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Gauss' Law and an infinite sheet

  1. Jun 10, 2008 #1
    1. The problem statement, all variables and given/known data

    a small circular hole of radius R = 2.03 cm has been cut in the middle of an infinite, flat, nonconducting surface that has a uniform charge density σ = 4.61 pC/m^2. A z axis, with its origin at the hole's center, is perpendicular to the surface. What is the magnitude (in N/C) of the electric field at point P at z = 3.05 cm? (Hint: See Eq. 22-26 and use superposition.)

    There is supposed to be a figure, but it really doesn't lend much to this. It is a flat sheet laid on the horizon, with the z axis going through a hole in the middle of the sheet. Point P is on the z axis, and R is just shown as the radius of the hole in the sheet. Which, is pretty much what was said in the problem....

    2. Relevant equations

    the equation mentioned above is
    E = (σ / 2ε) *( 1- z/ (√z^2 + R^2))

    but how I'm supposed to use that and superposition, I am not sure.


    3. The attempt at a solution
    I want to just plug in the given values, but I don't think that it right, because the question mentions superposition, but what am I adding together?! There was an additional hint about using a disc of equal magnitude and such, but oppostire direction. Wouldn't I then need a different equation? Help! (and Thanks)
     
  2. jcsd
  3. Jun 10, 2008 #2

    dynamicsolo

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    There is a favorite trick for dealing with "holes" in charge distributions. You use the superposition of the field for an infinite sheet of uniform surface charge density σ , together with the field for a disk the size of the "hole", having uniform surface charge density -σ .
     
  4. Jun 10, 2008 #3
    oooo, so for the sheet I would use sigma/2*epsilon and the disc would have a -sigma value.....then I add those numbers and viola! I have the solution. Thanks!
     
  5. Jun 10, 2008 #4

    dynamicsolo

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    Yes, for its electric field, since this is a non-conducting sheet.

    Yes, in the equation you were given for the field along the axis for a uniformly charged disk at a distance z from the plane of the disk.

    That should do it.
     
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