Time Verying Electromagnetic Fields
It is known that static electric and magnetic fields can be arranged in any manner. Meaning, it is possible to arrange the electric field parallel to the magnetic field. A more interesting question arose within the last 30 years as to whether this is possible for time varying electromagnetic fields.
Are there time varying solutions to Maxwell's equations such that the electric field and the magnetic fields of an electromagnetic wave can be purely parallel.
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1 solution
The electric and magnetic components of a time varying electromagnetic wave that is a solution to Maxwell's equations can have any angle with each other. Somehow, conventioanl wisdom was that the electric and magnetic components must be perpendicular to each other. This is actually true for a monochromatic single harmonic solution. However, more complex solutions lead to that any angle is possible between the electric and magnetic componentns. If we start from the condition that the Poynting vector (which measure the direction energy flow), S = E x B , must be zero, we get E || B solutions. This was the subject of a debate in the journal Physics Review Letter A in 1985 that was settled in favor of that all angles are possible.