Friday, July 11, 2014

condensed matter - Ohm's Law: Drude Model


For a very long time now, I've been thinking about the Drude Model derivation of Ohm's Law. I know that a rigorous derivation requires a Quantum Mechanical approach. However, the mere fact that the Drude Model churns out the right equation seems to suggest to me that it is at least partially sound from a qualitative viewpoint. A particular assumption strikes me. Electrons are assumed to collide with protons. However, a direct collision doesn't seem possible to me (the kind you think of when you typically think of collisions). And in these electron-proton collisions, the momentum of electrons is assumed to be reset, and protons are assumed to be fixed. The only way I can think of this is that certain electrostatic interactions take place that cause protons to gain all the momentum, and electrons lose it all (for conservation of momentum to hold). And in such a scenario, protons will move very slowly, thus having a negligible effect. Over time, as the momentum on proton builds up, the rate of collisions, and increases. This seems to explain the temperature-resistance relationship at least qualitatively. However, something else that strikes me is how energy is released during the "collisions". I've heard that accelerating charges produce EM waves, and therefore find reason to believe that this is how energy is released.


This also makes Kirchhoff's Loop Rule appear reasonable. I could not accept it at first because it seemed to suggest that a non-conservative "collision" force opposed the work done by the electric force, and I could not think of what would cause such a force at the microscopic level. But, if EM waves are released, this alternate picture of energy loss seems much more reasonable; the work done by the electric force is released as heat. I guess this is "friction" on the macroscopic scale.


I just want to know, does this mechanism seem reasonable, and can I accept it till such time I learn Quantum Mechanics, and learn the true story? Or is the Drude Model simply too flawed to accept?


Also, I want to know if momentum is actually transferred to the proton.




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