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Don't bite! This is a very deep question!
From the theoretical perspective, the intensity of the em wave is not
zero when the electric field is zero instantaneously. Why? The
magnetic field is in its maximum.
For the case of plane waves in vacuum, the electric and magnetic fields
are in phase with each other. When the electric field is zero, the
magnetic field is zero.
See, for instance, Classical Electrodynamics 2nd Edition, by John David
Jackson, page 271, where Jackson writes: "If [bold] n is real, (7.11)
implies that [script bold] E and [script bold] B have the same phase."
(Equation 7.11 reads: B = sqrt(mu epsilon) n x E where the n is printed
in boldface, the B and E are printed in script boldface, and the x is
the cross product symbol.)