-resistant silicone packings would go between each piece to prevent ingredients from falling, without affecting the up-and-down movements."
Well, it is concept work after all.
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I have spent a lot of time thinking about this issue. I think this is a pretty good solution. The first thing to confirm is how to get in the induction coils to work concentrically.