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Manipulation of Electromagnetic fields using curls clarification

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data
    Question 1. General Plane Waves.
    We may represent a general electromagnetic plane wave by (real part of the complex exponentials)
    [itex]E=E_{0}*e^(i*k*r-iwt) B=B_{0}*e^(i*k*r-iwt)[/itex]

    Show that Faraday's Law becomes iwB0=-ik x Eo
    2. Relevant equations

    dB/dt=- curl of E

    3. The attempt at a solution
    I transformed dB/dt into iwB0e^(ikr-iwt).

    Attempted to perform curl of E on Eoe^(ikr-iwt) but not sure how to work with the r. I thought you might use curl in spherical polars but then you have theta and phi components and I think there's only x, y and z
     
  2. jcsd
  3. Feb 11, 2014 #2

    tiny-tim

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    hi gedanken6! :smile:
    just because there's an r, that doesn't mean it stands for "radius"!

    k*r simply means kxi + kyj + kzk :wink:

    (erm … different k)
     
  4. Feb 11, 2014 #3

    vanhees71

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    No, it's the dot product:
    [tex]\vec{k}\cdot \vec{r}=k_x x+k_y y+k_z z.[/tex]
     
  5. Feb 12, 2014 #4

    tiny-tim

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    oops! :redface:

    thanks, vanhees71! :smile:
     
  6. Feb 12, 2014 #5

    rude man

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    Start with faraday's law, use Stokes' theorem to produce Maxwell's law for del x E, then just use the given plane wave equations to show the validity of the given relationship between E0 and B0, which is just a matter of some differential calculus.
     
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