I'm given the following vector field equation which is in cylindrical form: $$\vec{D} = \rho^4 \hat{\rho}$$
I want to find the flux through the surface of two cylinders which are both centered at the origin, of radius $1$ and $4$ respectively from $z = 0$ to $z = 6$. I need to find the flux in two ways. The first using surface integrals, and the second using he divergence theorem. I know how to do this if the vector field was given in cartesian form, but I have no idea how to do it when given in cylindrical form, since I don't know how to do the dot product in cylindrical coordinates.
I tried converting the vector function to cartesian, but it gave me some messy vector field that doesn't look right at all.
The picture for the question here.
