# What does the magnetic field term in Ampere's Law signify?

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.

## 1 Answer

It’s all the B field.

A (somewhat forced) analogy is Gaus’s law. The E field flux through a surface is given by the charge inside. That E field might also have contributions from other sources outside, but when integrating over the entire surface, those sum to zero.

Same here. The integral around the path comes from all the current that passes through the path. Currents that don’t pass through might induce a bit of B here or there, but that will sum to zero over the entire path.