Force between two charges in closed universe

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Spinnor

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Say we have two charges in a closed spherical universe, of radius R, a distance r apart. If the charges are close, r<<R, we might guess that the force would go as 1/r^2?

Let the two charges move away from each other till they are as far apart as possible. At this point the force between charges is zero?

How might we modify the 1/r^2 force to fit the above criteria?

Thank you for any help.
 
I do not know, if I understood your question well, correct me if I got it wrong.

Let the two charges move away from each other till they are as far apart as possible. At this point the force between charges is zero?
The force will not ever be zero, because electric field extends to infinity.
 
Are you inventing a toy universe? Then you can make the force behave any way you want. why not something like (2R-r)/2Rr^2, which behaves like 1/r^2 for small r, and vanishes when the particles are on the opposite sides of the "universe"
 

Spinnor

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I do not know, if I understood your question well, correct me if I got it wrong.



The force will not ever be zero, because electric field extends to infinity.
Imagine the two charges on the surface of a sphere, S^2, located at each pole. Because of the symmetry the field will go to zero at the poles. I think the same will occur in S^3.
 

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