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 (

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?

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Helga 4 years 2021-08-02T08:03:12+00:00 1 Answers 12 views 0

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  1. Edana
    0
    2021-08-02T08:04:37+00:00
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    Answer:

    2.761\times 10^{-10}\ T

    Explanation:

    \mu_0 = Vacuum permeability = 4\pi \times 10^{-7}\ H/m

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

    r = Radius = 8.6 km

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

    Electric field is given by

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

    The electric component is 0.0828 V/m

    Magnetic field is given by

    B=\dfrac{E}{c}\\\Rightarrow B=\dfrac{0.0828325923501}{3\times 10^8}\\\Rightarrow B=2.761\times 10^{-10}\ T

    The magnetic field is 2.761\times 10^{-10}\ T

    Power is given by

    P=IA\\\Rightarrow P=I2\pi r^2\\\Rightarrow P=9.1\times 10^{-6}\times \pi\times 8600^2\\\Rightarrow P=2114.404\ W

    The power of transmission is 2114.404 W

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