An airplane flying at a distance of 8.3 km from a radio transmitter receives a signal of intensity 15 μW/m2. What is the amplitude of the (a

Question

An airplane flying at a distance of 8.3 km from a radio transmitter receives a signal of intensity 15 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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Jezebel 5 years 2021-07-31T06:49:02+00:00 2 Answers 21 views 0

Answers ( )

  1. thanhha
    0
    2021-07-31T06:50:05+00:00
    Reply

    Answer:

    a) = 0.106 V/m

    b) = 354.52 pT

    c) = 6.5 W

    Explanation:

    Given,

    Intensity, I = 15 μW/m²

    Distance, d = 8.3 km

    E = √(2Iμc)

    where

    c = speed of light = 2.99*10^8

    μ = permeability of free space = 4π*10^-7

    E = √(2 * 15*10^-6 * 4*3.142*10^-7 * 2.99*10^8)

    E = √(30*10^-6 * 1.257*10^-6 * 2.99*10^8)

    E = √1.13*10^-2

    E = 0.106 V/m

    B = E/c

    B = 0.106 / 2.99*10^8

    B = 354.52 pT

    P = IA

    Where A = 1/2 * 4πr²

    A = 0.5 * 4 * 3.142 * (8.3*10^3)²

    A = 4.33*10^8

    P = I A

    P = 15*10^-6 * 4.33*10^-8

    P = 6495 W

    P = 6.5 kW

    Therefore

    a) = 0.106 V/m

    b) = 354.52 pT

    c) = 6.5 W

  2. Eirian
    0
    2021-07-31T06:50:36+00:00
    Reply

    Answer:

    a) Amplitude of the electric field, E = 0.1063 V/m

    b) Magnetic field, B = = 3.545 x 10⁻¹⁰ Tesla

    c) Transmission power, P = 6492.73 W

    Explanation:

    Intensity, I = 15 μW/m²

    Distance, R = 8.3 km = 8300 m

    a) The electric field amplitude  

    Relationship between the amplitude and intensity of a signal is given by:

    I = \frac{E^{2} }{2c \mu}……….(1)

    c = 3 * 10⁸ m/s

    μ = 4 π * 10⁻⁷

    Substitute these values into equation (1)

    15 * 10^{-6} = \frac{E^{2} }{2* 3 * 10^{8} * 4\pi * 10^{-7} }\\15 * 10^{-6} * 240\pi = E^{2}\\ E^{2} = 0.0113097\\E = 0.1063 V/m

    b)Amplitude of the magnetic field component at the airplane

     B = E / c

    B = = 0.1063 / (3 x 10⁸ )

    B = = 3.545 x 10⁻¹⁰ Tesla

    3) The transmission power:

    Intensity, I = \frac{Power}{Area}

     P = I A

    Area of the hemisphere, A = 2πR²

    A = 2π * 8300²

    A = 432848635.8116 m²

    Power, P = 15 * 10⁻⁶ * 432848635.8116

    P = 6492.73 W

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