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Homework Help: Vector potential inside an infinite wire

  1. Apr 2, 2017 #1
    1. The problem statement, all variables and given/known data
    The problem statement is simply to find the vector potential inside and outside an infinite wire of radius R, current I and constant current density j using the Poisson equation.

    2. Relevant equations
    The Poisson law can be written A = μ0 /4π *∫(I/r*dl) or A = μ0 /4π *∫(i/r*dV)

    3. The attempt at a solution
    I already found out that A=-μ0 /2π * ln(r/R) outside of the wire. The problem is that I can't figure out how to calculate it inside the wire using the Poisson equation. Using the Biot-Savard law and the definition B=∇ x A, I found out that the vector potential should be μ0 j/4 * (R2-r2), but I can't find how to get this answer using the Poisson equation. By placing the wire on z-axis and using the second definition for Poisson, I have :
    A = μ0 j/2 * ∫∫r/(r2+z2)1/2 *dz dr

    Here, I have some trouble finding the borders of my integrals. Also, this equation seems false, since it doesn't seem to get me anywhere the expected result.
  2. jcsd
  3. Apr 8, 2017 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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