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Velocity of propagation of an EM field in vacuum

  1. Feb 20, 2016 #1
    1. The problem statement, all variables and given/known data

    In a region of empty space, the magnetic field is described by ##\vec{B} = B_0e^{ax}\sin{(ky-\omega t)} \hat{z}##. Find the speed of propagation ##\vec{v}## of this field.

    2. Relevant equations

    ##\Delta \vec{B} = \frac{1}{v^2}\frac{d^2\vec{B}}{dt^2}## , ##k=\frac{\omega }{ v}##

    3. The attempt at a solution

    I'm not sure of a way to calculate the velocity. Do I have to take into account the equation, or because the wave is propagating in empty space can I simply say ##v=c##? And I know the direction of propagation would be ##\hat{y}## if the term ##e^{ax}## didn't exist, but is it still ##\hat{y}## with it? I really don't understand how that term affects the velocity of propagation.
     
  2. jcsd
  3. Feb 20, 2016 #2

    phyzguy

    User Avatar
    Science Advisor

    Try plugging your expression for B into Maxwell's equations.
     
  4. Feb 21, 2016 #3
    I did that and got #\vec{E}#, but I still don't understand what equation to use to get the velocity.
     
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