Force between two charges in closed universe

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Discussion Overview

The discussion revolves around the behavior of the force between two charges situated in a closed spherical universe. Participants explore how the force might change as the charges move apart, particularly considering the implications of a finite universe on the traditional inverse square law of electrostatics.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant suggests that if two charges are close together (r << R), the force could be approximated as 1/r^2, but questions how to modify this force as the charges move apart.
  • Another participant argues that the force between the charges will never be zero because the electric field extends infinitely, challenging the assumption that the force could vanish at maximum separation.
  • A different viewpoint proposes a modified force equation, (2R-r)/2Rr^2, which behaves like 1/r^2 for small r and approaches zero when the charges are on opposite sides of the universe.
  • One participant elaborates on the symmetry of the situation, suggesting that if the charges are placed at the poles of a sphere, the electric field may approach zero at those poles, implying a similar behavior in a higher-dimensional sphere.

Areas of Agreement / Disagreement

Participants express differing views on whether the force can ever be zero and how the force should be modified in a closed universe. There is no consensus on the correct approach or model to describe the force between the charges.

Contextual Notes

Participants do not fully agree on the implications of the electric field's behavior in a closed universe, and there are unresolved assumptions regarding the nature of forces in such a context.

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

Spinnor said:
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"
 
Tominator said:
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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