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?
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