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 I will have a follow-up question)

  • $\begingroup$ Indeed, no matter what number is in the denominator the force is small but non-zero. $\endgroup$
    – Triatticus
    Aug 5 '18 at 1:48
  • $\begingroup$ Ok. So 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) $\endgroup$
    – fibo11235
    Aug 5 '18 at 1:52

Yes, a static (not screened) charge will produce very small Coulomb force at a very long distance of millions of light years, but only if the charge has been static for millions of years.

  • $\begingroup$ Ok. So it is possible for someone to see a charge at rest enact a force other than q1q2/r^2 radially on another charge which is also at rest in that frame? $\endgroup$
    – fibo11235
    Aug 5 '18 at 2:26
  • $\begingroup$ Static charges only feel the basic electric potential and the force between them is this. The mass of the charged particle will be interacting with the masses in its region, so there is another force acting, but not on the charge. $\endgroup$
    – anna v
    Aug 5 '18 at 3:23
  • $\begingroup$ @fibo11235 : I guess so, if the charge at rest was brought to rest recently, so there was not enough time for the Coulomb field to settle at a distant location. $\endgroup$
    – akhmeteli
    Aug 5 '18 at 4:12

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