- #1

Jean-C

- 5

- 0

## Homework Statement

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.

## Homework Equations

The Poisson law can be written A = μ

_{0}/4π *∫(I/r*dl) or A = μ

_{0}/4π *∫(i/r*dV)

## The Attempt at a Solution

I already found out that A=-μ

_{0}/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 μ

_{0}j/4 * (R

^{2}-r

^{2}), 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 = μ

_{0}j/2 * ∫∫r/(r

^{2}+z

^{2})

^{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.