A $12\mathrm{.}5-$cm$-$long, monopole wire$-$type antenna is made of a copper rod $($nonmagnetic$,$ Cu $=5\mathrm{.}8107$ S$/$m$)$ with a square cross$-$section and $1-$mm side length. The antenna is excited by a sinusoidal current with an amplitude I$0=5$ A$.$

Determine the antenna gain $($in db$)$ and the time average radiated power, if the operating frequency is

$($a$)1$ MHz$,$

$($b$)0\mathrm{.}6$ GHz$.$

$($c$)$ At what operating frequency the given antenna is more efficient and what is the ratio $($in db$)$ of powers emitted at $0\mathrm{.}6$ GHz and $1$ MHz$?$

Ans.: $($a$)-8\mathrm{.}24$ dB and $3\mathrm{.}5$ mW$,($b$)5\mathrm{.}16$ dB and $456$ W$,($c$)$ at $600$ MHz and ratio is $51\mathrm{.}2$ dB$.$