The combination of two circular, coaxial coils of radius a separated by a distance also equal to a, with equal currents I in each coil circulating in the same direction, is known as a pair of "Helmholtz Coils." Assuming the coils are parallel to the x-y plane at z=+a/2 and -a/2:
a) Determine the magnetic field on the z axis.
b) What is the value of the magnetic field at the origin?
c) What is the leading non-constant behavior of the magnetic field for small z?