Is Gauss's Law Applicable in Atomic Scales?

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Discussion Overview

The discussion centers on the applicability of Gauss's Law at atomic scales, particularly in relation to the electric field near electrons and protons. Participants explore the implications of quantum physics on classical electrostatics, specifically whether Gauss's Law remains valid at very small distances.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant questions the validity of Gauss's Law at atomic scales, particularly near electrons, due to a lack of knowledge in quantum physics.
  • Another participant cites Feynman's Lectures, suggesting that Coulomb's Law fails at distances of 10-14 cm and implies that Gauss's Law would also be invalid at such scales, proposing two possible explanations for this failure.
  • A different participant specifies a distance of about 10-10 m, noting that the electric field from electrons and protons is extremely high, making it seem practically impossible to remove an electron from the nucleus with an applied electrostatic field.
  • One participant expresses the belief that Gauss's Law should still be applicable at the specified distance, referencing Feynman's views.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Gauss's Law at atomic scales, with some suggesting it may fail at very small distances while others believe it remains valid at distances around 10-10 m. The discussion does not reach a consensus.

Contextual Notes

There are unresolved assumptions regarding the nature of charge at atomic scales and the definitions of distances relevant to the discussion. The implications of quantum mechanics on classical laws are also not fully explored.

Hassan2
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Hi all,

Can we use Gauss's law to find the electric field near an electron, or is Gauss's law invalid in atomic scales? I ask this basic question because I know nothing about Quantum physics.
 
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It depends how close of electron you want to go. Acoording to Feynman ( Feynman Lectures Volume 2, page 5-7), the Coulomb's law fails at distances of [itex]10^{-14}[/itex] cm and less. Since validity of Gauss's law depends upon the validity of Coulomb's law, it means that Gauss's law also fails at this distance or below it. Feynman thinks there are two possible explanations for this. One, that Coulomb's law fails at such small distances. Or second, the electrons and protons are not point charges, perhaps either the electron or proton ,or both ,is some kind of a smear. Then he says that most physicists prefer to think that the charge of proton is smeared
 
Last edited:
Thanks IssacNewton,

The scale I meant is about 10-10 m. Even at this distance , the electric field due to electrons and protons is extremely high. It seems practically impossible to take an electron away from the nucleus from with an applied electrostatic field.
 
For that distance I think Gauss's law should work if what Mr Feynman is saying...
 

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