= Solution
Use <retarded time> $t_r$ and reserve $r$ for the large observation distance. The source velocity is nonrelativistic, $|\mathbf u|/c\ll1$. There are two errors in the original PDF that must be corrected before the <radiation zone> calculation: the vector-potential prefactor contains an extraneous $1/r$, and the displayed magnetic radiation field has the wrong sign for the stated outward unit vector $\mathbf n$. The extra distance factor is dimensionally wrong; the magnetic sign would make the <Poynting vector> point inward. The following derivation uses dimensionally consistent retarded potentials and outgoing radiation.
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