91Ó°ÊÓ

Microwave signals: A microwave is an electromagnetic wave with a wavelength of less than one meter, according to the definition. The fundamental distinction between microwave signals and radio broadcasting signals is that radio waves are longer than a meter. They have a higher frequency than radio signals, indicating that they are higher in frequency.

Considering the given information,

Power broadcast by the satellite is${\mathrm{P}}_5=3\mathrm{kW}\left(\frac{1000\mathrm{W}}{1\mathrm{kW}}\right)=3×{10}^3\mathrm{W}$.

The area over which the power spread is ${\mathrm{A}}_{\mathrm{s}}=100{\mathrm{km}}^2$.

The diameter of the dish is $\mathrm{d}=0.45{\mathrm{m}}^2$.

Apply the formula,

The intensity formula is as follows:

$\mathrm{I}=\frac{\mathrm{P}}{\mathrm{A}}$

The signal intensity when it reaches the dish can be calculated as follows:

$$\begin{gathered} \mathrm{I}=\frac{{\mathrm{P}}_{\mathrm{s}}}{{\mathrm{A}}_{\mathrm{s}}} \\ =\frac{3×{10}^3\mathrm{W}}{100×{10}^6{\mathrm{m}}^2} \\ =3×{10}^{-5}\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

$$\begin{gathered} \mathrm{I}=\frac{{\mathrm{P}}_{\mathrm{s}}}{{\mathrm{A}}_{\mathrm{s}}} \\ =\frac{3×{10}^3\mathrm{W}}{100×{10}^6{\mathrm{m}}^2} \\ =3×{10}^{-5}\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$

The dish's power can be computed using the formula:

$$\begin{gathered} {\mathrm{P}}_{\mathrm{dis}\mathrm{h}}=\mathrm{I}×{\mathrm{A}}_{\mathrm{dish}} \\ =\mathrm{I}×4\mathrm{π}{\left(\frac{\mathrm{d}}{2}\right)}^{\frac{1}{2}} \\ =\left(3×{10}^{-5}\mathrm{W}/{\mathrm{m}}^2\right)×4×3.14×{\left(\frac{0.45}{2}\right)}^2 \\ =1.91×{10}^{-5}\mathrm{W} \end{gathered}$$

The maximal electric field strength can be computed using the following formula:

$$\begin{gathered} {\mathrm{E}}_0={\left(\frac{2\mathrm{I}}{{\mathrm{°äÎ\mu }}_0}\right)}^{\frac{1}{2}} \\ ={\left(\frac{2×\left(3×{10}^{-5}\mathrm{W}/{\mathrm{m}}^2\right)}{\left(3×{10}^8\mathrm{m}/\mathrm{s}\right)×\left(8.85×{10}^{-12}{\mathrm{C}}^2/\mathrm{N}.{\mathrm{m}}^2\right)}\right)}^{\frac{1}{2}} \\ =0.15\mathrm{V}/\mathrm{m} \end{gathered}$$

Therefore, the required power received by the dish is$1.91×{10}^{-5}\mathrm{W}$ and the maximum electric field strength of the microwave signals is$0.15\mathrm{V}/\mathrm{m}$.