Ampere's Law?

Question

Why "infinite length" and "negligible circular cross section" is used in the definition of Ampere's law?

Answer 1

By me Ampere's Law states that:

The magnetic field in space around an electric current is
proportional to the electric current which serves as its source, just as the electric field in space is proportional to the charge which serves as its source. Ampere's Law states that 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.