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I B field from E

  1. Jul 12, 2016 #1
    Hey guys, i just came across this on my classical physics course.
    So, i'm given that: [tex]E(z, t) = {E_{0}}sin(wt)sin(kz)\widehat{x}[/tex], and i'm supposed to find an expression for the associated magnetic field B.

    Usually, i just find the propagation direction, and do it's cross product with the direction of E, and then write it as [tex]\overrightarrow{B}(r,t)=\frac{1}{c}\widehat{k}\times \overrightarrow{E} [/tex]but in this case, it doesn't seem to be as straightforward.

    I thought of using [tex]\triangledown \times \overrightarrow{E} = -\frac{\partial \overrightarrow{B}}{\partial t}[/tex], finding the curl of E, and then integrate with respect to time, this would give me:

    [tex] B(z, t) = \frac{k}{w}{E_{0}}cos(kz)cos(wt)\widehat{y} [/tex]

    Is this right?
    Thank you.
  2. jcsd
  3. Jul 12, 2016 #2
    Yes seems right to me. It is just that the equation that is given for E, represents a standing wave, so the propagation vector cannot be defined (standing waves do not propagate).
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