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Axial multipole moments are a series expansion of the electric potential of a charge distribution localized close to the origin along one Cartesian axis, denoted here as the z-axis. However, the axial multipole expansion can also be applied to any potential or field that varies inversely with the distance to the source, i.e., as 1 R {\displaystyle {\frac {1}{R}}}. For clarity, we first illustrate the expansion for a single point charge, then generalize to an arbitrary charge density λ {\displaystyle \lambda } localized to the z-axis.

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