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Electric field in a solid cylinder with an offset hole

  1. Jan 26, 2008 #1
    [SOLVED] Electric field in a solid cylinder with an offset hole

    1. The problem statement, all variables and given/known data
    [​IMG]
    its teenie, but it says: Superposition: an infinite cylinder of radius R and uniform charge density (row) contains a cylindrical cavity of radius R/2 as shown. Find the electric field in the cavity.



    2. Relevant equations

    Gauss's Law I guess.



    3. The attempt at a solution
    My first thought was 'zero. duh'...but thats not exactly superposition. I know there has to be something about the whole cylinder minus the hole...but I'm not sure how to go about integrating with a common origin or...I've just gotten myself very confused. HELP!
     
  2. jcsd
  3. Jan 26, 2008 #2

    Doc Al

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    Staff: Mentor

    Here's a hint: A negative charge can cancel a positive charge. :wink:
     
  4. Jan 26, 2008 #3
    Let [itex]E_1[/itex] the wanted electric field, [itex]E_2[/itex] the electric field produced by the cylinder [itex]R/2[/itex] alone and [itex]E_3[/itex] the electric field produced by the cylinder [itex]R[/itex]. Then

    [tex]E_1+E_2=E_3\Rightarrow E_1=E_3-E_2[/tex]


    The electric fields [itex]E_2, E_3[/itex] are easily obtained by Gauss law.
     
  5. Jan 26, 2008 #4
    thank you thank you
    however...easily obtained by gauss's law...easily...I'm having a very blonde afternoon...I can't seem to pick a reference frame that works for both E1 and E2. And do I treat E2 as a cylindrical shell with uniform charge distribution? Or as nothing...not that it really matters...its still zero right?
     
  6. Jan 26, 2008 #5

    Doc Al

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    Come up with two solid uniform cylinders of charge which add up to give you the needed charge configuration.
     
  7. Jan 27, 2008 #6
    Hey there, I take it you're in Phys 231/239 as well?
     
  8. Jan 27, 2008 #7
    wow...lol.
    Yup 239.
    Have you finished it?
     
  9. Jan 28, 2008 #8
    I'm done the assignment except for this question. I too was having some trouble combining the two fields (awkward using two separate cylindrical coordinate systems). I think I've figured it out now though.

    I'm technically in 231, but it's just 239 renamed for us purple folk.
     
  10. Feb 15, 2010 #9
    Re: [SOLVED] Electric field in a solid cylinder with an offset hole

    Hi, I'm having trouble with the same problem. The center of the cavity is at a distance A from the center of the big cylinder. My calculations of superpositioning the two fields yields an electric field within the cavity equal to zero. Is this correct?
     
  11. Feb 15, 2010 #10

    Doc Al

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    Re: [SOLVED] Electric field in a solid cylinder with an offset hole

    No, that's not correct. Show how you came to that conclusion.
     
  12. Feb 15, 2010 #11
    Re: [SOLVED] Electric field in a solid cylinder with an offset hole

    I know, I discovered it was nonsense. I now have calculated the vector product of the vector field produced by the big solid cylinder with charge density rho and the vector field produced by the small cylinder with charge density minus rho. Because this adds up to the situation we have here (a big cylinder with a cavity with density of zero). The direction of the resulting vector field in an arbitrary point P within the cavity is in the direction of the vector connecting the center of the big cylinder and the center of the cavity.
     
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