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Solutions of maxwells equations in Vaccum

  1. May 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Show that the Fields E= Eo exp{i (k.r-ωt)} and B= Bo exp{i(k.r-ωt) are solutions of Maxwell's Equations in source free vaccum.Starting with maxwells equations in vaccum.
    And there by Derive the relations between the Magnitudes & Phases of
    Eo, Bo, ω, k, & c. And the directions of Unit vectors Eo,Bo,& k.

    Hint( Should only need the fact that Del (k.r) = k .

    2. Relevant equations

    Div E = 0.

    Div B = 0.

    Curl E= - (1/c)d/dt(B)

    curl B = (1/c) d/dt(E).

    atempt at a solution[/b]

    How to solve these Equations. to obtain the Electric & Magnetic Feilds.

    Atleast give me Hint.. how to start this..

    iam really trying hard on this...
     
  2. jcsd
  3. May 11, 2009 #2

    diazona

    User Avatar
    Homework Helper

    Really? I couldn't tell from your post :biggrin:

    Here's your first hint: read the question. (I've found that to be pretty useful myself) "Show that the fields [tex]\vec{E} = \vec{E}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}[/tex] and [tex]\vec{B} = \vec{B}_0 e^{i(\vec{k}\cdot\vec{r} - \omega t)}[/tex] are solutions of Maxwell's equations..." Surely you can do that? Just plug them in and see what you get.
     
  4. May 17, 2009 #3
    thank U very much diazona........
     
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