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Current through the conductor

  1. Sep 26, 2013 #1
    1. The problem statement, all variables and given/known data
    The current density in a cylindrical conductor of radius a placed along the z-axis is J=10e^-(1-ρ/a)Uz
    Find the current through the cross-section of the conductor.

    2. Relevant equations
    I=JA
    A=(pi)a^2

    3. The attempt at a solution
    So far I have this I=10e^-(1-ρ/a)Uz((pi)a^2) which I assume I am to integrate but what should I integrate with respect too and what should the limits be I am guessing from 0 to a?
     
  2. jcsd
  3. Sep 27, 2013 #2

    UltrafastPED

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    You integrate the flow normal to the cross section through which it is flowing.
     
  4. Sep 27, 2013 #3
    So that would be along the x or y?
     
  5. Sep 27, 2013 #4
    The normal is the perpendicular vector right?
     
  6. Sep 27, 2013 #5

    UltrafastPED

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    Yes, the normal is perpendicular to the surface.
     
  7. Sep 27, 2013 #6
    ok so a normal vector equals to Uz/Uz (where the bottom Uz is the length of Uz it is in between those two absolute value mark things). Do you have any more hints on how to set this up
     
  8. Sep 28, 2013 #7

    UltrafastPED

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    Your problem states that the current is flowing along the axis Uz, hence it is perpendicular to the cross section formed by the x-y plane.

    So you just have to integrate the density given as it crosses the circle of radius a defined by the cylinder of the wire. Since the axis passes along the center of the wire it would be easiest to switch to cylindrical coordinates for this integration.
     
  9. Sep 28, 2013 #8
    ∫JdS=Ienc where dS=ρd(phi)dρ in cylindrical right?
     
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