Correct. Ampere's Law can only be applied when B•dl is constant along the entire loop. It can be used for situations such as an infinitely long wire or solenoid because symmetry ensures that B is constant. There is no such symmetry in a single loop, so that's why Ampere's law isn't useful in...
Ampère's law only applies in magnetostatics. That is, \vec{B}\cdot d\vec{l} must be constant for all d\vec{l} in the loop. Is that the case for your ampèrian loop?
Magnetic field inside infinitely conductive hollow tube
Homework Statement
There exists a thin-walled hollow aluminum tube (assume σ=∞) of radius 10 cm centered around the z-axis. A long wire with 5 mm radius has a total current 2 mA in the z-direction and is centered initially at x=-5cm as...