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Flux from divergence

  • Thread starter -EquinoX-
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  • #1
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Homework Statement



Suppose [tex] \vec{G} [/tex] is a vector field with the property that [tex] div\vec{G} = 5 [/tex] for [tex] 2 \leq ||\vec{r}|| \leq 14 [/tex] and that the flux of [tex] \vec{G} [/tex] through the sphere of radius 4 centered at the origin is [tex] 20\pi [/tex]. Find the flux of through the sphere of radius 12 centered at the origin.


Homework Equations





The Attempt at a Solution



what I tried so far is

[tex] 20\pi \int_0^{2\pi} \int_0^{\pi} \int_0^{12} \rho^2 sin(\phi)d\rho d\phi d\theta [/tex]

is this wrong
 

Answers and Replies

  • #2
dx
Homework Helper
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No integration is needed for this problem. The flux through the region 2 < R < 4 is just

5(volume of region 2 < R < 4)

by the divergence theorem. Use this, together with the fact that the flux through 0 < R < 4 is 20π, to find the flux through the region 0 < R < 2.

Can you see how to take it from here?
 
  • #3
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ok so after I got the flux through region 2< r< 4and through 0 < r< 4 I just substract it right?
 
  • #4
dx
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Yes, but in which order are you going to do the subtraction?
 
  • #5
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it's the 0<r<4 - 2<r<4 correct?
 
  • #6
dx
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Correct.
 

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