The two circular coils of radius a and separation b of Problem 5.7 can be described in cylindrical coordinates by the current density

J = фIδ(ρ – a)[δ(z – b/2) + δ(z + b/2)]

(a) Using the formalism of Problem 5.8, calculate the internal and external multipole moments for L = 1,..., 5.

(b) Using the internal multipole expansion of Problem 5.8, write down explicitly an expression for B_z on the z axis and relate it to the answer of Problem 5.7b.