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

[rockyshephear]

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.

 

[HallsofIvy]

This is a physics question, not a math question.

If you are far back enough, then it is like a point source.

 

[rockyshephear]

I posted in the physics section.

 

[uart]

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