  Introductory calculus-based physics textbooks state that electromagnetic
waves are transverse and list many of their properties, but most such textbooks
do not bring forth arguments why this is so. Both physical and theoretical
arguments are at a level appropriate for students of courses based on such
books, and could be readily used by instructors of such courses. Here, we
discuss two physical arguments (based on polarization experiments and on lack
of monopole electromagnetic radiation), and the full argument for the
transversality of (plane) electromagnetic waves based on the integral Maxwell
equations. We also show, at a level appropriate for the introductory course,
why the electric and magnetic fields in a wave are in phase and the relation of
their magnitudes.
