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: Verify Divergence Theorem

  1. Jan 17, 2016 #1
    1. The problem statement, all variables and given/known data
    Verify the divergence theorem for the function
    V = xy i − y^2 j + z k
    and the surface enclosed by the three parts
    (i) z = 0, s < 1, s^2 = x^2 + y^2,
    (ii) s = 1, 0 ≤ z ≤ 1 and
    (iii) z^2 = a^2 + (1 − a^2)s^2, 1 ≤ z ≤ a, a > 1.

    2. Relevant equations

    7ec662d9708da6cde59c16ccc768f4bf.png 25px-OiintLaTeX.svg.png [PLAIN]https://upload.wikimedia.org/math/7/b/7/7b759968274f2f43cfaab3ce5672da74.png[PLAIN]https://upload.wikimedia.org/math/a/b/9/ab9fd5a4aaa36e402c98cbd36af3a70d.png [Broken]

    Divergence theorem, although on the RHS I put vector DS = nDS.

    3. The attempt at a solution
    So I solved the LHS and got the answer to be a*Pi

    on the RHS, splitting the 3 surfaces,
    (i) got 0 for integral
    (ii) got 0 for integral
    (iii) staying in cartesians, I have to integrate ((1-a^2)(-x^2 y +y^3 + x^2 +y^2) +a^2)/Sqrt(a^2+(1-a^2)(x^2+y^2) dxdy between -1 and 1 for x and y which even Wolfram can't do.

    Spent hours on this please help.
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Jan 17, 2016 #2


    User Avatar
    Science Advisor

    You haven't really said much about what you did. What did you get for [itex]\nabla\cdot\vec{V}[/itex]? What are s and a? Constants? Then "(ii) s= 1, [itex]0\le z\le 1[/itex]" makes no sense.
  4. Jan 17, 2016 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted