Proof Gauss's Law - Understanding, Deriving & Applying

Click For Summary
The discussion centers on the proof and derivation of Gauss's Law, with participants exploring both intuitive and mathematical approaches. A key point raised is the relationship between Gauss's Law and Coulomb's Law, with emphasis on using the Divergence Theorem to transition between integral and differential forms of Gauss's Law. Participants clarify that Stokes' Theorem is not applicable to Gauss's Law, which leads to confusion about the nature of rigorous proofs. The conversation also touches on the concept of flux and its connection to the inverse-square law, illustrating how these principles apply to electric fields. Ultimately, the discussion highlights the complexity of finding a satisfactory proof for Gauss's Law in various electromagnetic texts.
  • #31
I'm fairly sure this can be done with lagrangians as long as you are comfortable with the jump from lagrangians to lagrangian densities.
 

Similar threads

I Gauss' Law - Does it apply even when there are external fields?
  • · Replies 9 ·
Replies
9
Views
2K
I How Gauss’ Law is applied to cylinders
  • · Replies 20 ·
Replies
20
Views
2K
I Gauss' law, method of images, and force induced on conductor plates
  • · Replies 17 ·
Replies
17
Views
2K
I A question about the origin of Coulomb's law and point charge divergence
  • · Replies 13 ·
Replies
13
Views
561
I Understanding Gauss's Law and Special Cases in Maxwell's Equations
  • · Replies 7 ·
Replies
7
Views
2K
Derivation of coloumbs law without Gauss's law
  • · Replies 4 ·
Replies
4
Views
2K
B Determining whether the non-integral form of Gauss' law applies
  • · Replies 1 ·
Replies
1
Views
1K
I Conditions for applying Gauss' Law
  • · Replies 1 ·
Replies
1
Views
2K
I Gauss' Law applicability on any closed surface
  • · Replies 5 ·
Replies
5
Views
2K
I Is it possible to apply Gauss' law to a Klein bottle?
  • · Replies 1 ·
Replies
1
Views
969