This computer the electric field at {x,y,z} and time t for a particle moving along a trajectory w[t] with velocity v[t], acceleration a[t] - those functions must be defined globally - see the example below.

Efull[x_,y_,z_,t_] := Module[{tr,T,u,rvec,sr,srhat,pref,Eout},
pref = 1.0;
rvec = {x,y,z};
tr =T /.  FindRoot[c (t - T) - Sqrt[(rvec - w[T]).(rvec - w[T])],{T,t}];
sr = rvec - w[tr];
srhat = sr/Sqrt[sr.sr];
u = c srhat - v[tr];
Eout = pref Sqrt[sr.sr]/(u.sr)^3 ( (c^2 - v[tr].v[tr]) u + Cross[sr,Cross[u,a[tr]]]);
Return[Eout];
]

Example 1 - full E Field

Set the trajectory, velocity and acceleration.

w[t_] :={0,0, d Cos[wo t]}

v[t_] :={0,0, -d wo Sin[wo t]}

a[t_] := {0,0,-d wo^2 Cos[wo t]}

Set constants relevant to the trajectory.

c = 1.;
d= .01;
wo = 5;
T = 2 Pi/wo;

Calculate the fields in the y - z plane (for x = 0), make contour plots of the magnitude of the electric field, and plot the motion of the particle :

etabvel =Table[ Table[{y,z,Efull[0.,y,z,t].Efull[0.,y,z,t]},{y,-5.,5.,.1},{z,-5.,5,.1}],{t,0,2 T,T/10}];
veltab = Table[Partition[ Flatten[etabvel[[h]]],3],{h,1,Length[etabvel]}];
movvel = Table[ListContourPlot[veltab[[j]],PlotRange->{{-5,5},{-5,5},{-.01,.01}}],{j,1,Length[veltab]}];
charge = Table[Graphics[Point[{0, 5 d Cos[wo t]}],PlotRange->{{-5,5},{-5,5}}],{t,0,2 T,T/10}];
mov = Table[Show[charge[[j]],movvel[[j]]],{j,1,Length[charge]}];

Animate the flip - book.

ListAnimate[mov]