Induction works with magnetism generated by a coil under the glass plate.  The only part of the pan that is heated is the part that sits in the magnetic field, so a pan much larger than the coil will not heat well.
As our induction top was designed specifically to match the coffee machine, we haven't run cooking tests, but we would not recommend using a pan that is larger than the circle on the induction glass, which is 15cm.