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1) Non zero for an ideal solenoid (where the field outside the core of the solenoid is considered zero). Thus the only flux that will pass through the area of the loop will come from the core of the solenoid.

2) Zero for a real solenoid because the field outside the solenoid is not exactly zero (magnetic field lines will not just terminate outside the solenoid). Magnetic field lines, in reality, will continue outside the loop and return back to the core. And some of that flux will pass through the area of the amperian loop and cancel the some of flux from core of the solenoid. For an infinitely large radius of the amperian loop, it will be exactly zero because than ALL the flux will pass through the loop which will exactly cancel the oppositely directed flux from the core.

Does this make sense?