- #31
Killingtensor
- 3
- 0
I'm fairly sure this can be done with lagrangians as long as you are comfortable with the jump from lagrangians to lagrangian densities.
Proof Gauss's Law - Understanding, Deriving & Applying
- Context: Graduate
- Thread starter Swapnil
- Start date
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- Tags
- Gauss's law Law Proof
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Discussion Overview
The discussion revolves around the proof and understanding of Gauss's law, exploring both intuitive and mathematical derivations. Participants express interest in how Gauss's law can be derived from Coulomb's law and the implications of its validity for any closed surface.
Discussion Character
- Exploratory
- Technical explanation
- Debate/contested
- Mathematical reasoning
Main Points Raised
- One participant inquires about proving Gauss's law, suggesting a derivation from Coulomb's law.
- Several participants share links to resources that provide intuitive explanations of Gauss's law.
- There is a discussion about the use of Stokes' theorem versus the Divergence theorem in relation to Gauss's law, with some participants clarifying their understanding of these concepts.
- A participant proposes a simple derivation involving the definition of differential solid angle and the flux through surfaces surrounding a charge.
- Another participant questions the existence of a rigorous proof for Gauss's law, particularly regarding its applicability to any closed surface.
- Some participants mention that many electromagnetism textbooks provide proofs, but one expresses dissatisfaction with the explanations typically offered.
- A participant outlines a conceptual approach to understanding the inverse-square law using an analogy with light intensity and conservation of energy.
Areas of Agreement / Disagreement
Participants express differing views on the existence and nature of a rigorous proof for Gauss's law. While some assert that it can be found in textbooks, others feel that the explanations provided are unsatisfactory or overly simplistic.
Contextual Notes
Participants reference various mathematical tools and concepts, such as the Divergence theorem and the definition of solid angle, but there is no consensus on their application to derive Gauss's law from Coulomb's law.
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