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!

Verifying difvergence theorem

  1. Jun 4, 2010 #1
    1. The problem statement, all variables and given/known data
    verify that the divergence theorem in 3-d is true for the vector field F(r)=<3x,xy,2xz>
    on the cube bounded by the planes x=0 x=1 y=0 y=1 z=0 z=1


    2. Relevant equations



    3. The attempt at a solution

    so fristly div(F)=d/dx(3x)+d/dy(xy)+d/dz(2xz)=3+3x
    [tex]\int[/tex][tex]\int[/tex][tex]\int[/tex] 3+3xdxdydz=4.5

    now i need to evaluate flux through each faces of the cube seperately so i was just wondering if i am doing this write say i would want to evaluate the top surface of the cube
    then i would have to parametrize it so would the following be corret
    r(x,y,z)=(3x,xy,1)
    dr/dx=(3,y,0)
    dr/dy=(0,x,0)
    (dr/dx) X (dr/dy) = (0,0,3x)
    r(x,y,z).((dr/dx) X(dr/dy))= (3x,xy,1).(0,0,3x) = 3x
    [tex]\int[/tex][tex]\int[/tex] 3x dydx
    =3/2

    and i have to do the same for all other five surfaces so is this the correct way?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jun 5, 2010 #2

    vela

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    You're not using the correct r when calculating the normal. You want to describe the surface, not the vector field. For the top face, it would be r=(x, y, 1).
     
  4. Jun 5, 2010 #3
    ok thanks
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Verifying difvergence theorem
  1. Verify Stokes' theorem (Replies: 2)

Loading...