Lately, I've been solving a few problems based off on Ampere's circuital law which 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.
Mathematically $$\oint_C {Bd\ell = \mu _0 I_C }$$ My doubt is what magnetic field are we defining? is it the magnetic field ONLY due to the current element under consideration or is it due to all current-carrying elements in the surroundings as well?
I got this doubt and searched for explanations on the internet but couldn't find any.
I had this confusion because Ampere's law is the 'Gauss law equivalent' of Biot-Savart law and in Gauss law, the electric field defined in the closed line integral is due to all the charges inside and outside the Gaussian surface.