A simple derivation of the electromagnetic field of an arbitrarily   moving charge
  The expression for the electromagnetic field of a charge moving along an arbitrary trajectory is obtained in a direct, elegant, and Lorentz invariant manner without resorting to more complicated procedures such as differentiation of the Lienard-Wiechert potentials. The derivation uses arguments based on Lorentz invariance and a physically transparent expression originally due to J.J.Thomson for the field of a charge that experiences an impulsive acceleration. 
Hamsa Padmanabhan