During a test, a nato surveillance radar system, operating at 37 ghz at 182 kw of power, attempts to detect an incoming stealth aircraft at 104 km. assume that the radar beam is emitted uniformly over a hemisphere. (a) what is the intensity of the beam when the beam reaches the aircraft's location? the aircraft reflects radar waves as though it has a cross-sectional area of only 0.22 m2. (b) what is the power of the aircraft's reflection? assume that the beam is reflected uniformly over a hemisphere. back at the radar site, what are (c) the intensity, (d) the maximum value of the electric field vector, and (e) the rms value of the magnetic field of the reflected radar beam?

(a)

The intensity of an electromagnetic wave is given by

where

P is the power

A is the area of the surface considered

For the waves in the problem,

is the power

The area is a hemisphere of radius

so

So, the intensity is

(b)

In this case, the area of the reflection is

So, if we use the intensity of the wave that we found previously, we can calculate the power of the aircraft's reflection using the same formula:

(c)

We said that the power of the waves reflected by the aircraft is

If we assume that the reflected waves also propagate over a hemisphere of radius

which has an area of

Then the intensity of the reflected waves at the radar site will be

(d)

The intensity of a wave is related to the maximum value of the electric field by

where

c is the speed of light

is the vacuum permittivity

is the maximum value of the electric field vector

Solving the equation for ,

(e)

The maximum value of the magnetic field vector is given by

Substituting the values,

And the rms value of the magnetic field is given by