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Field in between two charged plates in a semi spherical arrangement

  1. May 5, 2014 #1
    1. The problem statement, all variables and given/known data
    We have two half-spherical electrodes, arranged so that they produce a spherically symmetric electric field. What is the magnitude of the electrical force on an electron between the two electrods?

    Specifications:
    Distance between electrodes: d=0.04 m
    Radius for first electrode: r=0.13 m
    Radius for second electrode: R=0.17 m
    Voltage across the electrodes: V

    2. Relevant equations
    F=q*E

    (force, charge, electric field)
    So what I need to know is the electric field between the plates.


    3. The attempt at a solution
    So I have basically had two lines of thought. One is to think of it as an entire sphere, in which case there is no electric field due to the outer electrode and just see the inner one as a point charge, to yield the Coulomb force. I am not certain this is okay for a half sphere though, and I cannot find any other deravation for the whole sphere case that Gauss's law and that doesn't work here since it's not a symmetric case (and I only know symmetric cases).

    The other though is to somehow relate the electric field to the potential. I mean, I know how to do that for some standard arrangements like point charge or between two sheets. But between half spheres? Is it possible to approximate them with sheets?
     
  2. jcsd
  3. May 5, 2014 #2
    Your first idea should work because the problem states that the field is spherically symmetric.
     
    Last edited: May 5, 2014
  4. May 5, 2014 #3

    rude man

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    I'd go with a Gaussian shell located between the two hemispherical shells. Compute what Q has to be to satisfy V, then E follows.
     
  5. May 6, 2014 #4
    What is a Gaussian shell? Don't the Gaussian surfaces have to be closed?
     
  6. May 6, 2014 #5

    rude man

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    You can close it on the bottom (max. diameter).
     
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