1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Calculus - Stokes' theorem

  1. Apr 2, 2008 #1
    [SOLVED] Calculus - Stokes' theorem

    1. The problem statement, all variables and given/known data
    I have F in Cartesian coordinates (F is a vector): F = (y , x , x*z) and a curve C given by the quarter-circle in the z-plane z=1 (so t : (cos(t) , sin(t) , 1) for t between 0 and Pi/4).

    I have found the line integral, and it equals 1/2.

    For fun I wanted to find the same line-integral using Stokes' theorem, so I find the curl of F to be (0 , -z , 0) and dS I find by finding the normalvector, which is the cross-product between n_r and n_t. This gives a z-component (of course) with magnitude r - but then the surface integral is zero?

    Where is my error?
  2. jcsd
  3. Apr 2, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    You can only use Stokes theorem if you have a closed contour. Try doing the contour integral around the whole boundary of the quarter circle. Then you should get zero.
  4. Apr 2, 2008 #3
    Ah man, of course; hadn't thought of that.

    You saved me again, thanks.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook