Gauss's law in electrodynamics

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Discussion Overview

The discussion revolves around the nature and derivation of Gauss's law in the context of electrodynamics, questioning its relationship to Coulomb's law and its status as a fundamental law or axiom.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant notes that most proofs of Gauss's law rely on Coulomb's law, which is applicable only in electrostatics, raising the question of how Gauss's law is justified in electrodynamics.
  • Another participant presents a mathematical formulation of Gauss's law and suggests that it can be derived without reference to Coulomb's law, indicating a more general approach using potentials and the Lorentz gauge.
  • A third participant mentions that while the historical development of electromagnetism began with Coulomb's law, the complete classical theory is encapsulated in Maxwell's equations, from which Gauss's law can be derived using the divergence theorem.

Areas of Agreement / Disagreement

Participants express differing views on the derivation of Gauss's law, with some emphasizing its dependence on Coulomb's law and others arguing for its generality and derivation from Maxwell's equations. The discussion remains unresolved regarding the foundational status of Gauss's law in electrodynamics.

Contextual Notes

There are limitations in the discussion regarding the assumptions made in the derivations and the dependence on specific mathematical formulations, which are not fully explored.

bigerst
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most(or all) proofs i have seen of gauss's law is based on coulumb's law. however coulumb's law is based off of electrostatics which certainly does not hold in electrodynamics. however gauss's law is used extensively in electrodynamics. is gauss's law derived otherwise or is it just a law like an axiom?

thanks

bigerst
 
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Gauss law is,
∇.E=ρ/ε0 .now in most general form
E=-∇ψ-∂A/∂t, if you put it into above you get,
-∇2ψ-∂/∂t(∇.A)=ρ/ε0...(1)
now using lorentz gauge(more preferable) we have ∇.A=-1/c2 ∂ψ/∂t
if you will put it into (1) you will get the the general form of potential equations.this proof starts with gauss law but the converse can also be done in order to arrive at gauss law.here it does not refer to any coulomb law,and so it is more general.
 
Although EM started with Coulomb historically, the complete classical theory is based
on the four Maxwell equations. Applying the divergence theorem to Maxwell's div D equation gives Gauss's law. Coulomb is the electrostatic case.
 
alright thanks :)
 

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