I'm currently reading about EM waves in my physics course, but there is something that is not clear to me. I know, from Maxwell's equations, that a changing electric field produces a magnetic field and a changing magnetic field likewise produces an electric field. However, it seemed from my reading that the strengths of these fields were constant. Now, my book is talking about the self-propagation of EM waves, and from the sound of it; it would seem as if a changing electric field produces a changing magnetic field, which in turn produces a changing electric field, and so on; propagating forever. So, there are two things I can think of: either I am misunderstanding Maxwell's equations; or there is some other factor I am missing here in understanding what is going on. Does a changing E-field produce a changing B-field or one with a constant strength?