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Are the electric and magnetic fields of an electromagnetic wave perpendicular to each other even in the near-field zone or in the intermediate zone (when the radiation zone approximation is not valid)?

The example given by ProfRob is nice but I would like to know whether E and B fields are always perpendicular for any arbitrary radiation source when the radiation zone approximation is not valid.

Are the electric and magnetic fields of an electromagnetic wave perpendicular to each other even in the near-field zone or in the intermediate zone (when the radiation zone approximation is not valid)?

Are the electric and magnetic fields of an electromagnetic wave perpendicular to each other even in the near-field zone or in the intermediate zone (when the radiation zone approximation is not valid)?

The example given by ProfRob is nice but I would like to know whether E and B fields are always perpendicular for any arbitrary radiation source when the radiation zone approximation is not valid.

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