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EM waves

  1. Feb 7, 2009 #1
    Show that the electric field: E = Emsin(kx-ωt) and magnetic field: B=Bmsin(kx-ωt) satisfy the following equations:

    [tex]-\frac{\partial B}{\partial x} = \mu_{0}\epsilon_{0}\frac{\partial E}{\partial t}[/tex]

    and

    [tex]\frac{\partial E}{\partial x} = -\frac{\partial B}{\partial t}[/tex]


    I have no idea about this. Would you please guide me for solving this.

    Thanks.
     
    Last edited: Feb 7, 2009
  2. jcsd
  3. Feb 7, 2009 #2

    AEM

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    Your equations didn't come out properly so we can't help you.
     
  4. Feb 7, 2009 #3
    Sorry for my bad Latex typing. :redface:

    I've edited.
     
  5. Feb 8, 2009 #4

    AEM

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    In a situation like this, the usual procedure is to substitute the two given expressions into the differential equation, take the derivatives and see what happens. As I look at what you've been given (without working it out myself) I think you may have to figure out how to relate [tex] \mu_o \epsilon_o [/tex] to k and [tex] \omega [/tex].
    That should get you started. Let us know if you run into trouble.
     
  6. Feb 8, 2009 #5

    AEM

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    Upon reading my previous post, I see a small problem with what I wrote. When you substitute the expressions for E an B into each equation, you'll end up with a [tex] B_m [/tex] on one side and a [tex] E_m [/tex] on the other. That's a nuisance. However, I'll bet you can figure out a way to combine those two equations into one equation and then do the substitution.
     
  7. Feb 8, 2009 #6

    berkeman

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    Staff: Mentor

    IIRC, you would start with Maxwell's equations....
     
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