μ0=1;
σ=1;
v=1;
Asheety[z_]:=-μ0 σ v Abs[z]/2
VectorPlot[{Asheety[z],0},{y,-1,1},{z,-1,1},FrameLabel->{y,z}]
VectorPlot3D[{0,Asheety[z],0},{x,-1,1},{y,-1,1},{z,-1,1}]

μ0=1;
II=1;
z2=1;
z1=-1;
Asheetz[s_,z_]:=-μ0 II Log[(z-z2+Sqrt[s^2+(z-z2)^2])/(z-z1+Sqrt[s^2+(z-z1)^2])]/(4π)
VectorPlot[{0,Asheetz[s,z]},{s,.1,2},{z,-2,2},FrameLabel->{y,z}]
VectorPlot3D[{0,0,Asheetz[Sqrt[x^2+y^2],z]},{x,-3,3},{y,-3,3},{z,-3,3}]