# Flux through surface

1. Apr 26, 2009

### -EquinoX-

1. The problem statement, all variables and given/known data

Compute the flux of the vector field, $$\vec{F}$$ , through the surface, S.
$$\vec{F} = y\vec{i} + 7\vec{j} - xz\vec{k}$$ and S is the surface $$y = x^2 + z^2$$ with $$x^2 + z^2 \leq 36$$ oriented in the positive y direction.

2. Relevant equations

3. The attempt at a solution

$$\int\limit_R ((x^2+x^2)\vec{i} + 7\vec{j} - zx\vec{k}) \cdot (-2x\vec{i} -2z\vec{k} + \vec{j})dA$$

2. Apr 27, 2009

### Billy Bob

Are you trying to evaluate

∫∫R ( (x2+z2) i + 7 j - zx k ) · (-2x i + j -2z k) dA

where R is the disc x2 + z2 ≤ 36 in the xz plane?

So take the dot product, then convert to polar coordinates in the xz plane, is this what you mean?

I think this is correct if the unit normal to S is pointing "right" (i.e., into the parabolic bowl), but negate it if the unit normal to S is pointing "left" (i.e., out of the bowl). Also, you are assuming the bowl has no "lid."

3. Apr 27, 2009

thanks!