# Flux Through a surface

1. Feb 15, 2008

### jesuslovesu

1. The problem statement, all variables and given/known data
A volume in cylindrical coords is defined as [1,2]x[pi/6,pi/3]x[1,2]
Calculate the flux of the vector field A(rowe,phi,z) = 4z (rowehat)

Well I used the divergence theorem
Volume integral( div(A) dot A dV) = pi
I got pi as an answer, but apparently that is not correct.

Does anyone know why the divergence theorem in this case doesn't work? I tried converting to Cartesian coords, the surface integrals are really nasty so I haven't evaluated them.

My guess is that the flux is 0, however, how does one tell when the flux through a surface is 0 as opposed to a value? How do I know if the volume encloses a 'charge' in the case of gauss's law if I am just given a vector function?

2. Relevant equations

3. The attempt at a solution