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In this insight, we shall endeavor in the realm of classical electrodynamics and examine whether EM waves are always transverse. We shall make use of Jefimenko’s equations and Poynting’s Theorem and conclude that
EM waves are always transverse per the weak definition of transverse where we only require the fields to be perpendicular to the propagation vector
EM waves are not always transverse per the strong definition of transverse where we also require that the E and B fields are perpendicular to each other
For what follows we’ll assume that the region of interest where we examine the behavior of the fields is in a vacuum. Similar conclusions should hold for regions filled with linear, isotropic nondispersive materials. This is needed so that the Poynting vector equals a nice simplified form.
We also will assume that there are no boundaries that impose...
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