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Surface Integrals

  • Thread starter duki
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Homework Statement



Find the value of the surface integrals by using the divergence theorem
[tex]\vec{F} = (y^2z)\vec{i} + (y^3z)\vec{j} + (y^2z^2)\vec{z}[/tex]

S: [tex] x^2 + y^2 + z^2 [/tex]

Use spherical coordinates.

Homework Equations



The Attempt at a Solution



I've gotten the integral I think. I want to make sure before I go along with evaluating it.

[tex]\int _0^{2\pi} \int _0^{\pi} \int _0^2 { (7\rho^3 \sin^2{\phi} \sin^2{\theta} \cos{\phi} } \rho^2 d \rho d \phi d \theta[/tex]

My latex is all messed up... maybe a mod can fix it for me?
 
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Answers and Replies

  • #2
gabbagabbahey
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Homework Statement



Find the value of the surface integrals by using the divergence theorem
[tex]\vec{F} = (y^2z)\vec{i} + (y^3z)\vec{j} + (y^2z^2)\vec{z}[/tex]

S: [tex] x^2 + y^2 + z^2 [/tex]

Use spherical coordinates.
Do you mean [itex]x^2+y^2+z^2=4[/itex]?


I've gotten the integral I think. I want to make sure before I go along with evaluating it.

[tex]\int _0^{2\pi} \int _0^{\pi} \int _0^2 { (7\rho^3 \sin^2\phi \sin^2{\theta} \cos{\phi} } \rho^2 d \rho d \phi d \theta[/tex]

My latex is all messed up... maybe a mod can fix it for me?
That doesn't look quite right....what do you get for the divergence of F (in Cartesians and Sphericals)?
 
  • #3
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Yes, I meant = 4. Thanks.

I got [tex] 5y^2 2z [/tex]
 
  • #4
gabbagabbahey
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Yes, I meant = 4. Thanks.

I got [tex] 5y^2 2z [/tex]
I assume you mean [itex]5y^2 z[/itex]?...If so, you're right. What is that in spherical coordinates? What are you using for [itex]dV[/itex] (infinitesimal volume element) in spherical coordinates?
 
  • #5
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Ok, I have [tex]5y^2z[/tex] in my notes but I thought that was wrong. When I take the partial of [tex]y^2z^2[/tex] with respect to z, why does that come out to just z?
 
  • #6
gabbagabbahey
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[tex]\frac{\partial}{\partial z} (y^2 z^2)=y^2 \frac{\partial}{\partial z} (z^2)=2y^2 z[/tex]
 
  • #7
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OooOOooOOooooohhh
 
  • #8
HallsofIvy
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I fixed the Latex:
1) Use "\" in front of Greek letters: \theta, \phi, \rho.

2) [itex]\rho[/itex] is "rho", not "roe".
 

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