Let be a parameter and define new electric and magnetic field vectors as linear combinations of
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Let θ be a parameter and define “new” electric and magnetic field vectors as linear combinations of the usual electric and magnetic field vectors:
E' = E' cos θ + cBsin θ
cB' = −E sin θ + cB cos θ.
(a) Show that E' and B' satisfy the Maxwell equations without sources (ρ = j = 0) if E and B satisfy these equations.
(b) Discuss the implications of this result for source-free solutions of the Maxwell equations where E ⊥ B everywhere in space.
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