Why two formulas for the electric field intensity and the magnetic   induction created by a uniformly moving point charge?
  A derivation of the electric field intensity and of the magnetic induction generated by a uniformly moving point charge is presented. The derivation is in accordance with the fact that the electric and magnetic fields of moving charge are propagating from the charge with speed $c$ in empty space. The derivation is tailored for a special audience who knows the transformation of space, time and fields and Coulomb's law in the rest frame of the point charge. It avoids the use of Maxwell's equations and the concept of retarded potential. 
Bernard Rothenstein, Ioan Zaharie