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

  • Context: Graduate 
  • Thread starter Thread starter chientewu
  • Start date Start date
  • Tags Tags
    Coulomb's law Law
Click For Summary
SUMMARY

The discussion focuses on the implications of applying Coulomb's Law to a point within a uniformly charged sphere, specifically addressing the electric field at that point. The contributor raises concerns about the contribution from a source point located at the field point, noting that the distance becomes zero, which could imply an infinite contribution. However, the contributor acknowledges that while the charge is infinitesimal, the mathematical treatment of this scenario lacks rigorous proof to confirm that the contribution is zero. The conversation suggests that for a more accurate understanding of interactions at extremely small distances, one should refer to Quantum Electrodynamics (QED) and Maxwell's Equations.

PREREQUISITES
  • Coulomb's Law and its applications
  • Understanding of electric fields and charge distributions
  • Familiarity with Maxwell's Equations
  • Basic principles of Quantum Electrodynamics (QED)
NEXT STEPS
  • Study the derivation of Coulomb's Law from Maxwell's Equations
  • Explore the concept of electric fields within uniformly charged spheres
  • Research Quantum Electrodynamics (QED) and its implications for charged particle interactions
  • Investigate mathematical treatments of infinitesimal contributions in electrostatics
USEFUL FOR

Students of physics, electrical engineers, and researchers interested in electrostatics and the foundational principles of electromagnetic theory.

chientewu
Messages
7
Reaction score
0
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?
 
Physics news on Phys.org
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).
 

Similar threads

Undergrad Electric field of ring at any point
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Conditions for applying Gauss' Law
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Electrostatic force exerted on an electron inside a nucleus
  • · Replies 19 ·
Replies
19
Views
2K
High School Electric Fields inside Conductors & Gauss' Law
  • · Replies 7 ·
Replies
7
Views
1K
Undergrad Griffith, Electrodynamics, 4th Edition, Example 4.8. (First part)
  • · Replies 6 ·
Replies
6
Views
1K
Undergrad Apparent disagreement between Coulomb's Law and Gauss' Law
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Exploring the Electric Field of a Moving Charged Spherical Shell
  • · Replies 14 ·
Replies
14
Views
3K
Undergrad Using Ampere's Law for these two different integration paths
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad E-field from uniformly distributed charges on sphere?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Applying Lorentz Force correctly
  • · Replies 1 ·
Replies
1
Views
1K