Chapter 31: Q. 62 (page 904)

The radar system at an airport broadcasts $11 GHz$ microwaves with $150 kW$ of power. An approaching airplane with a $31 m^{2}$ cross section is $30 Km$ away. Assume that the radar broadcasts uniformly in all directions and that the airplane scatters microwaves uniformly in all directions. What is the electric field strength of the microwave signal received back at the airport $200 μ s$ later?

Short Answer

Expert verified

The electric field strength of the microwave signal received back at the airport $200 μ s$ later, $E = 9 .4 μV / m$

Step by step solution

Data given

$\begin{aligned} P = 150 kW \to 1.5 \times 10^{5} W \end{aligned}$

$c = 3 \times 10^{8} m / s$

$A = 31 m^{2}$

d = 3.0 \times 10^{3} m

Find the facility density which is received

The Electromagnetic wave's power flux volume was determined by:

$S = (ε_{0} \times \frac{c}{2}) \times E^{2}$

Then we have got,

$E = \sqrt{2 \times \frac{S}{ε_{o} \times c}}$

The intensity of power in airplane,

$S = \frac{P}{4 π d^{2}}$

Power reflected was shown as,

localid="1649163573499" $P r = A p \times \frac{P}{(4 π d^{2})}$

The receiving power density was

$\frac{P r}{(4 π d^{2})} = A p \times \frac{P}{{(4 π d^{2})}^{2}}$

Find the electrical strength

Then, we calculate

$E = \sqrt{\frac{2 A p \times P}{ε_{0} \times c {(4 π d^{2})}^{2}}}$

localid="1650238867378" $E = [\frac{1}{(4 π d^{2})}] \times \sqrt{\frac{2 P}{ε_{o} \times c}}$

localid="1650238853014" $E = [\frac{1}{(4 π {(3 .0 \times 10^{3})}^{2})}] \times \sqrt{\frac{2 (1 .5 \times 10^{5})}{8 .85 \times 10^{- 14} \times 3 \times 10^{8}}}$

localid="1649163969377" $E = 9.4 μ V / m$

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Short Answer

Step by step solution

Data given

Find the facility density which is received

Find the electrical strength

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