# Electromagnetic waves

I have learned about the electric fields of static charges and those of moving charges. From what I gather(although I have not really learned the specifics) when charges are accelerated they emit electromagntic waves which are essentialy an electromagnetic field progagating through space.

My question is the following: Based on the rules I have learned it seems that if a charge is static in a frame of reference, then its field in that frame of reference will extend out indefinetly. So to someone in that frame, the charge will seem to excert the regular q1q2/r^2 radial force on other charges even if they are millions of light years away?

If yes then at the point in time when the person in the reference frame looks at the distant object and observes the radial force, the distant object has no knowledge of the electrons previous locations in the past x years(x beeing the distance in light years). Can one predict the electromagnetic waves produced by accelerating charges by using relativity arguments based on this?( And also predict the field of moving charges and the same with the magnetic field through similiar arguments)

Can one predict the electromagnetic waves produced by accelerating charges by using relativity arguments based on this?
Predict the waves emanating from the distant object, or from the static frame?

Nugatory
Mentor
the charge will seem to excert the regular q1q2/r^2 radial force on other charges even if they are millions of light years away?
Yes, in principle. In practice, the ##1/r^2## factor means that any great distance the field becomes much too small to detect.
Can one predict the electromagnetic waves produced by accelerating charges by using relativity arguments based on this?( And also predict the field of moving charges and the same with the magnetic field through similiar arguments)
That line of thought is used in at least one undergraduate textbook (Purcell) to explain the origin of electromagnetic radiation. You have to consider the magnetic field together with the electric field and work through Maxwell's equations to get a complete (as opposed to hand-waving heuristic) explanation, but this is a reasonable start.

No relativity is needed, and in fact the history goes the other way: Einstein started with an open problem in classical electromagnetism to arrive at relativity - he introduced relativity in a paper entitled "On the electrodynamics of moving bodies".