Potential on the inner surface of a spherical shell

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Discussion Overview

The discussion revolves around the concept of electric potential on the inner surface of a charged spherical shell, exploring whether a potential exists and how it can be defined or calculated. It touches on theoretical implications, gauge transformations, and the nature of potential in electrostatics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether there is a potential on the inner surface of a charged spherical shell, noting that while there is no electric field, the potential could still be a nonzero constant.
  • Another participant states that the potential is not uniquely defined due to gauge transformations, allowing for the potential to take any value inside the shell without affecting measurable effects.
  • A later reply emphasizes that all measurable effects remain unchanged regardless of the potential's value, suggesting that the choice of potential is often made for mathematical convenience.
  • One participant argues that the phrase "is there a potential" is meaningless, asserting that even if the potential is zero, it still exists as a value of zero.

Areas of Agreement / Disagreement

Participants express differing views on the nature and significance of potential within the spherical shell, with no consensus reached on whether the potential can be meaningfully defined or calculated.

Contextual Notes

Participants acknowledge the dependence of potential on gauge choices and the implications of these choices for theoretical discussions. There is also an unresolved discussion regarding the implications of having a potential value of zero.

G Cooke
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Is there a potential on the inner surface of a charged spherical shell?

I know that there is no electric field on the inner surface, as shown by Gauss's Law, but that isn't enough information to say that the potential (V) there is zero since E = dV/dr, so V could be a nonzero constant.

If there is a potential on the inner surface, then I must clarify that what I'm curious about is what I'll call the "effective potential." That is, given this spherical geometry, for every point on the inner surface, there is a point of equal potential directly across from it. The closer these points are to each other (i.e., the smaller the sphere's radius), the smaller the effective potential at either point becomes, right? So how would one calculate this radius-dependent effective potential? Is there a formula?
 
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G Cooke said:
Is there a potential on the inner surface of a charged spherical shell?
The potential is not uniquely defined. You can do a gauge transformation and leave the fields and all measurable effects the same. So this means that you can choose a gauge so that the potential can be any value you like inside the shell.
 
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Dale said:
The potential is not uniquely defined. You can do a gauge transformation and leave the fields and all measurable effects the same. So this means that you can choose a gauge so that the potential can be any value you like inside the shell.

Interesting. So in other words, it wouldn't matter for any practical purposes. All measurable effects would be the same whether there were a potential there or not.
 
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G Cooke said:
Interesting. So in other words, it wouldn't matter for any practical purposes. All measurable effects would be the same whether there were a potential there or not.
Yes, exactly. In fact, usually the potential is chosen to make the math simpler.
 
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Actually the phrase (or question) "is there a potential" is meaningless.
Even assuming that the potential is zero, there is still a potential. One with value zero.
There is no way to have a situation in which there is no potential, is there?
 

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