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E-field & hollow non-conducting sphere

  1. Nov 10, 2013 #1
    I know that the E-field around a hollow non-conducting sphere charged with Q charge comes immediately from Gauss' Law but I'm wondering what the situation is if we somehow go inside the material, we make a very small hole through the material of the sphere and go inside it. What would there be the E-field?
     
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  3. Nov 10, 2013 #2

    Meir Achuz

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    If the charge is a uniform surface charge, then the field inside would be zero by Gauss's law.
     
  4. Nov 11, 2013 #3
    Even inside the hole when being half outside, half inside the sphere?
     
  5. Nov 11, 2013 #4

    Meir Achuz

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    Inside the hole, at radius R, the E field is one half Q/R^2.
    The E field goes from Q^2/R to zero as r decreases through the hole.
    The decrease in E takes place in a distance of the order of \Delta r=d, where d is the diameter of the hole.
     
  6. Nov 11, 2013 #5
    So right on the surface it would be E = Q/ (4R^2 pi * epsilon_0), but when going through the hole, right inside the sphere it is already 0. Does it follow from Gauss' Law to be more obvious? E.g.: we choose the Gaussian sphere with radius R such that it goes through the charge layer. Thus, the total amount of charge inside the Gaussian sphere is Q/2 so E inside the hole is indeed 1/2 * Q/ (4R^2 pi * epsilon_0).
     
  7. Nov 11, 2013 #6

    Meir Achuz

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    That happens anywhere at the surface, not just at the hole.
     
  8. Nov 12, 2013 #7
    Interesting, thanks!
     
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