Stability of electrical charges

AI Thread Summary
Earnshaw's Theorem indicates that point charges cannot achieve stable stationary equilibrium, leading to questions about the implications for negative electric potential energy. The discussion suggests that while individual charges in a crystal may not be stable, work is required to separate them, hinting at the possibility of oscillation and dynamic equilibrium. It is emphasized that crystals are not purely classical systems, necessitating a quantum mechanical approach to fully understand atomic bonding. The conversation highlights the limitations of classical electromagnetism in explaining the stability of charges within crystalline structures. Overall, the interplay between classical and quantum mechanics is crucial for understanding charge stability in crystals.
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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:
 
Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

Thread 'Motional EMF in Faraday disc, co-rotating magnet axial mean flux'

So here is the motional EMF formula. Now I understand the standard Faraday paradox that an axis symmetric field source (like a speaker motor ring magnet) has a magnetic field that is frame invariant under rotation around axis of symmetry. The field is static whether you rotate the magnet or not. So far so good. What puzzles me is this , there is a term average magnetic flux or "azimuthal mean" , this term describes the average magnetic field through the area swept by the rotating Faraday...
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