Let's speak in the classical context (non quantum). We assume that point charges move in a conductor following Newtonian mechanics. How do point charges move along the boundary of the conductor and how do they stop (equilibrium) in the end?
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1$\begingroup$ What end? In the classical model the free electrons do not stop. They are in thermal equilibrium with the atoms. $\endgroup$– R.W. BirdJul 3, 2021 at 15:27
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$\begingroup$ OK. What about ignoring thermal motion, then will free electrons ever stop? $\endgroup$– feynmanJul 5, 2021 at 8:17
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1$\begingroup$ Feynman, In a non-driven conductor, the free electron configuration will be stable when the resultant field within the conductor is zero. In a driven conductor, electrons are continuously added (and removed) and the resultant field causes the free electrons to experience a continuous “drift”. $\endgroup$– R.W. BirdJul 5, 2021 at 14:19
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$\begingroup$ What's a driven conductor and non driven conductor? $\endgroup$– feynmanJul 6, 2021 at 4:25
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$\begingroup$ A driven conductor is connected to a source of voltage. $\endgroup$– R.W. BirdJul 6, 2021 at 13:18
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1 Answer
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There is a potential barrier at the boundary (surface) of a conductor, knowing as the work function. Work function is defined as the energy requied to remove an electron from inside the metal to the vacuum.
The typical number of work function for metal is about $4 eV$ ($3-5 eV$) which forms a barrier for electron to escaping the metal (due to effects of electron-ion attraction and the electron-electron exchange). The surface reigion is about $10 \dot A$, forming an electric field of intensity $10^7 volts/cm$ at the boundary of a metal to prevent the electron from escaping.
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$\begingroup$ Thanks a lot for the answer. We know about work function. The question is about how they move on the boundary rather than how they can be kept inside the conductor nor about work function $\endgroup$– feynmanJul 5, 2021 at 8:19
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$\begingroup$ That depends on how you define the boundary, microscopically. And What is the driving force? $\endgroup$– ytluJul 5, 2021 at 16:22
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$\begingroup$ The boundary is just the boundary of the conductor. The driving force is driven by the electrostatic field due to the charges $\endgroup$– feynmanJul 6, 2021 at 4:26