Why doesn't an open-secondary transformer violate Ampere's law?
Ampere's law is applied to closed circuits only, the statement itself says:


  For any closed loop path, the sum of the length elements times the magnetic field in the direction of the length element is equal to the permeability times the electric current enclosed in the loop. (Hyperphysics)


Now when you are saying open circuit there is no question that we are applying the Ampere's law on it.