On Wed, May 25, 2011 at 6:35 PM, <mix...@bigpond.com> wrote:
>>Maxwell's equations were developed to describe laboratory electricity and >magnetism experiments. >...from which the peculiar perpendicular nature of the phenomenon was already evident. Not really. Electric and magnetic fields in the laboratory do not need to be perpendicular. The question was about em waves, and why they are perpendicular in waves. The reason was only partly evident pre-Maxwell in Faraday's law which indicates that induced electric fields are perpendicular to the changing magnetic field. The understanding that electromagnetic waves are possible required Maxwell's generalization of Ampere's law (his displacement current) which postulated that a changing electric field would also induce a perpendicular magnetic field. This was not observed directly, but only postulated based on the symmetry of the two fields and the ambiguity in Ampere's law as it stood. With this addition, the back-and-forth induction between electric and magnetic fields was recognized, and the displacement current was verified only by the observation of electromagnetic waves. So, the reason the fields in a wave are perpendicular is because the wave is sustained by induced fields, and induced fields are perpendicular to the inducing field. Of course I know, and wrote in the first post, that this merely pushes the question back to why are induced fields perpendicular. Why Faraday's law? Faraday's law (and all of Maxwell's equations) exist because of Coulomb's law and relativity, but unfortunately, the connection is not a simple one to visualize. Then, why Coulomb's law and relativity… >>The equations also require that the field are perpendicular. > I think that was already evident from the experiments, and the maths was designed specifically to encompass this fact (otherwise it would have yielded incorrect results). Again, this is only partly true. The fields don't have to be perpendicular. Only induced fields do, and a wave consists of induced fields, since they can exist in the absence of sources. Since the question was specifically about waves, the explanation comes from Faraday's and the generalized Ampere's laws. If he wanted to know why induced fields must be perpendicular, i.e. why those laws exist, he could have asked that. > Note that Maxwell actually brought together the work done by a number of others and created an encompassing mathematical treatment of their work, but the perpendicular aspect was already in that work. And I said as much in the first post. You must have missed it, which is understandable, since it was pretty dry, and perhaps not explicit enough. Here's what I said, with a small clarification bracketed: "Now, you can ask why induced fields are perpendicular, or what is the reason for Faraday's law. Historically, of course, these laws [like Faraday's law, discovered by others] (Maxwell's laws collectively) were discovered empirically in the laboratory (except for Maxwell's displacement current, which was his stroke of genius)." But as I said above, Maxwell added a critical component, essential to understanding electromagnetic waves, and therefore also why the fields are perpendicular in a wave.
