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EM wave

  1. Oct 2, 2009 #1
    1. The problem statement, all variables and given/known data
    A 550 nm harmonic wave whose electric field is in the z direction is traveling in the y direction in vacuum.

    a)find the frequency of the wave
    b)determine [tex]\omega[/tex] and k.
    c)if the electric field amplitude is 600 V/m find the amplitude of the magnetic field.
    d)write an expression for both E(t) and B(t) given that each is zero at x=0 and t=0.


    2. Relevant equations
    [tex]\Psi[/tex](x,t)=Acos(kx-[tex]\omega[/tex]t)+Csin(kx-[tex]\omega[/tex]t)


    3. The attempt at a solution
    I've solved all the other questions but part d is giving me a bit of trouble.

    [tex]\Psi[/tex](x,t)=Acos(kx-[tex]\omega[/tex]t)+Csin(kx-[tex]\omega[/tex]t)
    [tex]\Psi[/tex](0,0)=Acos(0) + Csin(0)
    0=A(1) + C(0)
    therefore A=0 but not necessarily C so i wrote
    E(t)=[tex]\hat{y}[/tex]Csin(kx-[tex]\omega[/tex]t) and
    B(t)=[tex]\hat{z}[/tex]Csin(kx-[tex]\omega[/tex]t)

    This is the part I'm stuck on, I'm unsure on how to solve for the constant C, the amplitude of the function.

    *edit the formatting is a bit off, it should be kx-wt, the w isn't a power of anything.
     
  2. jcsd
  3. Oct 2, 2009 #2

    gabbagabbahey

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    First, [itex]\textbf{E}(\textbf{r},t)=C_E\sin(kx-\omega t)\mathbf{\hat{y}}[/itex] describes an electric field, with amplitude [itex]C_E[/itex], polarized in the [itex]y[/itex]-direction, and traveling in the [itex]x[/itex]-direction....that isn't what the problem statement you've posted asks you to describe....
     
  4. Oct 3, 2009 #3
    Thank you for the quick reply. Since my idea is wrong, could you give me a hint on the correct way to solve the problem.
     
  5. Oct 3, 2009 #4

    gabbagabbahey

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    Remember, the general form of a plane wave, traveling along the direction of [itex]\mathbf{k}[/itex] and polarized in the [itex]\mathbf{\hat{n}}[/itex] direction is [itex]\textbf{E}(\textbf{r},t)=C\sin(\mathbf{k}\cdot\textbf{r}-\omega t)\mathbf{\hat{n}}+D\cos(\mathbf{k}\cdot\textbf{r}-\omega t)\mathbf{\hat{n}}[/tex]

    What would you expect [itex]\mathbf{\hat{n}}[/itex] to be if the field is polarized in the [itex]z[/itex]-direction?

    What would you expect [itex]\mathbf{k}\cdot\textbf{r}[/itex] to be if the field is traveling in the [itex]y[/itex]-direction?
     
    Last edited: Oct 3, 2009
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