GATE Electronics and Communications (EC) 2016 Shift 1 Solved Paper

The far-zone power density radiated by a helical antenna is approximated as:
${\overrightarrow{\mathit{W}}}_{\mathit{r}\mathit{a}\mathit{d}}={\overrightarrow{\mathit{W}}}_{\mathit{a}\mathit{v}\mathit{e}\mathit{r}\mathit{a}\mathit{g}\mathit{e}}\approx \widehat{{\mathit{a}}_{\mathit{r}}}{\mathit{C}}_0\frac{1}{{\mathit{r}}^2}{\cos }^4\mathit{\theta }$
The radiated power density is symmetrical with respect to φ and exists only in the upper
hemisphere: 0 ≤ 𝜃 ≤ 𝜋/2 ; 0 ≤ 𝜙 ≤ 2𝜋; 𝐶₀ is a constant. The power radiated by the antenna (in watts) and the maximum directivity of the antenna, respectively, are