I have an induction cooker like the one in the image below. Is it safe to place it on a wooden table?
Induction cookers utilize electromagnetic induction to heat the pots on them rather than the plate itself.
Induction cooking works by creating a magnetic field that is constantly oscillated (north and south pole are switched). This causes an electric current to run in the bottom of the pot and heat it up via resistive heating. Since the current literally runs in circles (around the bottom of the pot) it's safe to touch and you won't get electrocuted.
The magnetic field spreads out like an invisible ball around the cooker's plate, therefore it can interact with the table the cooker stands on. That's why you shouldn't put it on a metal table, the table could heat up like the pot (in reality this is very unlikely but not impossible).
Wood, on the other hand, doesn't interact with a magnetic field and doesn't conduct electricity. Therefore it's safe to place an induction cooker on a wooden table.
Wikipedia has additional information:
Persons with implanted cardiac pacemakers or other electronic medical implants are usually instructed to avoid sources of magnetic fields; the medical literature seems to suggest that proximity to induction cooking surfaces is safe, but individuals with such implants should always check first with their cardiologists. Radio receivers near the induction-cooking unit may pick up some electromagnetic interference.
If you've spent enough time on youtube you will see induction cookers on wood, usually cutting boards or butcher blocks, a lot of the time. In general I would say this is safe, but as Telsujin says, "check the manual" for safety guidance.
I would guess that wood, non-metallic, base is recommended. There could be a small chance that the induction could interact with any metal surfaces. Unlike the old school electric coils hotplate, which can be dangerous on a wood surface as they heat-up the induction plates should not get hot at all, causing only the metallic/magnetic cookware to get hot.
The manual will be your definitive source.
Side note, due to fear of fire on ships/boats induction cookware is getting more common than open flames or hot-coils for cooking.