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Flux through cube

  • Thread starter dpa
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  • #1
dpa
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Flux through sphere

Homework Statement


Given [itex]\vec{F}=\frac{\vec{r}}{r^2} [/itex] and unit sphere, find the flux through the surface of the cube.


Homework Equations


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


The Attempt at a Solution


After the above formula, I do not have idea how to use divergence in spherical coordinate system.
 
Last edited:

Answers and Replies

  • #2
BruceW
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why not do it the easier way by using F dS ?
 
  • #3
CAF123
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I do not have idea how to use divergence in spherical coordinate system.
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.
 
  • #4
vanhees71
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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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