E-field & hollow non-conducting sphere

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    E-field Sphere
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Discussion Overview

The discussion revolves around the electric field (E-field) inside a hollow non-conducting sphere that is uniformly charged. Participants explore the implications of Gauss' Law in determining the E-field both inside the material of the sphere and within a small hole made in it.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the E-field inside a hollow non-conducting sphere when a small hole is made through the material.
  • Another participant asserts that if the charge is uniformly distributed on the surface, the E-field inside the sphere would be zero according to Gauss' Law.
  • A question is raised about the E-field inside the hole, particularly when it is partially outside and partially inside the sphere.
  • One participant proposes that inside the hole, the E-field at radius R is one half Q/R^2, suggesting a gradient in the E-field as one moves through the hole.
  • It is noted that at the surface of the sphere, the E-field is given by E = Q/(4R^2 pi * epsilon_0), but inside the sphere, it is zero, leading to a discussion on the application of Gauss' Law in this context.
  • Another participant comments that this behavior is consistent at any point on the surface, not just at the hole.
  • A later reply expresses appreciation for the insights shared in the discussion.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of the E-field inside the hole and the sphere, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

There are assumptions regarding the uniformity of the surface charge and the specific geometry of the hole that may affect the conclusions drawn about the E-field.

Who May Find This Useful

Readers interested in electrostatics, particularly those studying the implications of Gauss' Law in non-conducting materials and electric fields in geometrically complex situations.

CsLevi
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I know that the E-field around a hollow non-conducting sphere charged with Q charge comes immediately from Gauss' Law but I'm wondering what the situation is if we somehow go inside the material, we make a very small hole through the material of the sphere and go inside it. What would there be the E-field?
 
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If the charge is a uniform surface charge, then the field inside would be zero by Gauss's law.
 
Even inside the hole when being half outside, half inside the sphere?
 
Inside the hole, at radius R, the E field is one half Q/R^2.
The E field goes from Q^2/R to zero as r decreases through the hole.
The decrease in E takes place in a distance of the order of \Delta r=d, where d is the diameter of the hole.
 
So right on the surface it would be E = Q/ (4R^2 pi * epsilon_0), but when going through the hole, right inside the sphere it is already 0. Does it follow from Gauss' Law to be more obvious? E.g.: we choose the Gaussian sphere with radius R such that it goes through the charge layer. Thus, the total amount of charge inside the Gaussian sphere is Q/2 so E inside the hole is indeed 1/2 * Q/ (4R^2 pi * epsilon_0).
 
That happens anywhere at the surface, not just at the hole.
 
Interesting, thanks!
 

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