Derivation of gauss's law for electrical fields

AI Thread Summary
The discussion revolves around the derivation of Gauss's Law and the confusion regarding its application to all closed surfaces. A participant expresses embarrassment over their question about why the electric flux due to a charge is independent of the radius of the sphere. The response suggests calculating electric flux for spheres of varying radii using the formula φ = ∫E·dA to clarify the concept. It emphasizes understanding electric flux as the number of electric field lines passing through a unit area and encourages exploring different geometries, such as hemispheres and annuli, to grasp the principle. Ultimately, the discussion aims to solidify the understanding of Gauss's Law through practical calculations and conceptual exploration.
Ragnar
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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!
 
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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...
 
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.
 
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