Question

An airplane flying at a distance of 8.6 km from a radio transmitter receives a signal of intensity 9.1 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

`2.761* 10^(-10)\ T`

Step-by-step explanation:

`\mu_0` = Vacuum permeability =
`4\pi * 10^(-7)\ H/m`

I = Intensity =
`9.1\ \mu W/m^2`

r = Radius = 8.6 km

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

Electric field is given by

`E=√(2I\mu_0c)\\\Rightarrow E=\sqrt{2* 9.1* 10^(-6)* 4\pi * 10^(-7)* 3* 10^8}\\\Rightarrow E=0.0828\ V/m`

The electric component is 0.0828 V/m

Magnetic field is given by

`B=(E)/(c)\\\Rightarrow B=(0.0828325923501)/(3* 10^8)\\\Rightarrow B=2.761* 10^(-10)\ T`

The magnetic field is
`2.761* 10^(-10)\ T`

Power is given by

`P=IA\\\Rightarrow P=I2\pi r^2\\\Rightarrow P=9.1* 10^(-6)* \pi* 8600^2\\\Rightarrow P=2114.404\ W`

The power of transmission is 2114.404 W