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.