$4.$ A $5$ G base station cellular communication system operating at $3\mathrm{.}4$ GHz has an antenna with a maximum gain of $10$ dB $.$ The input power to the antenna is $10$ W and the total efficiency of antenna is $\backslash (90\backslash \%\backslash ).$

a$)$ Find power density $\backslash ($ W$\_\{\backslash$text $\{$rad $\}\}\backslash$left$(\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$right$)\backslash )$ at a distance of $20$ km $.$

b$)$ Find maximum power density $\backslash ($ W$\_\{\backslash$max $\}\backslash$left$(\backslash$mathrm$\{$W$\}/\backslash$mathrm$\{$m$\}^\{2\}\backslash$right$)\backslash )$ at the same distance.

c$)$ Suppose you are at the same distance and your mobile phone's receiver antenna is a quarter$-$wavelength monopole operating at the same network frequency. Calculate the aperture $($effective$)$ area $\backslash ($ A$\_\{$e m$\}\backslash )(\backslash ($ m$^\{2\}\backslash ))$ of the monopole and the power received $\backslash ($ P$\_\{$r$\}(\backslash$mathrm$\{$~W$\})\backslash )$ ignoring all the losses due to the surrounding.

d$)$ If sensitivity of the monopole is $-70$ dBm $($it cannot receive signals below this level$),$ can you make a clear call with your friend on the phone? If the answer is no$,$ calculate how much distance you should move to the base station?