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Vector Calc Homework Help! Divergence Free Vector Fields

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data
    Let S be the ellipsoid where a,b, and c are all positive constants.
    x2/(a+1)+y2/(b2)+z2/(c2) = 1

    → → → → →
    Let F = (r - ai) / ||r - ai|| [* r and i are vectors = I tried inserting the arrows]

    a)Where is F undefined?
    b)Find divF at points where divF is defined.
    c) Find ∫s F dA.


    2. Relevant equations
    Divergence theorem


    3. The attempt at a solution
    I know that the divF=0 making it a divergence free vector field, but I am not sure how to solve for the flux through the ellipsoid.

    I really would like to understand the actual concept of divergence free theorems and a step by step explanation would really help.

    Thanks for your time and help!
     
  2. jcsd
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