electromagnetismeveryday-lifeinductance
According to the Wikipedia, one of the limitations of the induction cooker is that the bottom surface of the pot should be flat.
Accordingly, I commented on a question on Seasoned Advise, but I'd like to know whether this is actually true (My username is BaffledCook there).
For a wok, it seems reasonable to believe the induction cooker will not be effective, but how about a wobbly pan? How wobbly should it be before it really affects efficiency?
When you are clear about eddy current (in superconductors) and Lenz's law then you can easily find out the answer. Eddy current will be created in superconductors when they exposed to external magnetic field, that eddy current will induce an electromagnetic field and the direction of the magnetic field will always be opposite to the original magnetic field (applied field). Hence these two opposite lines of force will oppose each other which causes the object with the induced magnetic field to float.
Your first assumption is not really correct. The induction cooker creates an electromagnetic field with a frequency in the range of 10 kHz to 100 kHz. The coil used in the cooker looks as follows:
The coil and the frequency are choosen in such a way that the field does not extend more than a few centimeters along the axis of the setup. Now when you put a ferromagnetic material on top it will rapidly get magnetized and demagnetized with with field created by the coil. Every ferromagnetic material exhibits hysteresis, which leads to dissipation. This dissipation heats the pot. This is not connected to the resistivity of the material, as eddy currents are not the main cause of the heating (a copper pot works poorly on an induction cooker).
With the field strength rapidly decreasing with distance, it is clear why the top of the pot and the lid do not become hot. There is no even current flow through the cookware.
To the second part of your question: Almost all electric energy is converted into heat, the total efficiency of input energy versus the heating of the food inside the pot is 84%, so very high compared to other methods but not perfect.
An electric shock is unlikely but not impossible. The Swiss health board recommends non-metallic spoons to avoid any current going through your body (Best practices, in German). Modern cookers have metallic or graphite surface to provide a path to ground for the pot which minimizes this issue.
Best Answer
An induction cooker works with a flat coil setup similar to the one shown below. The diameter of this coil depends on the exact model (in the range of 30 cm). This implies that the field is also extending quite a bit into the air above the cooker.
As the large field can be potentially hazardous (think metal ring on finger) there are relatively strict safety standards for induction cookers. The field of of the coil measured at a horizontal distance of 30 cm from the end of the coil and along the vertical axis (z=0 is the center of the coil) is shown below (the absolute values are not comparable with the field above the center but the profile is certainly comparable). The data is from this study: "B-Field Exposure From Induction Cooking Appliances" by C. Viellard and coworkers.
As you can see the field strength decreases by about an order of magnitude in a vertical distance of 200 mm. A very wobbly pan might be less effective but only if it is warped by more than a few cm.