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Homework Help: Using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

  1. Sep 3, 2011 #1
    1. The problem statement, all variables and given/known data

    A wire of length L and negligible transverse dimensions, made of an insulating material, is placed on the x axis between the origin and the point (L,0). The wire has a uniform line charge density lambda.

    using Gauss' theorem and exploiting the cylindrical symmetry of the system, show that the electric field at the point (x,y)=(L/2,L/100) is

    E=(100lambda)/(2pi epsilon0 L)

    3. The attempt at a solution

    integral (S) E.da=E 2 pi r l
    Q/(epsilon 0)=(lambda l)/(epsilon0)

    2pi r l E=lambda l/epsilon0

    E=(1/2 pi r l) (lambda l/epsilon0)
    =lambda/(2 pi epsilon0 r)

    but I don't know how to proceed from here
     
  2. jcsd
  3. Sep 3, 2011 #2

    Doc Al

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    Staff: Mentor

    Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    Plug in for the given value of r.
     
  4. Sep 3, 2011 #3
    Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    oh right! so r is just L/100 because it the wire is along the x axis, so I don't have to do L-L/2?
     
  5. Sep 3, 2011 #4

    Doc Al

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    Staff: Mentor

    Re: using Gauss' theorem ande exploiting the cylindrical symmetry of the system, show

    Right. The point where you want to evaluate the field is at a distance of L/100 from the wire, so that's the value of r you need to use.
     
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