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. Aug 8, 2007 #1
    1. The problem statement, all variables and given/known data
    Solve the following question by using Stokes' Theorem.

    (Line integral on C) 2zdx + xdy + 3ydz = ? where C is the ellipse formed by
    z = x, x^2 + y^2 = 4.

    2. Relevant equations



    3. The attempt at a solution

    We have the vector A=(2z,x,3y) which is cont. differentiable and
    curl(A) = (3,2,1). Now we have to parametrize the smooth surface S whose boundary is C and obtain a normal. I'm confused here how to choose the parameters. I solved it using the usual way and got -8*Pi. Can you help me to arrange the double integral in order to solve it by using Stokes' Thm.? Thanks.
     
  2. jcsd
  3. Aug 8, 2007 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The normal to the ellipse is the same as the normal to the plane x=z. So it's a constant vector. Your curl is also a constant vector. So the integrand of the double integral is just a constant. This means you only need to know the area of the ellipse and the value of the integrand. No need to actually integrate anything.
     
  4. Aug 8, 2007 #3
    Okay, i got it. The normal to the plane is n=(1,0,-1) but we need an outward normal so we take n=(-1,0,1). We get (3,2,1)(-1,0,1) = -2. Projection onto xy-plane is a circle whose area is 4*Pi and multiplying it by -2 we obtain 8*Pi.
     
  5. Aug 8, 2007 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    I guess I would normalize the normal by dividing by sqrt(2) and then multiply by the real area of the ellipse which is sqrt(2) times the area of the circle. But of course, you get the same thing.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Application of Stokes' Theorem
Loading...