Electrons in Metal: Explaining Free Electron Theory

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In metals, according to free electron theory, electrons experience a constant potential throughout. The nuclei generate a 1/r type field that is periodic due to the arrangement of atoms in the metal. However, not all electrons perceive this periodic potential because some of it is screened by other electrons. While qualitative analyses can utilize a sinusoidal potential, achieving quantitative results necessitates more precise potential models. Understanding these dynamics is crucial for a comprehensive grasp of electron behavior in metals.
ranju
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I just wanted to clear one thing... in metals what type of potential the electrons are subjected to..??
Is it constant , sinusoidal , square or non-periodic..?? pleasez explain a bit in accordance with free electron theory.>!
 
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In a metal, it's constant throughout the metal for the free electron theory.

See http://www.teknik.uu.se/ftf/education/ftf1/forelasningar/overview/Freelectronmodel.pdf
 
It's complicated. The nuclei produce their 1/r type fields, and since they a periodic in a metal, the net field is periodic. Now not all the the electrons necessarily see this periodic 1/r type potential, b/c part of the potential is being screened by electrons. You can get qualitative results by using a sinusoidal potential, but quantitative results require more accurate potentials.
 
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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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