Magnetic flux, current and magnetic field confusion

  • #1
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4
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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