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

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    Gauss Gauss' law Law
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SUMMARY

Gauss' Law, a fundamental principle of electromagnetism, is confirmed to hold for all source charge motions and various flux integration surfaces, including spheres, ellipsoids, and non-standard shapes like eggs. Despite traditional texts like Feynman and Griffiths stating its applicability is limited to electrostatics, the discussion reveals that Gauss' Law remains valid in dynamic scenarios, provided it is used alongside other Maxwell's equations. The participants agree that while the electric field from a moving charge does not conform to the 1/r² dependency, Gauss' Law itself is not violated. The consensus is that Gauss' Law is universally applicable in classical electrodynamics.

PREREQUISITES
  • Understanding of Maxwell's Equations
  • Familiarity with Gauss' Law and its implications
  • Knowledge of electric fields from point charges
  • Basic concepts of electrostatics and electrodynamics
NEXT STEPS
  • Study the implications of Gauss' Law in dynamic systems using "Introduction to Electrodynamics" by David J. Griffiths
  • Explore the relationship between electric fields and charge motion in "The Feynman Lectures on Physics" Vol. II
  • Investigate the application of Maxwell's Equations in non-static scenarios
  • Examine the divergence of electric and magnetic fields in various electromagnetic wave contexts
USEFUL FOR

Physicists, electrical engineers, and students of electromagnetism seeking to deepen their understanding of Gauss' Law and its applications in both static and dynamic electric fields.

  • #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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