= Reciprocal Hertzian-dipole echo
{title2=$P_{\rm echo}/P_t=[G^2\lambda^2/(16\pi^2r^2)]^2$}
Two aligned lossless <Hertzian dipoles> in one another's broadside <radiation zone> have gain $G=3/2$ and one-way received-power fraction $\eta=G^2[\lambda/(4\pi r)]^2$. If the second remains conjugately matched, its <matched-load scattering of a Hertzian dipole> reradiates the same <power> as its load absorbs. Applying the reciprocal far-field link on the return gives $P_{\rm echo}=P_t\eta^2$, proportional to $r^{-4}$. The statement concerns physical dipole reradiation; a pure <antenna load-mismatch echo> model omits that scattering and is not interchangeable with it.
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