(Solved): Say you have a thin sheet of current that extends infinitely far in the z=0 plane, flowing in the ...

Say you have a thin sheet of current that extends infinitely far in the $$z=0$$ plane, flowing in the y direction, such that $${\mathbf{J}}_s=K\hat{y}$$. The units of $$K$$ are $$A/m$$, because this is the current density in a sheet rather than our usual volumetric current density $$\mathbf{J}$$. Draw a fictitious loop ("Amperian loop") as shown below, and calculate the magnetic field $$B$$ both above and below the sheet of current.