What is the electric field of a point charge?

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Discussion Overview

The discussion revolves around the electric field of a point charge, specifically addressing whether the electric field at the origin, where the charge is located, is zero or undefined. The scope includes theoretical considerations and conceptual clarifications regarding point charges and electric fields.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the electric field at the origin of a point charge is undefined.
  • Others question why the electric field cannot simply be assigned a value of zero, arguing that a charge cannot exert force on itself.
  • One participant introduces the concept of size, suggesting that a zero electric field would imply a constant potential over a region, which leads to contradictions in the context of point charges.
  • Another participant points out that while the electric field is zero at the center of a spherical charge distribution, this does not apply to point charges.
  • There is a reference to Gauss's theorem, with some participants arguing that it does not hold when considering a point charge within zero volume.

Areas of Agreement / Disagreement

Participants generally disagree on whether the electric field at the origin of a point charge is zero or undefined, with multiple competing views presented throughout the discussion.

Contextual Notes

Participants express uncertainty regarding the implications of defining the electric field at a point charge, particularly concerning the concepts of size and volume in relation to electric fields and potentials.

Amin2014
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Assuming the point charge lies at the origin, what is the electric field at the origin? Zero or undefined?
 
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undefined
 
BvU said:
undefined
I checked some books and you are right. However, I don't understand why we can't we just assign it a value of zero? After all, the charge cannot apply force on itself.
 
There is the issue of size. Equal to zero for a point. Zero E would mean constant potential over some region with size. Contradiction !
Amin2014 said:
After all, the charge cannot apply force on itself
No, but it can apply force on a test charge, however close it comes...
No place where that force suddenly drops from near infinity to zero.
 
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BvU said:
There is the issue of size. Equal to zero for a point. Zero E would mean constant potential over some region with size. Contradiction !

Ok I see. The field is zero at the center of a spherical charge distribution, no matter the size of sphere. So if our charge had dimensions (unlike a point charge), then the field would be zero at the origin.
 
Same difference: you refer to Gauss theorem: some charge density times zero volume. Doesn't fly when charge is within zero volume.
 
BvU said:
Same difference: you refer to Gauss theorem: some charge density times zero volume. Doesn't fly when charge is within zero volume.
I was validating your answer and completing it. The field would be zero only if the charge has dimensions.
 

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