Derivation of gauss's law for electrical fields

[Ragnar]

This is a very stupid question. extremely stupid. In fact I'm extremely embarassed.

I was reading a text on electromagnetism, and it said that since the flux due to a charge does not depend on the radius of the sphere then the formula, q/permitivitty applies to all closed surfaces. This is where i got confused. why does that make it apply to all closed surfaces?

please don't laugh at me.

Please I need an answer!

 

[Hootenanny]

Try calculating the electric flux of spheres with various radii using $\phi = \int\vec{E}\cdot d\vec{A}$ and see where that gets you. Intuitively, one can consider the definition of electric flux (number of electric field lines passing through a unit area) and the definition of the electric field and how it relates to the density of electric field lines...

 

[robphy]

After calculating for spheres, try (say) a "northern" hemisphere at radius r₁ and a "southern" hemisphere at radius r₂ with an http://mathworld.wolfram.com/Annulus.html" joining their "equators". Note the flux through this annulus.

Then, approximate ANY closed surface by portions of spheres and portions of annuli. ...take limits.