F(x,y,z) = (cos(y/z), (-x/y)sin(y/z), (xy/z^2)sin(y/z)). Compute the downward flux of F across S. The rectangular surface S is given by 0

Question

F(x,y,z) = (cos(y/z), (-x/y)sin(y/z), (xy/z^2)sin(y/z)). Compute the downward flux of F across S. The rectangular surface S is given by 0<x<1, 0<y<pi and z=1. Please help!!

anonymous · Answer

F(x,y,z) = (cos(y/z), (-x/y)sin(y/z), (xy/z^2)sin(y/z)

is that supposed to be a vvf?

anonymous · Answer

vvf?

anonymous · Answer

vector valued function.

anonymous · Answer

yes

anonymous · Answer

i think i have to parameterise the surface but not really sure how to do it

anonymous · Answer

the surface area is just a vector  |area| k
so only the k component of F will contribute to the flux...

anonymous · Answer

ie F dot n is just dot < 0 i 0 j |area| k >

anonymous · Answer

how come only the k component contributes to the flux?

anonymous · Answer

flux is like flow...  imagine you have a balloon and consider the 'mouth' of the balloon to be the surface with which you're concerned about flux across (you're planning on blowing up the balloon).
say you put the mouth of the balloon in the xz plane and then blow in the in the z direction :
|dw:1350454288387:dw|