Divergence of electric field and charge density

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Discussion Overview

The discussion centers on the concept of divergence in relation to electric fields and charge density. Participants explore the mathematical definition of divergence, its physical interpretation, and its implications in the context of electric fields generated by point charges.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the divergence of the electric field at a point is proportional to the charge density at that point.
  • Others argue that divergence is defined as a specific combination of partial derivatives, and that it is zero except at the location of a point charge, where it becomes singular.
  • One participant challenges the notion that divergence relates to the rate of change with distance, suggesting it is more about the relationship between total flux coming out of a volume versus flux going into it.
  • Another participant proposes that divergence can be viewed as a microscopic version of Gauss's Law, relating the field diverging from a differential volume to the charge density within that volume.
  • There is a disagreement regarding the interpretation of divergence, with some emphasizing the outward aspect of field strength changes and others contesting this view.

Areas of Agreement / Disagreement

Participants express differing interpretations of divergence, with no consensus reached on its definition or its relationship to charge density and electric fields. Multiple competing views remain present in the discussion.

Contextual Notes

Participants highlight potential ambiguities in the definitions and interpretations of divergence, particularly regarding its dependence on distance and the nature of electric fields from point charges.

vin300
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The divergence of electric field at a point is proportional to the charge density at the point. Divergence is the rate of change with distance, the rate of change of electric field due to a distant charge is not zero, so how can it be said that the divergence at a point depends only on the charge density there?
 
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vin300 said:
Divergence is the rate of change with distance

No, the divergence is a particular combination of partial derivatives. You should compute the divergence of the electric field of a point charge yourself. You'll find that it is zero except at the position of the charge, where it is singular.
 
Divergence is not about the rate of change with distance.
 
vin300 said:
The divergence of electric field at a point is proportional to the charge density at the point. Divergence is the rate of change with distance, the rate of change of electric field due to a distant charge is not zero, so how can it be said that the divergence at a point depends only on the charge density there?

The_Duck said:
No, the divergence is a particular combination of partial derivatives. You should compute the divergence of the electric field of a point charge yourself. You'll find that it is zero except at the position of the charge, where it is singular.

Leland said:
Divergence is not about the rate of change with distance.

i don't know if i agree with you guys (Duck and Leland). divergence is about rate of change with distance. it is about how rapidly the field strength changes with distance outward from the point where the charge density is.

divergence is essentially a microscopic version of Gauss's Law. and Gauss's Law works only for inverse-square fields and it gives you the amount of charge contained in the volume surrounded by a closed surface. then squeeze that volume and closed surface down to a teeny-little differential volume. then the field diverging out of that differential volume is equal to the teeny charge contained inside which is the charge density times the teeny differential volume.
 
rbj, I agree with your definition, but the way I interpret it your definition is quite different from 'rate of change with distance'. The word 'outward' is the key.
 
Isn't divergence defined as the difference between total flux (or field strength) coming out of a volume versus flux (or field strength) going into it? (a source-sink relationship)
 
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