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Homework Help: Flux through cube

  1. Sep 18, 2013 #1


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    Flux through sphere

    1. The problem statement, all variables and given/known data
    Given [itex]\vec{F}=\frac{\vec{r}}{r^2} [/itex] and unit sphere, find the flux through the surface of the cube.

    2. Relevant equations
    Surface Integral of F dS=volume integral of Div. F d^3r

    3. The attempt at a solution
    After the above formula, I do not have idea how to use divergence in spherical coordinate system.
    Last edited: Sep 18, 2013
  2. jcsd
  3. Sep 18, 2013 #2


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    Homework Helper

    why not do it the easier way by using F dS ?
  4. Sep 18, 2013 #3


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    You do not need to worry so much about the divergence in SPs. Just compute the divergence of ##\vec{F}## using the identity for ##\nabla \cdot (\phi \vec{a})##, where ##\phi## and ##\vec{a}## are scalar and vector fields respectively.
  5. Sep 18, 2013 #4


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    First of all you have to specify the cube, i.e., its location and orientation. If the origin is contained inside the cube, it's not a good idea to use Gauss's Law and the volume integral over the divergence, because you have to find out how to treat the non-trivial singularity at the origin.

    Last but not least, it's a pretty unusual long-ranged field. Are you sure that there isn't [itex]r^3[/itex] in the denominator? Better check your problem again!
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