Potential on the inner surface of a spherical shell

In summary, the conversation discusses the potential on the inner surface of a charged spherical shell and the fact that it is not uniquely defined. The potential can be any value and can be chosen to make calculations simpler. This means that for practical purposes, the presence or absence of a potential on the inner surface does not make a difference.
  • #1
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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  • #2
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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  • #3
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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  • #4
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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  • #5
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?
 

1. What is the formula for calculating the potential on the inner surface of a spherical shell?

The formula for calculating the potential on the inner surface of a spherical shell is V = kQ/R, where V is the potential, k is the Coulomb's constant, Q is the charge of the shell, and R is the radius of the shell.

2. How does the potential on the inner surface of a spherical shell change with the charge of the shell?

The potential on the inner surface of a spherical shell is directly proportional to the charge of the shell. As the charge increases, the potential also increases.

3. Is the potential on the inner surface of a spherical shell affected by the thickness of the shell?

No, the potential on the inner surface of a spherical shell is not affected by the thickness of the shell. It only depends on the charge and radius of the shell.

4. Can the potential on the inner surface of a spherical shell be negative?

Yes, the potential on the inner surface of a spherical shell can be negative if the charge of the shell is negative. This means that the electric field on the inner surface is directed towards the center of the shell.

5. How does the potential on the inner surface of a spherical shell compare to the potential inside the shell?

The potential on the inner surface of a spherical shell is the same as the potential inside the shell. This is because the electric field inside a conductor is zero, so the potential remains constant throughout the interior of the shell.

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