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Show that a longitudinal wave is electrostatic

  1. Jan 13, 2009 #1
    1. The problem statement, all variables and given/known data
    Show that all longitudinal waves must be electrostatic by using Faraday's law.


    2. Relevant equations
    Faraday's law:

    [tex]\frac{\partial \vec{B}}{\partial t} = - \nabla \times \vec{E}[/tex]


    3. The attempt at a solution
    Where should I start??
     
  2. jcsd
  3. Jan 13, 2009 #2

    gabbagabbahey

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    A good place to start would be to write down any equations for the electric and magnetic fields (or auxiliary field H) for longitudinal EM waves. Then calculate dB/dt (or dH/dt)....what do you get?
     
  4. Jan 13, 2009 #3
    I tried with

    [tex]\vec{B} = B_0 \sin{[i(kx-\omega t)]}[/tex]

    so

    [tex]\nabla \times \vec{E} = i \omega B_0 \cos{[i(kx-\omega t)]}[/tex]

    But that doesn't really help me.
     
  5. Jan 13, 2009 #4

    gabbagabbahey

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    Don't you mean:

    [tex]\vec{B} = \vec{B_0} \sin{[i(kx-\omega t)]}[/tex]

    and

    [tex]\nabla \times \vec{E} = \Re[i \omega \vec{B_0} \cos{[i(kx-\omega t)]}][/tex]


    ....what is the real part of a purely imaginary number?:wink:
     
  6. Jan 13, 2009 #5
    Sometimes I feel so smart that I dunno what to do with myself. ;) Thanks!
     
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