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!

Application of Stokes Theorem

  1. Dec 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Use Stokes's Theorem to evaluate [tex]\int F · dr[/tex]
    In this case, C (the curve) is oriented counterclockwise as viewed from above.


    2. Relevant equations
    F(x,y,z) = xyzi + yj + zk, x2 + y2 ≤ a2
    S: the first-octant portion of z = x2 over x2 + y2 = a2


    3. The attempt at a solution
    "Use Stoke's" is code for "stick the dot product of curl F and the normal vector into the integral". If this problem behaves nicely, this should become a double integral like every other Stoke's problem in the book and will need a new area of integration as well.

    curl F would be <0, xy-yz, -xz>
    G(x,y) = z-x2
    the normal is <-Gx,-Gy,1>
    which is <-2x, 0, 1>
    F · N = 0+0-xz = -xz because of convenient canceling

    So now -xz has to be integrated over some area. The "first octant" is simple enough, and x2 + y2 ≤ a2 is a cylinder of infinite height and radius a centered around the Z-axis (a fixed circle for every Z). I'm picturing a a parabola-cum-trough looking thing that got stamped by a circular cookie cutter.

    If that's the case, the x's get restricted which means the z's get restricted to a constant. How do you set up the integral to get rid of all variables (the radius a is a constant and obviously stays undefined).

    Thanks!
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Application of Stokes Theorem
  1. Clairaut's theorem? (Replies: 0)

  2. Navier Stokes? (Replies: 0)

Loading...