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Electromagnetic waves waves review

  1. Jun 10, 2012 #1
    1. The problem statement, all variables and given/known data
    The figure below shows a plane electromagnetic sinusoidal wave propagating in the x direction. Suppose the wavelength is 56.0 m and the electric field vibrates in the xy plane with an amplitude of 20.0 V/m.

    34-p-013.gif


    (a) Calculate the frequency of the wave.

    (b) Calculate the magnetic field when the electric field has its maximum value in the negative y direction.

    (c) Write an expression for with the correct unit vector, with numerical values for Bmax, k, and ω, and with its magnitude in the form
    B = Bmax cos (kx − ωt).
    (Assume B is measured in nT, x is measured in m and t in s.)

    2. Relevant equations

    c = 1/(μ0ε0)1/2

    c = 299609581 m/s

    f = c / λ

    E = Emax cos(kx - ωt)

    B = Bmax cos(kx - ωt)

    E max / B max = E / B = c


    k = 2π/λ

    ω = 2πf

    3. The attempt at a solution

    I only found the frequency, which is 5.35 x 106 Hz


    I would like some hints how to find E max then I can just use the third equation listed.


    I'm thinking that E = Emax cos(kx - wt) and I think

    E = (20V/m) cos[(0.1121)(x) - (33615041)(t)]

    where 0.1121 is k (k=2pi / λ)

    and where 33615041 is ω (ω = 2πf)



    What would I do with regards to x and t in the equation?
     
  2. jcsd
  3. Jun 10, 2012 #2
    The amplitude of the wave is given to you, and that is the magnitude of the electric field when it is maximal, isn't it?

    Edit: wait, why are you asking about [itex]E_\text{max}[/itex] when you already observed it's [itex]20 \; \text{V/m}[/itex]
     
  4. Jun 10, 2012 #3
    I didn't really see that... thanks

    I got the rest of the problem as well.
     
    Last edited: Jun 10, 2012
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