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).

 

[astrokreng]

Hello,

Thank you for your question about Coulomb's Law and the impact of a source point just at the field point. This is a valid concern and one that has been studied and addressed by scientists. The concept of a point charge, which is used in Coulomb's Law, is an idealization and does not exist in reality. In reality, all charges have a finite size and distribution. Therefore, the distance between the source point and the field point is never truly zero.

In cases where the source point and field point are very close together, the contribution from the source point can become very large. However, as the distance between the two points approaches zero, the electric field becomes increasingly complex and unpredictable. This is because at such small distances, the assumptions made in Coulomb's Law (such as point charges and infinite distances) are no longer valid.

To address this issue, scientists have developed more sophisticated models and equations to calculate the electric field at very close distances. These models take into account the finite size and distribution of charges and provide more accurate results. Additionally, experimental measurements can also be used to validate the predictions of Coulomb's Law in these extreme cases.

In summary, while Coulomb's Law is a useful tool for understanding and predicting electric fields, it is important to keep in mind its limitations and seek more advanced models when dealing with extreme cases such as a source point just at the field point. I hope this helps to clarify the impact of a source point in Coulomb's Law.