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Thread: charge radius of the proton

  1. #31
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    Quote Originally Posted by Hornblower View Post
    Let me remind everyone that the Shell Theorem is exact only in a thought exercise in which the charge is continuous in distribution. If we have a real world shell on which the charged entities were discrete particles and their separation was large compared to the separation of an interior particle and a shell particle, then there will be departures up close to the shell. These departures become virtually zero as we move away inside.
    Lets say we have a positive charge, surrounded by 12 negative charge in a cuboctahedron structure. They are very close. Because of the shell theorem, there is no field. But because they are very close, there will be some departures close to the shell. How close to the shell do these departures take place. Do we know the mechanisms, what the field lines look like, the exact distances to these departures, or do we just know there are departures. Are the distances on the order of nanometers, femtometers or what? Thanks for any insights.
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  2. #32
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    Quote Originally Posted by Copernicus View Post
    Lets say we have a positive charge, surrounded by 12 negative charge in a cuboctahedron structure. They are very close. Because of the shell theorem, there is no field. But because they are very close, there will be some departures close to the shell. How close to the shell do these departures take place. Do we know the mechanisms, what the field lines look like, the exact distances to these departures, or do we just know there are departures. Are the distances on the order of nanometers, femtometers or what? Thanks for any insights.
    You would need to quantify what "very close" means. You would need to specify the exact size of this structure and the magnitude of the charges.

    But maybe someone could derive a general equation for this setup, that you could plug the appropriate numbers into to calculate the field strength at any point. It would probably require slightly more knowledge/experience with calculus than I have (I have forgotten most of what I knew, which was limited to being with!)

    I am pretty certain that the field would only be exactly zero at the centre of this geometry. But the strength of the field would fall off very rapidly as you moved away from the charges.

    But, really, you need to learn how to calculate this yourself.

  3. #33
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    Twelve charges at the vertices of a cuboctahedron are not even a remote approximation to a spherical shell. They're just twelve charges in a regular array, and would need to be treated as such.

    Grant Hutchison

  4. #34
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    Quote Originally Posted by Copernicus View Post
    Lets say we have a positive charge, surrounded by 12 negative charge in a cuboctahedron structure. They are very close. Because of the shell theorem, there is no field.
    The shell theorem is about a continuous shell, not a discontinuous cuboctahedron, and so cannot be applied. You would have to calculate the electric field from this specific arrangement.

  5. #35
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    How does charge all get to the edge of a sphere.
    The moment an instant lasted forever, we were destined for the leading edge of eternity.

  6. #36
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    Your question is unclear.

    Grant Hutchison

  7. #37
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    Quote Originally Posted by Copernicus View Post
    How does charge all get to the edge of a sphere.
    It depends on what sort of set up you are defining. You started out saying, "If I had a, large, negatively charged, spherical shell" so it is up to you to say how the charge gets there.

    The most practical method I can think of is a sphere of conducting material that is either empty of filled with some insulation material.

  8. #38
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    Quote Originally Posted by Strange View Post
    It depends on what sort of set up you are defining. You started out saying, "If I had a, large, negatively charged, spherical shell" so it is up to you to say how the charge gets there.

    The most practical method I can think of is a sphere of conducting material that is either empty of filled with some insulation material.
    Perhaps if I had a conductive hollow sphere and electric charges either positive or negative were injected into the nonconductive interior.
    The moment an instant lasted forever, we were destined for the leading edge of eternity.

  9. #39
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    The charged particles would repel each other and migrate to the shell. What happens afterward depends on the microscopic properties of the shell and the introduced particles, and in my opinion is beyond the scope of this thread.

  10. #40
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    Quote Originally Posted by Hornblower View Post
    The charged particles would repel each other and migrate to the shell. What happens afterward depends on the microscopic properties of the shell and the introduced particles, and in my opinion is beyond the scope of this thread.
    Thanks.
    The moment an instant lasted forever, we were destined for the leading edge of eternity.

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