A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area of 0.500 m2 . At the wind

Question

A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area of 0.500 m2 . At the window, the electric field of the wave has an rms value 0.0600 V/m .
How much energy does this wave carry through the window during a 30.0-s commercial? Express your answer with the appropriate units.

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Dâu 5 years 2021-07-29T16:33:07+00:00 1 Answers 568 views 1

Answers ( )

  1. minhkhang
    0
    2021-07-29T16:34:34+00:00
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    Answer:

    The energy of the wave is 1.435 x 10⁻⁴ J

    Explanation:

    Given;

    area of the window, A = 0.5 m²

    the rms value of the field, E = 0.06 V/m

    The peak value of electric field is given by;

    E_o = \sqrt{2} *E_{rms}\\\\E_o = \sqrt{2}*0.06\\\\E_o = 0.0849 \ V/m

    The average intensity of the wave is given by;

    I_{avg} = \frac{c \epsilon_o E_o^2 }{2}\\\\I_{avg} = \frac{(3*10^8)( 8.85*10^{-12}) (0.0849)^2 }{2}\\\\I_{avg} = 9.569*10^{-6} \ W/m^2

    The average power of the wave is given by;

    P = I x A

    P = (9.569 x 10⁻⁶ W/m²) (0.5 m²)

    P = 4.784 x 10⁻⁶ W

    The energy of the wave is given by;

    E = P x t

    E = (4.784 x 10⁻⁶ W)(30 s)

    E = 1.435 x 10⁻⁴ J

    Therefore, the energy of the wave is 1.435 x 10⁻⁴ J

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