I'm reading about electromagnetic waves and I can't make sense of their self-sustaining nature. If a charge accelerates for a moment and then stops a disturbance in the electric field is sent out. This changing electric field creates a changing magnetic field and they continue to sustain each other, propagating infinitely outward. Now, if the source charge were to vanish there would still be a changing E/B field in its immediate vicinity which will continue to exist. Wouldn't this mean that the waves are emitted forever?