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Flux of vector field proportional to 1/r^3 through sphere

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Consider the vector field [tex] \vec F=\frac{\vec r}{r^3}[/tex] with [tex]\vec r=x\hat{i}+y\hat{j}+z\hat{k} [/tex]. Compute the flux of [tex] \vec F[/tex] out of a sphere of radius "a" centred
    at the origin.
    2. Relevant equations
    The Gauss Divergence Theorem [tex]\int_D dV \nabla \bullet F=\int_S F\bullet dA [/tex]

    3. The attempt at a solution
    I think I'm either missing or not understanding something in this question. When I compute [tex] \nabla \bullet F[/tex], I get zero, which means the flux is zero, I think. But this doesn't seem right at all. What am I missing?
  2. jcsd
  3. Feb 1, 2010 #2
    The vector field [tex]\vec{F}[/tex] has a singularity at the origin, so you can't use the divergence theorem (at least not in its most common form). Compute the flux directly from the definition instead.
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