Parametrize sphere for Stoke's Thm

[swraman]

Homework Statement

compute the flux of $$\stackrel{\rightarrow}{F} = <x,y,z>$$ through the sphere $$x^{2} + y^{2} + z^{2} = 1$$

Homework Equations

$$\int\int_{S}Curl(\stackrel{\rightarrow}{F})\bullet ds = \int_{C}\stackrel{\rightarrow}{F}\bullet d\vec{r}$$

The Attempt at a Solution

I am having trouble parametrizing the surface S (the sphere of radius 1). I know I have to find a normal vector for the surface (which I know intuitivley is <x,y,z>) but I don't know how to get there if I have a different problem that is not so easy to see.

I tried parametrizing it in Spherical cordinates using two angles $$(\phi, \vartheta$$. Then I get for parametrzed equation

$$x = sin(\phi)cos(\vartheta)$$
$$y = sin(\phi)sin(\vartheta)$$
$$z = cos(\phi)$$

which gives the Normal vector as

$$n = < sin^{2}(\phi)cos(\vartheta), -sin^{2}(\phi)sin(\vartheta), cos(\phi)sin(\phi) >$$

This isn't right obviously...
How am I suposed to parametrize a function in such as the ball?

Thanks

 

[swraman]

OK I found out what I needed...I was actualy mostly correct, aside from small computation errors :) Thanks anyway though