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## Main Question or Discussion Point

First I need to post some pages of a book that I'm reading...

[PLAIN]http://img824.imageshack.us/img824/5153/42785753.png [Broken] [Broken]

[PLAIN]http://img824.imageshack.us/img824/5153/42785753.png [Broken] [Broken]

EQ 34

[PLAIN]http://img525.imageshack.us/img525/2407/49364360.png [Broken]

Now I have some questions...

1. Why do the supposed scalar functions of vector function F depends on x, y and z? We have Fx(x,y,z), why does it depend on x, y and z? It should depend just on x, shouldn't it?

2. "Whether some other shape will yield the same limit is a question we must face later.". What limit is he talking about? Did he say that because these two equations are equivalent? [PLAIN]http://img801.imageshack.us/img801/2570/15683468.png [Broken]

3. Why does the flux through the two faces he's considering depends only on the z component? It should depend on x and y (because the top and the bottom faces are in the xy-plane), shouldn't it? I'm confused ;S

4. What is Fz representing here? The flux through the faces? ;S

5. I understand that the difference between the flux at the top face and the flux at the top face is the net flux through these faces. But why the net flux is the difference between the averages of the flux in the two faces? Shouldn't it be only the difference between the TOTAL flux of the top face and the TOTAL flux of the bottom face?

6. Why the net flux is equal to [tex]\frac{\partial F_{z}}{\partial z} \Delta z[/tex]?

7. What does he mean "first-order variation of Fz"?

I have more questions but I think if I get the answer the these first I may understand the others...

I know that are too many questions but I really need to understand the concept of divergence...

If someone could help me I would be grateful...

Thank you,

Rafael Andreatta

[PLAIN]http://img824.imageshack.us/img824/5153/42785753.png [Broken] [Broken]

[PLAIN]http://img824.imageshack.us/img824/5153/42785753.png [Broken] [Broken]

EQ 34

[PLAIN]http://img525.imageshack.us/img525/2407/49364360.png [Broken]

Now I have some questions...

1. Why do the supposed scalar functions of vector function F depends on x, y and z? We have Fx(x,y,z), why does it depend on x, y and z? It should depend just on x, shouldn't it?

2. "Whether some other shape will yield the same limit is a question we must face later.". What limit is he talking about? Did he say that because these two equations are equivalent? [PLAIN]http://img801.imageshack.us/img801/2570/15683468.png [Broken]

3. Why does the flux through the two faces he's considering depends only on the z component? It should depend on x and y (because the top and the bottom faces are in the xy-plane), shouldn't it? I'm confused ;S

4. What is Fz representing here? The flux through the faces? ;S

5. I understand that the difference between the flux at the top face and the flux at the top face is the net flux through these faces. But why the net flux is the difference between the averages of the flux in the two faces? Shouldn't it be only the difference between the TOTAL flux of the top face and the TOTAL flux of the bottom face?

6. Why the net flux is equal to [tex]\frac{\partial F_{z}}{\partial z} \Delta z[/tex]?

7. What does he mean "first-order variation of Fz"?

I have more questions but I think if I get the answer the these first I may understand the others...

I know that are too many questions but I really need to understand the concept of divergence...

If someone could help me I would be grateful...

Thank you,

Rafael Andreatta

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