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Homework Help: Electromagnetic waves and vector calculus

  1. May 23, 2007 #1
    I'm having trouble with electromagnetic waves, perhaps just a vector calculus issue. I'd much appriciate some help in idenfiying it.

    If given say an example in an assignment of an electromagnetic wave:

    E = E_0 cos (omega(sqrt(sigma.mu) z - t )) X
    + E_0 sin (omega(sqrt(sigma.mu) z - t )) Y

    Where bold X & Y have hats on their heads :-D

    If so , what is the vector B
    I'd immediatley assume that it was the same equation, replaced with B_O's instead of E_0's and swapping the cos's with sins's or the X & Y's.

    Simplistic assumption based on the two assumably being mutuall perpendicular and in phase.

    That would lead me to be able to identify the poynting vector S
    I'm wondering if it is the same solution as a monochromatic plane wave, and furthermore what relationship the magnetic energy density and the electric energy density have, over a suitable averaging.

    Thanks for reading, and if you have anything to comment, i'd love to hear it. I'm reading from Griffith Intro to Electro chapter 9 to attempt understanding...

    Andy :-D
  2. jcsd
  3. May 24, 2007 #2


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    Homework Helper
    Gold Member

    That's not right. Remember that [itex]\vec{E}[/itex] satisfies Maxwell's equations. So, what do the first 2 equations in vaccum tell you? From this, can you find the magnetic field?
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