# Why doesn't the changing field of a moving charge create EM waves? [duplicate]

EM wave phenomenon is usually described as "changing electric field creates changing magnetic field which creates a changing electric field etc."

But fields of a uniformly moving (not accelerating) charge also change, and as far as I can see, all the second-order derivatives in time and space required by the wave equation are in place (because of the 1/r^2 dependence).

So, why doesn't the field of a uniformly moving charge create EM waves all by itself, because of all the second-order derivatives? It seems to me that mathematics requires it.

• A moving charge does emit EM waves, in the form or EM-radiation. This is how radios work. – D. W. Apr 23 '16 at 22:10
• @D.W., shouldn't it be accelerating rather than moving? – Alfred Centauri Apr 23 '16 at 22:26
• Yes, that's true. Charges emit radiation when accelerated. But charges produce electric fields, and their motion (even when moving at constant speed) counts as a changes in the electric field. Jefimenko's equations, will tell the corresponding change in the vector potential, and therefor the EM-fields. – D. W. Apr 23 '16 at 22:32
• @D.W., right but, and again, moving charge does not necessarily radiate. – Alfred Centauri Apr 23 '16 at 22:37
• Thanks for posting everyone. I do mean "moving at constant speed", we are not talking about acceleration here. Just imagine the field of a uniformly moving charge - it will be changing both in space and in time. So the question is why those changes do not start the waves (in every point everywhere, actually). – Vitaly Korzhik Apr 23 '16 at 22:38