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Electric field in cylinder with missing section

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data
    A uniformly charged, non-conducting, infinitely long cylinder of radius A is parallel to the z-axis, and its central axis intersects the x-y plane at the origin. It has a charge density p (C/m^3). Material is removed from the cylinder leaving a cylindrical void of radius A/2 running parallel to the z-axis, but its central axis intersects the x-y plane at the point x = A/2, y =0. Calculate the electric field at the points x = 0, x = A/4, x = A/2, and x = A.


    2. Relevant equations
    flux = E A cos(theta)
    total charge = (p)(volume)
    flux = total charge/e0
    area of cylinder cross section before removal: piA^2
    area of void cross section: (piA^2)/4
    area of cylinder cross section after removal: (3piA^2)/4


    3. The attempt at a solution
    We're working on Gauss's Law in class so I'm guessing I'm supposed to use that, and I think I understand how to do this if a section wasn't missing, but I have no idea how to take into account the off-center missing section.

    Thanks!
     
  2. jcsd
  3. Apr 10, 2009 #2

    Doc Al

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    Staff: Mentor

    Hint: You can cancel a positive charge by adding a negative charge.

    What kind of negative charge would you need to add to produce the given charge distribution with its missing section?
     
  4. Apr 10, 2009 #3
    I'm not sure I understand...
    You mean, in order to keep p of the area as a whole constant before and after material is removed?
     
  5. Apr 10, 2009 #4

    Doc Al

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    Staff: Mentor

    Here's what I'm getting at. Finding the field from a solid cylinder (or two solid cylinders) is easy. But having a missing piece makes it hard. So see if you can model the charge distribution with the missing piece as being composed of two solid cylinders, one of which happens to be negatively charged.
     
  6. Apr 10, 2009 #5
    I think I got it now. thanks a lot!
     
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