Divergence Problem

  • Thread starter luju
  • Start date
  • #1
11
0

Homework Statement



Find the flux of the vector field out of the closed surface bounding the solid region x^2 + y^2 ≤ 16, 0 ≤ z ≤ 9, oriented outward.

F = x^3 + y^3 + z^3


Homework Equations





The Attempt at a Solution


I found the divergence which is 3x^2+3y^2+3z^2.

And then i'm stuck. I know Flux is divergence * Volume, in a simplifed way. So i factored 3 out, and i got 3(x^2+y^2) + 3z^2. I do not know where to go from here. Thanks in advance
 

Answers and Replies

  • #2
ptr
28
0
Integrate over the surface using the transformation to cylindrical co-ordinates, using x = square_root(16) cos(theta) and similarly for y, and the divergence theorem gives support to your integrating over the vector field, once you have added in the jacobian, from zero to two pi for theta, and from zero to 9 for z.
 

Related Threads on Divergence Problem

  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
9
Views
696
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
1
Views
880
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
4
Views
1K
Top