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Electrodynamics textbooks, like Zangwill's Modern Electrodynamics, introduce the Hertz potentials $\boldsymbol{\Pi}_m$ and $\boldsymbol{\Pi}_e$(see Chapter 20 of the fore-mentioned book). While they seem like powerful tools, I've found few examples of utilizing these potentials beyond the typical dipole case. Even Zangwill introduces them without applying them to an actual problem.

Are there any books/ other sources where I could find problems utilizing these? I'm looking mostly for the full Maxwell equation solutions.

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Have you looked at Stratton's Electromagnetic Theory textbook? Chapter VI is devoted to cylindrical waves in which he makes use of these.

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