What is the force between two point charges when they are touching?

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Discussion Overview

The discussion revolves around the nature of the force between two point charges when they are in close proximity, specifically when they are considered to be touching. Participants explore the implications of the inverse square law in this context, the concept of point charges, and the behavior of forces at very small distances, including quantum considerations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • One participant notes that the force between two point charges approaches an undefined state as the distance between them approaches zero, questioning whether the force would be zero or undefined.
  • Another participant argues that point charges are theoretical constructs, suggesting that two charged objects cannot occupy the same space, even if they are touching.
  • It is proposed that as point charges are brought closer together, the electrostatic force increases indefinitely, implying that they cannot actually occupy the same point without requiring infinite force.
  • A participant mentions that the inverse square law is derived from Gauss' law and that different formulas may apply at or inside the surface of charged objects.
  • Questions arise regarding whether the force remains finite at small distances, particularly on the scale of atomic particles.
  • One participant asserts that in classical physics, the electrostatic field diverges to infinity at a point charge, while quantum physics introduces complexities that mitigate this divergence.
  • There is a discussion about the nature of vacuum in quantum physics and its implications for charge interactions, along with a query about the relative strengths of forces and charges in atomic structures.
  • A participant seeks clarification on the force between a proton and an electron at the average distance in a hydrogen atom, indicating a desire for more specific numerical insight.

Areas of Agreement / Disagreement

Participants express differing views on the implications of point charges and the behavior of forces at very small distances. There is no consensus on whether the force becomes undefined or infinite when charges are considered to be touching, and the discussion remains unresolved regarding the nature of forces in quantum contexts.

Contextual Notes

Participants highlight limitations in understanding the behavior of forces at zero distance and the implications of quantum mechanics, indicating that assumptions about point charges and their interactions may not fully capture the complexities involved.

joeyjo100
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We all know the equations for inverse square laws, such as force between two masses or between two charged particles. We were told the force is inversely propotional to the distance between the masses or charges, squared.

But what would the force equal if the distance between, say two point charges, was zero ie they are touching. Common sense says there would be no force, as neither will move, but this situation would mean that the force would equal the product of the two charges divided by zero squared. As far as my limited maths knowledge stretches, dividing by zero leads to an undefined number.

What does this then say about the force? Would it eqaul zero as you might expect? Or would it be undefined?
 
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Point charges are imaginary. Two charged objects with real mass cannot occupy the same space, although they could be "touching" each other, with a finite distance between their center of mass and charge.
 
As the two charges are brought closer together, the electrostatic force between them becomes larger and larger. For hypothetical, classical point charges, it would be impossible to exert enough force to actually make them occupy the same point -- the required force would be infinite.
 
The inverse square law is a product of using Gauss' law in a 3-dimensional space. At/inside the surface of the object of mass or charge a new formula has to be derived. For spherically symmetric objects of ~uniform density (such as an ideal planet for example) the new field equation becomes linear.
 
Does this keep the force from becoming infinite at small distances? On the scale of atomic particles i mean.
 
No, because elementary charge carriers are still point-particles as far as we can tell. In pure classical physics, electrostatic field diverges to infinity at point charge, and that's just the way it is. In quantum physics, fact that vacuum is not just empty space mostly takes care of that.
 
K^2 said:
No, because elementary charge carriers are still point-particles as far as we can tell. In pure classical physics, electrostatic field diverges to infinity at point charge, and that's just the way it is. In quantum physics, fact that vacuum is not just empty space mostly takes care of that.

What do you mean by the vacuum not being empy space?

Also, if you compare the strength of the attraction of an electron orbiting a proton, the hydrogen atom, is that attraction more or less than the two absolute electric charges of the proton and the electron? I guess I'm asking at what distance from a particle is their charge measured as it is?
 
Drakkith said:
Does this keep the force from becoming infinite at small distances? On the scale of atomic particles i mean.
At a small but nonzero distance, the force is not infinite; just a lot larger than it is at larger distances.

As for the distance equaling zero, the uncertainty principle forbids two charges from having exactly the same location.

Drakkith said:
Also, if you compare the strength of the attraction of an electron orbiting a proton, the hydrogen atom, is that attraction more or less than the two absolute electric charges of the proton and the electron?
This question does not make a whole lot of sense. You can't ask if a force is greater than or less than a charge -- that's like asking if an inch is smaller than an ounce.

The charges on the proton and the electron are always the same value, if that helps.
I guess I'm asking at what distance from a particle is their charge measured as it is?
I don't understand.
 
Last edited:
Alright, let me put it a better way. Given the electric charge of the proton and electron, what is the force between the two at a distance equal to the average distance of an electron around a proton in a Hydrogen atom?
 

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