Question

An airplane flying at a distance of 9.9 km from a radio transmitter receives a signal of intensity 12 μW/m2. What is the amplitude of the (a) electric and (b) magnetic component of the signal at the airplane? (c) If the transmitter radiates uniformly over a hemisphere, what is the transmission power?

Answer 1

0.09511 V/m

`3.17033* 10^(-10)\ T`

7389.7799 W

Step-by-step explanation:

I = Intensity of signal =
`12* 10^(-6)\ W/m^2`

`\epsilon_0` = Permittivity of free space =
`4\pi * 10^(-7)\ H/m`

c = Speed of light =
`3* 10^8\ m/s`

A = Area of the hemisphere

Intensity of Electric field

`I=(E^2)/(2* \epsilon_0 c)\\\Rightarrow E=√(2 \epsilon_0 c I)\\\Rightarrow E=\sqrt{2* 4\pi * 10^(-7)* 3* 10^8* 12* 10^(-6)}\\\Rightarrow E=0.09511\ V/m`

Electric field of the wave is 0.09511 V/m

Magnetic field

`B=(E)/(c)\\\Rightarrow B=(0.09511)/(3* 10^8)\\\Rightarrow B=3.17033* 10^(-10)\ T`

Magnetic field of the wave is
`3.17033* 10^(-10)\ T`

Power

`P=IA\\\Rightarrow P=I* 2\pi r^2\\\Rightarrow P=12* 10^(-6)* 2\pi * 9900^2\\\Rightarrow P=7389.7799\ W`

The transmitter radiates 7389.7799 W of power