Potential on the inner surface of a spherical shell

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SUMMARY

The discussion centers on the potential on the inner surface of a charged spherical shell. It is established that while there is no electric field inside the shell, the potential (V) is not necessarily zero and can be defined as a nonzero constant due to gauge transformations. The concept of "effective potential" is introduced, emphasizing that for any point on the inner surface, there exists a corresponding point of equal potential directly across from it. The potential is not uniquely defined, allowing for flexibility in its value without affecting measurable outcomes.

PREREQUISITES
  • Understanding of Gauss's Law in electrostatics
  • Familiarity with electric potential and its mathematical representation
  • Knowledge of gauge transformations in electromagnetic theory
  • Basic concepts of spherical geometry and its implications in physics
NEXT STEPS
  • Research the implications of gauge transformations on electric fields and potentials
  • Explore the mathematical derivation of electric potential in spherical coordinates
  • Learn about the concept of effective potential in electrostatics
  • Investigate practical applications of electric potential in charged spherical shells
USEFUL FOR

Physicists, electrical engineers, and students studying electromagnetism, particularly those interested in electrostatics and the behavior of electric fields and potentials in spherical geometries.

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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