A rectangular loop carrying current I is placed on the xy-plane. Assume that the corners of the loop are at (0,0), (a,0), (0,b), (a,b). Find the magnetic field intensity above the loop. Specifically, let a=2, b=1:
A. Find the magnetic field intensity H at any point in the region 0<x<a, 0<y<b, 0<z<2
B. Plot the magnitude of H when 0<x<a, 0<y<b, z=0,1,2
C. This configuration is used as part of loop detectors installed under pavement at many traffic stop lights. Write a small essay about the function and applications of loop detectors.