Let us say I have an accelerating charge. At each point x,y,z in its path from my understanding there is a transverse electromagnetic wave being radiated (could also be viewed as a photon). The electric field at any point x1,y1,z1 in the path is disturbed. The moving charge does the same thing all along its path so many electromagnetic waves are created - an infinite amount, one at each point in the path. My question is about what happens to the wave/disturbance created at X1,Y1,Z1 after the charge has passed the point - let's say in some magical way the charge disappears infinitesimally right after X1,Y1, Z1 - there is no more moving charge. Let's also assume that the charge appeared magically an infinitesimal distance from X1,Y1, Z1. So the charge moved a very small distance and then disappeared. What is the fingerprint of the charge after it disappears in the vicinity of X1,Y1, Z1? I am assuming the disturbance spreads out over time from X1,Y1, Z1 - let's assume it's a vacuum that this is happening in. If I put a compass/charge close to X1,Y1, Z1 how long would it show the effect of the moving charge? How would it be calculated? What would happen to compasses/charges put further and further away from X1,Y1, Z1? Would the disturbance die down at all points - some points sooner than others, some points weaker effect than others? One zillion light year away would a super powerful detector of some kind detect the fact that the charge passed X1,Y1, Z1?
As always any feedback is appreciated in advance.