Eddy currents in conductors

Eddy current formation in a conductor does not rely on the material being ferromagnetic. The magnitude of eddy currents and the overall heating in the conductor depends on the "number" of current loops the conductor geometry permits, and the electrical resistance along these loops. This electrical resistance in turn depends on the electrical conductivity of the material. Thus, eddy currents will form in conductive non-ferromagnetic materials. A short-circuited coil placed in a time-varying magnetic field will indeed be heated, however the heating rate will likely be less than a uniform block of the same conductive material, because the coil only permits one current loop, the resistance along which can be high since it consists of multiple windings in series.

Along each current loop, the current is driven by the emf $mathcal{E} = -dPhi/dt$, i.e. the negative rate of change of the magnetic flux linked by the loop. A "voltage" is more difficult to define precisely because it's not clear what voltage difference you are speaking of, you can think of the current in each loop as resulting from a voltage of $V = dPhi/dt$.

I don't understand what you mean by the magnetic field canceling out in a conduit, you will need to provide a more detailed description, or preferably include a diagram.

Eddy currents occur in any conducting object, including the induction coil. However, heating power release in a body is, when I simplify, proportional to three things:

• square of magnitude of induced electric field inside the body

• conductivity of the medium that the body is made of

• volume of the body

The shape of the body and distance of the body from the coil also matter, but let us ignore those now.

Iron body gets much greater induced electric field inside than copper body of same shape, due to the fact that iron is ferromagnetic; it boosts the field created by the induction field to greater orders of magnitude. On the other hand, iron has worse conductivity than copper. It turns out that the first effect is much more significant, so the heat release in iron body is much bigger than in copper body of same shape.

The induction coil is designed in such a way as to make heat generation in it weak enough that the device fan or other cooler can keep the coil at operational temperatures. In case of kitchen cooker it is made of many thin copper wires which makes the ohmic resistance of the coil small (it is a way to combat the skin effect which increases resistance) and heat generation inside the wires is weak enough. In efficient operation, most of energy that comes from power outlet is transferred by the coil via EM field to the heated body, only small part of that energy heats the induction coil.