(Solved): For a dipole, the power density of a radiated field is given by S=322r2I2l22sin2ar. S ...

For a dipole, the power density of a radiated field is given by $\vec{S}=\frac{I^2{l}^2}{32{?}^2{r}^2}?{?}^2{\sin }^2?{\vec{a}}_r$. Sketch the approximate shape for the radiated power pattern in the $x?z$ plane. A magnetic field strength of $?H_{?s}?=5?\mathrm{A}/\mathrm{m}$ is required at a point on $?=\frac{?}{2}$, which is $r=2\mathrm{Km}$ from an antenna in air. If the antenna is a half-wave dipole (length $=\frac{?}{2}$ ), calculate the power the antenna must transmit. Given the radiation resistance, $R_{\text{rad }}=73?$, use the given formulas and neglect ohmic loss. $?H_{?s}?=\frac{I_o\cos \left(\frac{?}{2}\cos ?\right)}{2?r\sin ?}\text{ and }{P}_{\text{rad }}=\frac{1}{2}{I}_o^2{R}_{\text{rad }}$