Relativistic derivations of the electric and magnetic fields generated   by an electric point charge moving with constant velocity
  We propose a simple relativistic derivation of the electric and the magnetic fields generated by an electric point charge moving with constant velocity. Our approach is based on the radar detection of the point space coordinates where the fields are measured. The same equations were previously derived in a relatively complicated way2 based exclusively on general electromagnetic field equations and without making use of retarded potentials or relativistic equations 
Bernhard Rothenstein, Stefan Popescu, George J. Spix