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Homework Help: Intensity of Electromagnetic Waves

  1. Mar 25, 2012 #1
    1. The problem statement, all variables and given/known data
    A plane monochromatic electromagnetic wave with wavelength λ = 2.2 cm, propagates through a vacuum. Its magnetic field is described by
    [itex]\vec{B}[/itex] = (Bx[itex]\vec{i}[/itex] + By[itex]\vec{j}[/itex])cos(kz+ωt)
    where Bx = 1.8E-6 T and By = 3.8E-6 T, and i-hat and j-hat are the unit vectors in the +x and +y directions, respectively.

    What is I, the intensity of this wave?

    2. Relevant equations
    I = P/A = (1/2)cεoE^2
    k = (2π)/λ
    ω = ck
    Bo*c = Eo

    3. The attempt at a solution
    I found frequency to be c/λ = 13.63GHz.

    I have tried setting t to zero in the given equation and plugging in k and ω to find B, then multiplying that by the speed of light to find E.
    I then plugged that into I = (1/2)cεoE^2, but that gave me the wrong answer.

    I've also tried adding to the two vectors and assumed that equaled Bo (which I don't think it does), and used Bo = (√2ZoI)/c where Zo = 377 ohms.
    I've tried <B^2> = (Bo^2)/2 as well.

    Is there an important equation I'm missing?
  2. jcsd
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