Solve Stokes' 2 Homework with Flux Calculation

[asi123]

Homework Statement

Ok, so I need to solve this integral (bottom of the pic) using Stokes' theorem.
What I did first is to find the Curl, then I used the UV surface as usual and then found the normal.
After that, I switched to an area integral of the dot product between the curl and the normal over the UV surface.
It's all in the pic.
My question is this, what this integral actually finds is the flux, right? the flux that goes through the Spiral, so if it's correct, do I also need to find the flux that goes through the plot z=2, that goes downward?

Damn, my English sucks

Homework Equations

The Attempt at a Solution

 

[asi123]

Any idea, guys?

 

[asi123]

I don't see any spiral. The integral is meant to evaluate the flux through a closed surface by the divergence theorem. I go zero as well. What do you mean by the plot where z=2?

Do u mean using Gauss' law?

 

[Defennder]

Oh shucks I just responded to the wrong thread! This is meant for the other thread.

 

[Defennder]

Ok I still don't see what spiral you're talking about. You're evaluating the closed line integral corresponding to the closed curve interesection between the sphere and the plane z=2. So, you found curl F, but you seem to have taken the surface to be the sphere itself. While it's still possible, it makes for tedious calculation. Pick an easier surface to parametrise.

 

[asi123]

Ok I still don't see what spiral you're talking about. You're evaluating the closed line integral corresponding to the closed curve interesection between the sphere and the plane z=2. So, you found curl F, but you seem to have taken the surface to be the sphere itself. While it's still possible, it makes for tedious calculation. Pick an easier surface to parametrise.

Sorry, I meant sphere, I said my English sucks.
Anyway, I need to find the flux that comes out of this surface between Z=2 and the sphere, and I don't think I can parametrize both of them together, should I use Gauss' law?
10x.

 

[asi123]

Yeah, I mean the surface is a closed surface, it's between the plot z = 2 and the sphere, so I thought maybe I can use Gauss' law somehow, no?

 

[Defennder]

No, you're supposed to evaluate the closed line integral formed by the intersection of the plane and the sphere. That is if I interpret $$\oint$$ correctly to mean a line integral on a closed path. You should pick an easy surface bound by this closed curve to parametrise. There's only one surface to parametrise. And I still don't know what you mean by Gauss law.

EDIT: It's not a closed surface. Otherwise you can't use Stoke's theorem.

 

[asi123]

No, you're supposed to evaluate the closed line integral formed by the intersection of the plane and the sphere. That is if I interpret $$\oint$$ correctly to mean a line integral on a closed path. You should pick an easy surface bound by this closed curve to parametrise. There's only one surface to parametrise. And I still don't know what you mean by Gauss law.

EDIT: It's not a closed surface. Otherwise you can't use Stoke's theorem.

I don't get it, the intersection of the plane and the sphere is the circle in Z=2, should I parametrize it?

 

[asi123]

Oh, is it the circle?

 

[Defennder]

Yes the circle is the closed curve. You can evaluate the line integral directly or use stokes theorem to calculate the flux through any closed surface bound by the circle.

 

[asi123]

Yes the circle is the closed curve. You can evaluate the line integral directly or use stokes theorem to calculate the flux through any closed surface bound by the circle.

Oh, I was way off, I thought I need to find the flux through part of the sphere (from Z=2 up to the top) which is not even a line...
That's way I talked about guess's low.
Ok, thanks a lot.

 

[asi123]

Is that right?