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Gauss's Law on cylinders

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    The figure below shows a portion of an infinitely long, concentric cable in cross section. The inner conductor has a linear charge density of λ = 6.10 nC/m and the outer conductor has no net charge.

    http://www.webassign.net/tipler/23-36alt.gif

    (a) Find the electric field for all values of R, where R is the perpendicular distance from the common axis of the cylindrical system. (Use R as necessary.)
    1.50 cm R 4.50 cm
    R 6.50 cm

    (b) What are the surface charge densities on the inside and the outside surfaces of the outer conductor?

    2. Relevant equations

    ∫EdA = Qinside/ɛo



    3. The attempt at a solution

    Using the above equation I would get E(2pi*r^2*h) = Qenclosed/ɛo, but it is infinite in length and therefore no height is given. Any help appreciated.
     
  2. jcsd
  3. Feb 4, 2010 #2
    Then you would just have a surface charge per unit length of the infinitely long conductor. That is the beauty of the infinitely long objects.

    Thanks
    Matt
     
  4. Feb 4, 2010 #3
    Hi ndoc,

    Surface density (λ) = Total charge (Q)/Length.

    If you set Gauss's law equivalent to a general form of Coulomb's law, EA=Q/ɛo, you will find that the cylinder's height, or length, does not have any significance.

    i.e.,

    E*[2pi(r^2)*h]= (λ*h)/ɛo =>

    E=λ/[2piɛo*(r^2)]
     
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