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In this lecture, Professor Shankar Ramamurthi says that the superposition principle for force vectors of Coulomb's Law is experimentally observed and is not a product of logical analysis. In fact, the principle fails to hold at Quantum level and is nothing but an excellent approximation of the actual forces acting on a test charge. That is to say, the vector sum of individual Coulombic Forces on a test charge is not exactly equal to the total force acting on it. When and why does it fail? I suspect it has to do with some non-linear equation that defines the interaction between charges at minuscule level. But then, why would we call it Coulomb's Law in the first place at Quantum level?

Kraken
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    https://physics.stackexchange.com/questions/142159/deriving-the-coulomb-force-equation-from-the-idea-of-photon-exchange This answers your question essentially.. I know that it sounds you’re at an intro level, but the only way I know how to explain it is with Feynman diagrams.. I can try to give a lay-explanation if you’d like.. just let me know – InertialObserver Dec 22 '18 at 07:27
  • @inertialObserver The answer of Willy W for this here question makes some sense to me. Would that account for an explanation in layman terms? – Kraken Dec 22 '18 at 08:10
  • @InertialObserver Also, I learnt a little about Feynman Diagrams and how all the simple and not-so-simple possibilities in a QED interaction affect the final result. I am now acquainted with the idea of photon (virtual and otherwise) as a force carrier for EM field. If that's enough background, please go with the Feynman Diagram explanation. – Kraken Dec 22 '18 at 08:17
  • Take it and keep it simple. Coulomb law works for a rather macroscopic system. A Proton and an electron behave according to it til they eventually form a hydrogen atom. Indeed to explain a H atom and atomic scale phenomena a new physics, quantum mechanics, had to emerge. While there is a coulombic interaction at minuscule level it does not mean that Coulomb law holds alone or as it is. – Alchimista Dec 22 '18 at 09:36
  • @Alchimista I am not talking about the limitations of Coulomb's Law. I am talking about the limitations of superposition principle regarding the Coulomb's Law; i.e., why the vector sum of Coulombic forces is only an excellent approximation to actual (static electric) forces acting on a test charge. At least, that is what Prof. Shankar say. – Kraken Dec 22 '18 at 13:27
  • Can you give the point in time in the lecture where this statement is made? The lecture takes over one hour. – my2cts Dec 22 '18 at 13:29
  • Ok. I misunderstood. To me superposition (I think is sum of vectors) always holds. Are the laws giving the individual vectors that do not. I still see this as a limitation of the law bur perhaps it is semantic. My comment it is unchanged but likely I misunderstood what you ask for. It is an approximation because the components are. But for a microscopically static point charges distribution Coulomb law should holds, and as such holds the "superposition". I apologise if wrong but it would be a catastrophe for me unless motion is at play. – Alchimista Dec 22 '18 at 15:49
  • And unless you cannot longer consider the charges as point-like. It might be he spoke about a real case so we are back to quantum realm. .. – Alchimista Dec 22 '18 at 15:56
  • You have to realize that in physics "laws" are axioms needed to build a mathematical model, in this case classical electromagnetism. Laws are a distillate of measurements and observations and are not to be questioned , in the way that mathematics axioms are not questioned. Different frameworks ( classical, quantum, thermodynamics etc) have different "laws" " postulates" 'principles" but in overlap regions the transition is mathematically smooth, though complicated. – anna v Dec 22 '18 at 18:49
  • Errata corrige: in my last comment microscopically reads mAcroscopically. Keyboard :( – Alchimista Dec 23 '18 at 08:38

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