The radar system at an airport broadcasts 11 Ghz microwaves with 150 kW of power

Question

The radar system at an airport broadcasts 11 Ghz microwaves with 150 kW of power. An approaching airplane with a 35 m^2 cross section is 33 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 220 µs later? The radar system at an airport broadcasts 11 Ghz microwaves with 150 kW of power. An approaching airplane with a 35 m^2 cross section is 33 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 220 µs later?

Explanation / Answer

The intensity at the air plane is I = P / 4 p r ^2                                                      = 150 k W / 4 p * ( 33 * 10^3 m ) ^2                                                       = 1.09 *10^-5 W / m ^2              The air plane then acts as a source of a microwave                       P = I A                           = 1.09 *10^-5 W / m ^2 * 35 m ^2                             = 38.3 *10^-5 W The intensity of reflected beam at radar air port is                     I = P / 4 p r ^2                          = c e_0 E_0^2 / 2                 E_0 = v 2 P / 4 p e_0 c r^2        = v 2 * 38.3 *10^-5 W   / 4 p * 8.85 *10^-12 * 3* 10^8 m/s * ( 33 km )^2          = 4.59 * 10^ -6 V /m         

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