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: Stoke's theorem

  1. Apr 24, 2007 #1

    Calculate the line integral F*T ds around C where

    F=(-xz-2y,x^2-yz,z^2+1) and

    C is the boundary curve between the cylinder x^2+Y^2=1 and the top half of the sphere X^2+Y^2+z^2=10.

    My work:

    Surely I'm supposed to use Stoke's theorem here. First I replace x^2+y^2 with 1 in the sphere equation, to find that C lies in the plane z=3.

    Then I need the normal unit vector. But how do I find that?

    Is it simply the partial of the surface eq. f(x,y,z)=x^2+y^2+z^2-10=0?
  2. jcsd
  3. Apr 24, 2007 #2
    Isn't it just a circle on the plane z=3? Or am I missing something?
  4. Apr 25, 2007 #3


    User Avatar
    Science Advisor

    Are you really required to use Stoke's theorem? As Glass said, the boundary curve is just the circle x2+ y2= 1 with z= 3. It should be easy to integrate F around that boundary directly.

    However, it is true that the gradient (which I presume is what you mean by "partial of surface") of x^2+y^2+z^2-10 is normal to that surface. It may not be a "unit" normal though.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook