The FM radio station KAMB broadcast from an antennae atop a 150 meter tall radio tower at a frequency of 90 MHz with a total radiated power of 40 kilowatts. Neighbors have complained about problems they attribute to excessive radiation from the tower, but the city engineer who measured the radiation level near the base of the tower found it to be well below the accepted standard. You have been hired by the HOA to assess the engineer's report. You know a few things about electromagnetic radiation and therefore conclude that we must find the optimum place on the ground to measure the maximum radiation emitted from the antennae. From your extensive knowledge in physics, you know that the intensity of radiation, I, is given by the formula:
I=12/32π*Psin2(θ)/r^2
where P is the power output, r is the distance from the top of the tower to the point on the ground, and θ is the angle measured from the tower to r.

Find the distance R from the base of the tower to the optimum location for taking the radiation reading. (m)
What is the maximum radiation reading from the ground in kw/m^2
If the city code requires that electromagnetic radiation be under 200 microwatts per square meter, is this antenna operating within city code? Yes or No

Answer: 150 m, 5.305*10^-5 kW/m^2, No

Step-by-step explanation:

See attachment, hope this helps

Using the radiation intensity formula we will have to:

a) [tex]150 m[/tex]

b) [tex]5.305*10^{-5} kW/m^2[/tex]

c)No

From the data informed, we have:

[tex]h=150m\\P=40KW[/tex]

Using the given formula and performing some mathematical operations:

[tex]I=\frac{12Psin^2(\theta)}{32(\pi)r^2} \\I= \frac{12(40)(R/r)^2}{32(\pi)r^2} \\= \frac{15R^2}{r^2\pi } \\= \frac{15R^2}{(R^2+150^2)^2\pi} \\[/tex]

deriving the given equation, we will have:

[tex]=\frac{(R^2+150^2)^22R-R^2(2(R^2+150^2))2R}{(R^2+150^2)^2}[/tex]

So from this equation we have that the answer of the letter A corresponds:

[tex]R=150[/tex]

For letter B we will have to develop this equation:

[tex]I= 5.30X10^{-5}[/tex]

As for the letter C, when converting the value found, it should give 200 microwatts, which is false.

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