1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Integral along a closed loop

  1. Apr 19, 2006 #1
    i want to prove that this integral along a closed loop:

    [tex]\oint (1/r^2) dr[/tex]

    is equal to zero. but i'm not sure how to prove it. i was wondering if someone can show me a rigid proof for this. I think i'm missing something here because I'm not really that familiar with loop integrals.
  2. jcsd
  3. Apr 20, 2006 #2
    Pick two points, A and B, and two curves, C_1 and C_2 where C_1 goes from A to B and C_2 from B to A.

    Now calculate the line integral along the curve C_1 and C_2. They should both be equal, in which case, the loop integral will be 0.
  4. Apr 20, 2006 #3
    Since [tex]1/\tau^2[/tex] is an analytic function with a singularity in 0 (a pole of order 2), the contour your want to use is closed, then you can use the Cauchy's theorem on residues.

    [tex] \oint 1/\tau^2 \, d\tau = 2i\pi \cdot 0 [/tex]

    where 0 is the residue of [tex]1/\tau^2[/tex]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Integral along a closed loop
  1. Loop integral (Replies: 0)