A copper wire is bent into a square whose sides have length L, and is placed in the xy plane with its center at the origin. A current I flows through the square in a counterclockwise direction when viewed from the +z axis.

A. Determine the magnitude AND direction of the magnetic field due to the current flowing through the square loop at an arbitrary location robs=<0,0,z> on the z axis.

B. Show mathematically that the magnetic field of the square loop at the limit zL is a dipole field, and determine the magnetic moment of the square.