First we compute x -component E 1 of the electric field (parallel to v → → ): E 1 ( ω ω ) = 2 i q ε ε ( ω ω ) ( 2 π π ) 3 / 2 ∫ ∫ d 3 k e i b k 2 ( ω ω ε ε ( ω ω ) v c 2 − − k 1 ) δ δ ( ω ω − − v k 1 ) k 2 − − ω ω 2 c 2 ε ε ( ω ω )