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**[SOLVED] Maxwell Equations: What are all the assumptions used in derivation?**

I am trying to refute some of the theories of Tesla which are based on his idea that electromagnetic energy is also transmitted via a longitudinal wave. As far as I know Maxwell's equations do not support a longitudinal wave solution.

I would like to understand exactly what are all the assumptions that go into their derivation -- so that essentially for Tesla's theory to be correct one or more of those assumptions must be violated.

Thank you.