At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 71.9 V/m. Find the magne

Question

At some instant and location, the electric field associated with an electromagnetic wave in vacuum has the strength 71.9 V/m. Find the magnetic field strength B, the total energy density u, and the power flow per unit area, all at the same instant and location.

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Neala 4 years 2021-08-22T17:38:09+00:00 1 Answers 10 views 0

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  1. Cherry
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    2021-08-22T17:40:01+00:00
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    Answer:

    a) Magnetic field strength, B = 2.397 * 10⁻⁷ T

    b) Total energy density, U = 4.58 * 10⁻⁸ J/m³

    c) Power flow per unit area, S = 13.71 W/m²

    Explanation:

    a) Electric field strength, E = 71.9 V/m

    The relationship between the Electric field strength and the magnetic field strength in vacuum is:

    E = Bc where c = 3.0 * 10⁸ m/s

    71.9 = B * 3.0 * 10⁸

    B = 71.9 / (3.0 * 10⁸)

    B = 23.97 * 10⁻⁸

    B = 2.397 * 10⁻⁷ T

    b) Total Energy Density:

    U = \frac{1}{2} \epsilon_0E^2 + \frac{1}{2} \frac{B^2}{\mu_0} \\U = \frac{1}{2}* 8.85 * 10^{-12}*71.9^2 + \frac{1}{2} \frac{(2.397*10^{-7})^2}{4\pi*10^{-7}}\\U = 2.29 * 10^{-8} + 2.29 * 10^{-8}\\U = 4.58 * 10^{-8} J/m^3

    c)Power flow per unit area

    S = \frac{1}{\mu_0} EB\\S = \frac{1}{4\pi * 10^{-7} } * 71.9 * 2.397 * 10^{-7}\\S = 13.71 W/m^2

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