Electric Field: Does a Circular Set of Charges Appear as One?

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Discussion Overview

The discussion revolves around whether a perfectly circular set of point charges or dipoles would appear as a single point charge when observing the electric field. The inquiry is based on visual representations and theoretical implications of charge distributions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions if a circular set of point charges would be perceived as a single point charge in the electric field, referencing an illustration that suggests this possibility.
  • Another participant asserts that from a sufficient distance, a charge distribution can be treated as a point source.
  • A further contribution states that any charge distribution with spherical symmetry will produce an electric field equivalent to that of a point charge located at the center, with the charge value equal to the total charge within a sphere of radius "r".
  • This last point is linked to the Gauss divergence theorem, although the implications of this theorem are not fully explored in the discussion.

Areas of Agreement / Disagreement

Participants express varying degrees of agreement on the idea that a circular charge distribution can resemble a point charge under certain conditions, but the discussion does not reach a consensus on the specifics or implications of this observation.

Contextual Notes

The discussion does not clarify the assumptions regarding the distance from the charge distribution or the conditions under which the electric field is observed. There is also no resolution on the applicability of the Gauss divergence theorem to the specific cases discussed.

rockyshephear
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Would a perfectly circular set of point charges appear to be one point charge if you could see the electric field?
Same question with perfectly circular set of dipoles.
My question is posed because I saw an illustration

http://images.google.com/imgres?img...ric+Field&hl=en&rlz=1G1GGLQ_ENUS337&sa=X&um=1

that seems to indicate that a collection of charges can show as one point charge.
 
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This is a physics question, not a math question.

If you are far back enough, then it is like a point source.
 
I posted in the physics section.
 
rockyshephear said:
Would a perfectly circular set of point charges appear to be one point charge if you could see the electric field?

Any system with a charge distribution that has spherical symmetry will have the same electric field at any given radius "r" as you would get from a simple system containing just one point charge (at the center), where the value of this point charge is equal to the sum of all the charge which lay within a sphere of radius "r" in the original system.

BTW. This is a direct consequence of the Gauss divergence theorem. http://en.wikipedia.org/wiki/Divergence_theorem
 

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