Sources of Electromagnetic Waves

A stationary charge is not enough. A charge sitting perfectly still produces only a static electric field around it, unchanging in time -- no magnetic field, and certainly no wave. A charge moving with CONSTANT velocity produces a steady magnetic field as well (this is exactly Oersted's and Ampère's original discovery), but this field, too, does not radiate outward as a wave; it simply moves along with the charge. It is only when a charge ACCELERATES -- speeds up, slows down, or, most usefully, oscillates back and forth (which is a continuous acceleration/deceleration) -- that both its electric and magnetic fields begin to change with time at every point in the surrounding space, and it is precisely this time-varying pair of fields that becomes a self-propagating electromagnetic wave, detaching itself from the charge and travelling outward long after the charge's own motion has stopped influencing it directly.

The self-sustaining chain. Once set going, the wave needs no further help from the original charge to keep travelling. At any point just ahead of the disturbance, the changing electric field there acts, by the Ampère-Maxwell law of Section 8.2, as a displacement current, and so produces a changing MAGNETIC field a little further along. That changing magnetic field, in turn, by Faraday's law (met in the Electromagnetic Induction chapter), induces a changing ELECTRIC field still further along. Each field regenerates the other, indefinitely, so the disturbance keeps recreating itself and moving forward through space -- a genuinely self-sustaining process needing no external agent once it has begun, and, since it needs no material medium to carry the disturbance the way a mechanical wave needs air or a string, it can travel just as well through empty vacuum (Exercise 4 works through this point directly). …