Final answer:
Ampère's Law relates the magnetic field line integral around a current-carrying path to the net electric current passing through the area enclosed by the path. It's widely used for calculating the magnetic field created by various current configurations, with the integral summing over small segments of a path or loop.
Step-by-step explanation:
The question revolves around Ampère's Law, which is a fundamental concept in physics, particularly in the study of electromagnetism. Ampère's Law states that the line integral of the magnetic field (B) around a closed path is proportional to the electric current (I) passing through the enclosed area. In essence, for a path enclosing a net current, Ampère's Law can be mathematically expressed as ⋯B·dℓ = µ0I, where µ0 is the permeability of free space. When applied to specific configurations of current-carrying wires, Ampère's Law allows calculation of the magnetic field around those wires.
In practical terms, if you follow a loop around the wires and sum the contributions of magnetic field along this loop (dl being the small segment of the loop), the total integral will give us the net current multiplied by the vacuum permeability. However, if the net current enclosed by the path is zero, the integral of magnetic field along the loop also equals zero. This could happen if the currents are flowing in opposite directions through the loop such that they cancel out.