Derivation of gauss's law for electrical fields

In summary, the conversation discusses the application of the formula q/permitivity to all closed surfaces in the context of electromagnetism. The speaker is confused about why this is the case and asks for an explanation. They also express embarrassment and ask not to be laughed at. A possible solution is proposed, involving calculating the electric flux of spheres with different radii and then approximating any closed surface using portions of spheres and portions of annuli. This is followed by taking limits.
  • #1
Ragnar
23
0
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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  • #2
Try calculating the electric flux of spheres with various radii using [itex]\phi = \int\vec{E}\cdot d\vec{A}[/itex] 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...
 
  • #3
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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Related to Derivation of gauss's law for electrical fields

1. What is Gauss's law for electrical fields?

Gauss's law for electrical fields is a fundamental principle in electromagnetism that relates the electric field at a point to the charge enclosed by a closed surface surrounding that point. It states that the electric flux through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space.

2. How is Gauss's law derived for electrical fields?

Gauss's law can be derived using vector calculus and the divergence theorem. The derivation involves considering a small Gaussian surface enclosing a point charge and evaluating the electric field at each point on the surface. By taking the limit as the surface approaches zero size, the equation for Gauss's law is obtained.

3. What are the assumptions made in the derivation of Gauss's law?

The derivation of Gauss's law assumes that the electric field is continuous and differentiable, and that it follows the inverse square law for point charges. It also assumes that the charge enclosed by the surface is static and that there are no other sources of electric field present.

4. How is Gauss's law used in practical applications?

Gauss's law is used in a variety of practical applications in electromagnetism, such as calculating the electric field around charged objects, determining the charge distribution on conductors, and analyzing the behavior of electric fields in capacitors and other devices.

5. Can Gauss's law be applied to non-uniform electric fields?

Yes, Gauss's law can be applied to non-uniform electric fields as long as the electric field is still continuous and differentiable. In these cases, the surface integral of the electric field over a closed surface can still be used to determine the charge enclosed by that surface.

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