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- Apr 13, 2013

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Hello again!!!

I am given the following exercise:

Find the flux of the vector field $\overrightarrow{F}=zx \hat{i}+ zy \hat{j}+z^2 \hat{k}$ of the surface that consists of the first octant of the sphere $x^2+y^2+z^2=a^2(x,y,z \geq 0).$

That's what I did so far:

$\hat{n}=\frac{\nabla{G}}{| \nabla{G} |}=\frac{x \hat{i}+ y\hat{j}+ z\hat{k}}{a}$

Flux=$\int_C{\overrightarrow{F} \cdot \hat{n}}ds=\int_C{(zx \hat{i}+zy \hat{j}+z^2 \hat{k}) \frac{x \hat{i}+y \hat{j} +z \hat{k}}{a}}ds=\int_C{\frac{zx^2+zy^2+z^3}{a}}ds$

How can I continue? Do I have to use spherical coordinates? Or can I solve this with these coordinates?

I am given the following exercise:

Find the flux of the vector field $\overrightarrow{F}=zx \hat{i}+ zy \hat{j}+z^2 \hat{k}$ of the surface that consists of the first octant of the sphere $x^2+y^2+z^2=a^2(x,y,z \geq 0).$

That's what I did so far:

$\hat{n}=\frac{\nabla{G}}{| \nabla{G} |}=\frac{x \hat{i}+ y\hat{j}+ z\hat{k}}{a}$

Flux=$\int_C{\overrightarrow{F} \cdot \hat{n}}ds=\int_C{(zx \hat{i}+zy \hat{j}+z^2 \hat{k}) \frac{x \hat{i}+y \hat{j} +z \hat{k}}{a}}ds=\int_C{\frac{zx^2+zy^2+z^3}{a}}ds$

How can I continue? Do I have to use spherical coordinates? Or can I solve this with these coordinates?

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