Magnetic flux, current and magnetic field confusion

AI Thread Summary
The discussion centers on the confusion surrounding the application of Ampère's law and the use of the length element, dl. Participants clarify that dl represents the differential length along a path, such as the circumference of a circular loop, which is indeed 2πr. The confusion arises from the consistent appearance of 2π in various contexts, leading to uncertainty about its application. Additional resources, like HyperPhysics, are suggested to aid understanding. The conversation emphasizes the importance of correctly interpreting the equations in magnetic field problems.
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1. The problem statement

Relevant equations: I am confused. When dealing with Ampères law:
upload_2017-4-25_13-23-13.png

dl is supposed to be the length element? Like when we have Gauss' law for electric fields and we use a circular Gaussian surface, we have E(4πr^2)=Qenclosed/ε
So in this case, when we have a circular loop our dl will be 2πr, since that is the circumference of the loop ? Or do I just understand nothing of this type of problem?
I am confused because we seem to use 2π no matter what, like in this problem:
upload_2017-4-25_13-26-19.png


3. The attempt at the solution:
I don't see anyway to include 2π, but they still do:
upload_2017-4-25_13-27-0.png
 

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