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!

Divergence theorem over a hemisphere

  1. Dec 7, 2008 #1
    I was told this problem could be done with divergence theorem, instead of as a surface integral, by adding the unit disc on the bottom, doing the calculation, then subtracting it again.

    1. The problem statement, all variables and given/known data

    t03swo.jpg

    2. Relevant equations

    32c955a56b8e720af3b926c482107ae9.png

    3. The attempt at a solution

    for del . f I get i + j = 2. Which makes the integral equal twice the volume of the hemisphere, or 4/3 pi. Now I'm supposed to subtract the unit disc, but I get pi when I calculate that surface, which leaves me with 1/3 pi. The answer should be 7/6 pi.

    Thanks :)
     
  2. jcsd
  3. Dec 7, 2008 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    The outward pointing normal to the disk is -k. So F.(-k) is -1 and the contribution from the disk is -pi. The total integral from the divergence theorem is 4pi/3 (as you said). I think that makes the integral over the upper hemisphere 7pi/3, doesn't it? Not 7pi/6?
     
  4. Dec 7, 2008 #3
    Ya, I got that a couple times too (after I remembered the orientation), however the answer I was provided is 7/6 pi. That could be wrong. I'll re-do the surface integral the other way and see what I come up with I guess.
     
  5. Dec 7, 2008 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Good idea! Let me know what you get.
     
  6. Dec 7, 2008 #5
    well, I'm still getting 7pi/3, so I'm going to assume that the two of us combined are smarter than the given answer ;) Thanks for your help!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Divergence theorem over a hemisphere
  1. Divergence Theorem (Replies: 5)

  2. Divergence theorem (Replies: 1)

  3. Divergence theorem (Replies: 2)

Loading...