Surface charge density of a conducting spherical shell

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Discussion Overview

The discussion revolves around the surface charge density of a conducting spherical shell and its relationship to the electric field just outside the shell's surface. Participants explore the application of Gauss's law to derive the equation presented in a textbook.

Discussion Character

  • Technical explanation, Homework-related

Main Points Raised

  • One participant cites a textbook stating that the surface charge density σ is given by σ = ϵ0 * E, where E is the electric field just outside the surface of the conducting shell.
  • Another participant suggests applying Gauss's law with a Gaussian surface that is a sphere concentric with the charged sphere, indicating that this approach will lead to a relationship between E, σ, and the radius.
  • A third participant notes that the equation σ = ϵ0 * E is applicable to conductive surfaces of any shape.
  • There is a repeated suggestion to use Gauss's law and take the limit as dr approaches zero to derive the equation in question.

Areas of Agreement / Disagreement

Participants generally agree on the applicability of Gauss's law and the relationship between electric field and surface charge density, but there is no consensus on whether the original question is homework-related.

Contextual Notes

Some assumptions about the conditions under which the equation applies may be missing, and the discussion does not resolve whether the derivation is straightforward or requires additional steps.

Samanko
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The textbook says
' A conducting sphere shell with radius R is charged until the magnitude of the electric field just outside its surface is E. Then the surface charge density is σ = ϵ0 * E. '

The textbook does show why. Can anybody explain for me?
 
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Is this homework?

In any case apply Gauss's law with gaussian surface a sphere that has the same center as the charged sphere and radius ##R+dr## where ##dr## infinitesimal. You should get as result an equation that relates E (the electric field at distance R+dr) and ##\sigma## and ##R+dr##. Take the limit of that equation as ##dr\to 0## and you end up with the equation displayed in your textbook.
 
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Equation σ = ϵ0 * E applies to conductive surfaces, regardless of their shapes

E-Field 1.jpg
 
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Delta2 said:
Is this homework?

In any case apply Gauss's law with gaussian surface a sphere that has the same center as the charged sphere and radius ##R+dr## where ##dr## infinitesimal. You should get as result an equation that relates E (the electric field at distance R+dr) and ##\sigma## and ##R+dr##. Take the limit of that equation as ##dr\to 0## and you end up with the equation displayed in your textbook.
Got it! Thanks.
 
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