Classical Electrodynamics · Problem 5.9

Maxwell Equations, Macroscopic Electromagnetism, Conservation Laws — John David Jackson

Physics — E&M · two-coils-multipole-moments

Problem

The two circular coils of radius

a

and separation

b

of Problem 5.7 can be described in cylindrical coordinates by the current density

\mathbf{J} = \hat{\boldsymbol{\phi}} I\delta(\rho - a)[\delta(z - b/2) + \delta(z + b/2)]

(a) Using the formalism of Problem 5.8, calculate the internal and external multipole moments for

L = 1, \ldots, 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.