What is the impact of a source point just at the field point in Coulomb's Law?

[chientewu]

Hi there,

I have a question about Coulomb's Law. Assume there is a uniform sphere charge distribution RHO and I want to know the electric field at some point inside the sphere. I can simply apply Coulomb's Law to find it. However, I worry about the contribution from source point that is "just" at the field point. Based on Coulomb's Law, the distance between the source point and field point now is zero and the contribution might become infinity. Although the charge there is infinitesimal, the contribution from it is still unspecified. After all, no rigorous mathematical proof says that the contribution is zero. Can anyone give me an explanation about this point?

 

[jacksonwalter]

Coulomb's Law is an approximation and can be derived from the more general, yet still classical, Maxwell's Equations, which will probably be better to deal with this. To really answer a question about interactions between charged particles at extremely small distances you'd need to use QED (Quantum Electrodynamics).