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Note, in a plane electromagnetic wave, the wave travels parallel to ##\vec E\times \vec B##.wonderingchicken said:Can we actually distinguish an electric field from a magnetic field in reality?
(Since ##\vec B\times \vec E \neq \vec E\times \vec B## in general, we have that ##\vec E## and ##\vec B## are distinguishable.)
Note:
A proton would feel an electric force parallel to the electric field.
A proton would feel a magnetic force perpendicular to the magnetic field (and perpendicular to its velocity vector).
##\vec F_{Lorentz}=q\vec E + q\vec v\times \vec B##
(This is associated with the fact that electric field is an ordinary [polar] vector
and the magnetic field is an axial vector [so, a pseudovector] .)