Point charge configuration with zero potential energy

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SUMMARY

The discussion centers on the feasibility of constructing a system of a finite number of point charges with arbitrary magnitudes positioned at finite distances from each other, resulting in zero potential energy everywhere. The integral for potential energy, W = ∫(1/2)εE²dv, indicates that a zero total energy implies a zero electric field, which contradicts Gauss's law. However, participants conclude that it is indeed possible to arrange point charges to achieve zero mechanical energy, despite the complexities involved with electric fields and potential energy calculations.

PREREQUISITES
  • Understanding of point charge configurations in electrostatics
  • Familiarity with Gauss's law and its implications
  • Knowledge of potential energy calculations in electric fields
  • Basic grasp of electric field concepts and their mathematical representations
NEXT STEPS
  • Research the implications of Earnshaw's theorem on point charge stability
  • Explore the mathematical derivation of potential energy for discrete charge distributions
  • Study the conditions under which electric fields can be manipulated to achieve zero potential energy
  • Investigate alternative configurations of charge distributions that yield unique energy states
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Physicists, electrical engineers, and students studying electrostatics who are interested in advanced concepts of electric fields and potential energy in charge systems.

bigerst
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is it possible to construct a system with only finite number of point charges of arbitrary magnitude at finite distance from each other such that the total potential energy is zero everywhere?
i doubt earnshaw's theorem would prohibit this construction, hence is it possible?
thanks
 
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bigerst said:
is it possible to construct a system with only finite number of point charges of arbitrary magnitude at finite distance from each other such that the total potential energy is zero everywhere?

If by potential energy , you mean the following integral:

[itex]W=\int{\frac{1}{2}\epsilon E^{2}dv}[/itex],

then zero total energy means zero electric field everywhere . Zero field around a point charge means zero net flux and this contradicts Gauss law.
 
thanks for the reply.
i think that integral only apply to continuous charge distributions? doesn't it predict the energy of a point charge is infinite.
on another note i think i got the answer, apparently it is possible to assemble point charges such that they have no mechanical energy

bigerst
 

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