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We learned and prooved in class this property of plane waves: Bz(x,t) = Ey(x,t). So my question is, why doesn't this work for standing waves? I understand that standing waves are a superposition of two plane waves, and something about them doesn't setisfy the linearity of maxwell's equations.. but what exactly is the problem here..?

Thanks for your help :)

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It sounds to me like you already understand how a standing wave is formed. For each of the contributing plane waves, the relationship that the perpendicular components of the E-field and B-fields are in phase and of equal magnitude (for CGS units and vacuum) is true.

Maxwell's equations are linear. Any solutions to this equation can be superposed to make another solution. Hence the standing wave is also a solution.

The property of in phase, equal magnitude E- and B- fields is not a general property of these solutions though. It is true for things that have a form $\vec{E} = \vec{E_0} f(\vec{k}\cdot \vec{r} \pm \omega t)$.

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  • $\begingroup$ Thanks for the answer. I still don't understand one thing - what does "phase" has to do with the E and B magnitude? $\endgroup$
    – PhysicsPrincess
    Nov 23, 2015 at 9:42
  • $\begingroup$ @PhysicsPrincess I'm not with you. Surely your query was why are they not in phase? The phase is not necessarily related to the magnitude. Perhaps I should have rephrased it as "the properties of being in phase or that the E- and B-field have equal magnitude is not a general property..." $\endgroup$
    – ProfRob
    Nov 23, 2015 at 17:09

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