I have a very thin current sheet with constant current density K in the y-direction, length w in the x-direction, and infinitely long in the y-direction. I have to find an expressions for the magnetic field at a distance z above the current sheet. For an infinitely long sheet, I understand how to find the B field anywhere above using Ampere's law, but I cannot seem to translate that into an answer for a semi-infinite sheet. I tried Biot-Savart's law, but the integral is nasty. Any guidance on how to think about the semi-infinite sheet vs the infinite sheet example?
The Ampere's law is used in cases where the magnetic field B is uniform and known everywhere on the plane since it has the form of integral of B.dl. B often comes out of the loop integral because it's uniform. For a semi-infinite sheet, this form to find the magnetic field doesn't work because even though one edge is at infinity and the field can be considered uniform, one edge is still at a known co-ordinate and you do not know the field there. So simple, use the Biot-Savart law integral and calculate it.