If r=0 then will the electric charge of two points=infinity?

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Discussion Overview

The discussion revolves around the implications of electric charge and electric fields when the distance between two point charges approaches zero. Participants explore the mathematical behavior of electric fields and forces at this limit, questioning the validity of certain formulas and the concept of infinite charge.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant suggests that if two negative charges are placed infinitely close together, the electric field would be infinite, leading to the question of whether the charge would also be -infinity.
  • Another participant argues that the formula for electric force, ##F=Cq_1q_2/r^2##, does not apply at ##r=0##, indicating that this scenario is outside the valid range of the formula.
  • A participant points out the formula for electric field, ##E=k*Q/d^2##, and discusses its relationship to the force equation, suggesting that both equations describe the same physical phenomena when properly identified.
  • One participant emphasizes that while ##1/r## approaches infinity as ##r## approaches zero, it does not mean that one can reach a definitive value of +infinity in arithmetic terms.

Areas of Agreement / Disagreement

Participants express differing views on the implications of electric fields at ##r=0##, with some questioning the application of established formulas and others clarifying the mathematical behavior of these expressions. No consensus is reached regarding the nature of charge at this limit.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the applicability of formulas at ##r=0## and the undefined nature of certain mathematical expressions. The discussion does not resolve these issues.

Hami Hashmi
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I found that the electric field at r=0 equals infinity. What if two negative charges were put infinitely close together so the electric field was infinite, then would the charge of those two points be -infinity as well?
 
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The infinity that you found is telling you that the ##F=Cq_1q_2/r^2## formula doesn't apply and shouldn't be used when ##r=0##. It works anywhere outside of a charged sphere (a very large number of interesting and problems, which is why we use it), but ##r## is never zero if you are outside the charged sphere.
 
Hami Hashmi said:
I thought the formula for an electric field E=k*Q/d^2 (where k=constant, Q=source charge, and d=distance between the centers of the two objects)?
http://www.physicsclassroom.com/class/estatics/Lesson-4/Electric-Field-Intensity
That is the equation for the field. I gave the equation for the force, which is the product of the field and the charge the field is acting on. So replace the ##C## in my formula with ##k## - it's Coulomb's constant either way - and identify ##Q_1## as the source charge and the two equations are saying the same thing.
 
Hami Hashmi said:
I found that the electric field at r=0 equals infinity. What if two negative charges were put infinitely close together so the electric field was infinite, then would the charge of those two points be -infinity as well?
##\frac10 \ne +\infty##

##\frac10## is undefined.

What you can say is that:

As ##r \rightarrow 0, \ \frac1r \rightarrow +\infty##

What this means that as ##r## gets smaller, ##1/r## increases without bound. But, at no time do you arithmetically arrive at ##+\infty##.
 

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