1. ## Divergence Theorem

The question wants me to use Gauss's theorem
$\vec{F} = x\hat{i} + y\hat{j} + {z}^{2}\hat{k}$
Evaluate teh flux on the closed surface it is a cylinder:
${x}^{2} + {y}^{2} \leq {h}^{2}$
whereby
$0 \leq z \leq b$

---- attempt ----
$Flux = \iiint \nabla . \vec{F} dV$
$Flux = \iiint (2 + 2Z) dV$

Now i could say dV = dx dy dz but i do not have any arbitary values for x and y do i convert to cylindrical polar coordiantes and use r is between r and 0 and the angle is between 2pi and zero?

Thanks!

2. Originally Posted by imagemania
The question wants me to use Gauss's theorem
$\vec{F} = x\hat{i} + y\hat{j} + {z}^{2}\hat{k}$
Evaluate teh flux on the closed surface it is a cylinder:
${x}^{2} + {y}^{2} \leq {h}^{2}$
whereby
$0 \leq z \leq b$

---- attempt ----
$Flux = \iiint \nabla . \vec{F} dV$
$Flux = \iiint (2 + 2Z) dV$

Now i could say dV = dx dy dz but i do not have any arbitary values for x and y do i convert to cylindrical polar coordiantes and use r is between r and 0 and the angle is between 2pi and zero?

Thanks!
Your divergence is correct. The divergence of F

$\nabla \cdot \mathbf{F}=1+1+2z$

The radius of the cylinder is h and z goes from zero to b and your angle is correct. Try to evaluate the integral.

3. Ok sure, going from my original idea:
$\int^{b}_{0}\int^{2\pi}_{0}\int^{h}_{0} (2+2z) drd\phi dz$
Hence i obtain:
$2\pi hb(2+b)$

Is this satisfactory?

4. yes that is the correct solution