(Solution) - The two circular coils of radius a and separation b -(2025 Original AI-Free Solution)

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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 = ?I?(? ? a)[?(z ? b/2) + ?(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 Bz on the z axis and relate it to the answer of Problem5.7b.