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: Verifying Stoke's theorem

  1. Dec 17, 2014 #1
    1. The problem statement, all variables and given/known data
    Verfify Stokes' theorem for the given surface S and boundary ∂S, and vector fields F.

    S = [(x,y,z): x2+y2+z2=1, z≥0
    ∂S = [(x,y): x2+y2=1

    I did this problem and checked the answer - I chose the wrong integral bounds and I am wondering why they are wrong.

    2. Relevant equations

    Stokes' theorem:
    ∫∫(∇×F)dS = ∫F⋅ds

    3. The attempt at a solution
    I was able to do the left hand of the solution easily. I knew that I should get zero for the cross product, so that's all I had to do.

    For the right hand side:

    ∫F⋅dS = ∫xdx+ydy

    x= cosΘ


    Apparently this is the correct range for theta:


    Why is it just π?
  2. jcsd
  3. Dec 17, 2014 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You should write ##dx=-\sin\theta\,d\theta## and ##dy=\cos\theta\,d\theta##.

    0 to ##2\pi## is the correct interval.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted