= Power delivered to the second dipole
Integrating the $\sin^2\theta$ radiation pattern uses $\int\sin^2\theta\,d\Omega=8\pi/3$, so its lossless gain is
$$
G(\theta)=\frac32\sin^2\theta.
$$
The receiver lies on the $x$ axis, broadside to both $z$-directed dipoles. Thus $G_t=G_r=3/2$ and their linear polarizations match. At $f=100\,\mathrm{MHz}$, $\lambda=c/f\simeq3.00\,\mathrm m$, giving
$$
A_{\rm eff}=\frac{\lambda^2}{4\pi}\frac32\simeq1.07\,\mathrm{m^2}.
$$
At separation $r=100\,\mathrm m$, the incident flux is $P_0G_t/(4\pi r^2)$. The <Friis transmission equation> therefore gives the matched-load <power>
$$
\boxed{P_2=P_0G_tG_r\left(\frac{\lambda}{4\pi r}\right)^2
\simeq1.28\times10^{-5}\,\mathrm W=12.8\,\mu\mathrm W.}
$$
The far-field and weak-coupling approximations are well satisfied at a distance of about $33$ wavelengths for an electrically short dipole. Matching refers to the available received <power>, not interception of all <power> in a geometric area equal to the wire's physical size.
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