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Electromagnetic field

  1. Oct 24, 2009 #1
    1. The problem statement, all variables and given/known data
    We are given monochromatic point source of EM radiation which power is P=100W. The task is to compute E(r) and B(r). We can assume that r is large enough to treat wave as a plane wave.


    2. Relevant equations



    3. The attempt at a solution

    First of all - what for do we assume that for big r it is plane wave?
    My solution to this task is:

    In a sphere of radius r and thickness dr there is an amount of energy W: [tex]W = P dt = \frac{1}{\epsilon \mu} EB 4 \pi r^2 dr[/tex]
    Then [tex]P = \frac{1}{\epsilon \mu} EB 4 \pi r^2 c \iff EB = \ldots[/tex] and so on... I can easily calculate values of E and B but still - what for is the mentioned assumption?
     
  2. jcsd
  3. Oct 24, 2009 #2

    gabbagabbahey

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    First, why is there a factor of [itex]1/\epsilon[/itex] in your expression? Do the units make sense?

    If the fields aren't those of a plane wave, then the Poynting vector [itex]\textbf{S}=\frac{1}{\mu_0}\textbf{E}\times\textbf{B}[/itex] does not necessarily point in the radial direction and have magnitude [itex]EB[/itex]. The fields themselves could also depend on the polar and azimuthal angles,

    [tex]\implies P(r)=\oint\textbf{S}\cdot d\textbf{a}=\int_0^{\pi}\int_0^{2\pi}\textbf{S}\cdot\hat{\textbf{r}}r^2\sin\theta d\theta d\phi\neq\frac{4\pi r^2}{\mu_0}EB[/tex]

    in general.
     
  4. Oct 25, 2009 #3
    Ok, thanks. I used [tex]\frac{1}{\mu \epsilon} EB[/tex] as an energy density not an energy flux.
     
  5. Oct 25, 2009 #4

    gabbagabbahey

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    But that doesn't even have units of energy density....
     
  6. Oct 25, 2009 #5
    You're right - I made stupid mistake :( Should be: [tex]\frac{1}{\mu c} EB[/tex]
     
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