What happens to parts of induction cooker magnetic field not covered with the pan?
The manual of my induction cooker says:

The induction zones adapt themselves, until a certain limit, to the size of the cooking utensil. But the cooking-utensil must have a minimum size. 

Then follows a table like:


Right back : 145 - 180 mm
Right front: 125 - 145 mm
Left  back : 145 - 180 mm
Left  front: 180 - 210 mm


I leave to the expert how they adapt themselves. 



As to Andy's  fail safes: yes there are plenty. They even get annoying if they are hair triggered like in my induction cooker.


Nothing on surface (Switches off before you have time to get a pan from the cupboard)
No pan (Don't wait too long turning you pancakes)
Water/moisture on the surface (spill a bit and it switches off ) 
Too hot 
On for too long
Object on the control surface(even a loaf of bread triggers the latter)
Start beeping if I clean the surface with a wet cloth (whilst it is off!!)


Even the tiniest spillage causes mine to shut-down. I now dry my hands before touching the buttons.