My mind was blown when I saw it first, so ingrained was the “fact” that E and B are normal to each other for waves in vacuum. I had to recalculate B several times before I believed it. Which makes me worried that some other physics “facts” I now believe unquestioningly have similar holes.
Consider a circularly polarized standing wave with the electric field of the form E=E0cos(kz)(cos(wt)x-hat—sin(wt)y-hat).
Ah, I see. They’re offset along the z-direction, rather than in the x-y plane.
Huh.
My mind was blown when I saw it first, so ingrained was the “fact” that E and B are normal to each other for waves in vacuum. I had to recalculate B several times before I believed it. Which makes me worried that some other physics “facts” I now believe unquestioningly have similar holes.
… oh.