Stability of electrical charges

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SUMMARY

The discussion centers on Earnshaw's Theorem, which asserts that point charges cannot achieve stable stationary equilibrium in classical electromagnetism. Participants highlight that while negative electric potential energy suggests work is needed to separate charges, this does not imply stability. Instead, they propose that charges may oscillate, leading to a stable dynamic equilibrium. Furthermore, it is emphasized that crystals require quantum mechanics for accurate descriptions of atomic bonding, distinguishing them from classical systems.

PREREQUISITES
  • Understanding of Earnshaw's Theorem in classical electromagnetism
  • Basic knowledge of electric potential energy concepts
  • Familiarity with quantum mechanics principles
  • Comprehension of atomic bonding in crystalline structures
NEXT STEPS
  • Research the implications of Earnshaw's Theorem in practical applications
  • Explore the role of quantum mechanics in explaining crystal stability
  • Study the dynamics of oscillating charges in electromagnetic fields
  • Investigate the relationship between electric potential energy and charge separation
USEFUL FOR

Physicists, electrical engineers, and students of electromagnetism and quantum mechanics seeking to deepen their understanding of charge stability and crystal structures.

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I've just learned by chance about http://en.wikipedia.org/wiki/Earnshaw_theorem which states that point charges cannot be maintained in a stable stationary equilibrium.

But then, what does the negative electric potential energy (in this thread : https://www.physicsforums.com/showthread.php?t=334341) mean?
So the crystal wouldn't be stable, but I would need to do some work in order to separate the charges from each other. The only remaining explanation to me is that the charges must oscillate, so there would be a stable dynamic equilibrium. Am I right?
 
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Earnshaw's Theorem applies to classical electromagnetism. Crystals are not classical systems... you need quantum mechanics to describe them fully, in particular the bonding between atoms.
 
jtbell said:
Earnshaw's Theorem applies to classical electromagnetism. Crystals are not classical systems... you need quantum mechanics to describe them fully, in particular the bonding between atoms.

Thanks a lot. :smile:
 

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