Is Gauss' Law Applicable to Dynamic Charges and All Surfaces?

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Discussion Overview

The discussion revolves around the applicability of Gauss' Law to dynamic charges and various surfaces of flux integration. Participants explore whether Gauss' Law, traditionally associated with electrostatic situations, can be universally applied to all charge motions and geometries, including relativistic oscillating charges and electromagnetic wave scenarios.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that Gauss' Law is valid only in electrostatic situations, as stated in various EM texts like those by Feynman and Griffiths.
  • Others argue that Gauss' Law can hold for relativistically oscillating charges and different flux integration surfaces, citing personal findings that support this view.
  • A participant references Griffiths' work, suggesting that the electric field of a moving charge does not conform to the 1/r² dependence, which complicates the application of Gauss' Law.
  • Some participants contend that while Gauss' Law remains valid in dynamics, it may not be useful without additional information about the curl of the electric field.
  • There is a discussion about the validity of Gauss' Law in the context of Gaussian beams, with differing opinions on whether the law holds due to the behavior of the electric field in such scenarios.
  • One participant expresses skepticism about the applicability of Gauss' Law in dynamic situations, while another maintains that it is universally true despite the complexities involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the applicability of Gauss' Law to dynamic charges and all surfaces. While some believe it holds universally, others maintain that it is limited to electrostatic conditions. Disagreement persists regarding the interpretation of relevant texts and the implications of dynamic scenarios.

Contextual Notes

Participants reference specific equations and sections from Griffiths and Feynman, indicating that interpretations may depend on the edition of the texts. The discussion highlights the complexities of applying Gauss' Law in dynamic situations, particularly regarding the symmetry and behavior of electric fields.

Who May Find This Useful

This discussion may be of interest to students and professionals in electromagnetism, particularly those exploring the nuances of Gauss' Law in both static and dynamic contexts, as well as its implications in theoretical and applied physics.

  • #31
The issue is that textbooks (e.g. Griffiths: Introduction to electrodynamics) say that divergence of magnetization at the end of a magnet is infinite.
 
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  • #32
htg said:
The issue is that textbooks (e.g. Griffiths: Introduction to electrodynamics) say that divergence of magnetization at the end of a magnet is infinite.

Where in Griffiths does it say this?
 
  • #33
Third edition, page 276:

Griffiths said:
since M and H are [in linear media] proportional to B, does it not follow that their divergence, like B's must always vanish? Unfortunately, it does not: at the boundary between two materials of different permeability the divergence of M can actually be infinite. For instance, at the end of a cylinder of linear paramagnetic material, M is zero on one side but not on the other.

\nabla \cdot \vec M and \nabla \cdot \vec H being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.
 
  • #34
jtbell said:
Third edition, page 276:



\nabla \cdot \vec M and \nabla \cdot \vec H being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.

Yeah, the dirac delta that results in the divergence due to an discountinuous boundary condiion. But that is still ok for the reasons that you, jtbell, specified earlier. Gauss' Law makes constraints on the B field, not the H and M so the fact that these quantities are not always divergence free is not in contradiction with the law.
 
  • #35
At the end of section 6.4.1 (susceptibility and permeability) - at least in my Polish translation.
 
  • #36
jtbell said:
Third edition, page 276:



\nabla \cdot \vec M and \nabla \cdot \vec H being infinite simply reflects the idealization of the boundary as being perfectly "sharp," with M and H changing "instantaneously" as you cross the boundary.

It does not make much sense to pretend that we think matter is continuous, especially because here it leads to completely false conclusions.
 
  • #37
Gauss's law is verified experimentally for static charges, how is it verified for dynamic charges ?
 

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