Problem $6$:

Two X$-$band $(\backslash (8\mathrm{.}2-12\mathrm{.}4\backslash$mathrm$\{$GHz$\}\backslash ))$ rectangular horns, with aperture dimensions of $5\mathrm{.}5$ cm and $7\mathrm{.}4$ cm and each with a directivity of $16\mathrm{.}3$ dB at $10$ GHz $,$ are used as transmitting and receiving antennas. Assuming that the input power is $200$ mW $,$ the VSWR of each is $1\mathrm{.}1,$ the conduction$-$dielectric efficiency isv $\backslash (100\backslash \%\backslash ),$ and the antennas are polarization$-$matched, find the maximum received power when the horns are separated in air by $($a$)\backslash (\backslash$mathbf$\{5$ m$\}\backslash )($b$)\backslash (\backslash$mathbf$\{500$ ~ m$\}\backslash )$