Thread: Finding total outward flux?

Here is the question...

Let F=xi-yj+zk and the pyramid be as shown below. Find as a surface integral over all five faces.

I really need some help with figuring out the surface integrals of each face. I think that the normal vectors of the two angled faces are and , but I don't understand how to find the dS or the limits of integration since no real equation was given for the surface. I don't know whether I am just not seeing it or what, but can you guys help me out? Thanks in advance.

the normal vectors would definatly vary based on the dimensions of the pyrimyd. Have you done Stokes or Divergence theorems yet because you have a closed surface.

the divergence of the vector field is 1 so by the divergence theorem, the flux accross the surface should be equal to the volume of the pyramid.

Originally Posted by kd8bxz

the normal vectors would definatly vary based on the dimensions of the pyrimyd. Have you done Stokes or Divergence theorems yet because you have a closed surface.

the divergence of the vector field is 1 so by the divergence theorem, the flux accross the surface should be equal to the volume of the pyramid.

Yea, I already did it using the divergence theorem and I got 1/3 as my answer since all of the pyramids dimensions seem to just be 1. My professor told my class to also do it by taking the surface integral of every face of the pyramid just to prove that the answer will be the same. The answer I get is not 1/3 though, so I must be doing something wrong. Can anyone explain how to take the surface integral of the faces?

Can anybody help me with this? Thanks.