I want to show a 3D electric field changing with time in response to the path of a moving charged particle. I have an animation of a particle traveling along a helical path using the parametrization for a helix (cos[t],sin[t], t). I took derivatives of this parametrization to find velocity and acceleration and using geometrized units (q=e0=c=1), subbed this into the equation for the E field of a moving particle :
My plan was to make animations for the moving particle and changing field separately and then show them together. So far I was able to get the moving particle but I can't get an animation for the changing E field yet. I'm thinking this is because I have an E[t] whereas Vectorplot3D needs an x,y,z so I'm not sure how to proceed. Any suggestions would be helpful. Many thanks!
My code so far is as follows. I'm not very adept at this kind of thing yet so I apologize that my code is not as clear as it could be, hopefully what I'm trying to do is clear. (Note - I used a z component of t/4 to adjust the height of the helix to look nice in the animation and I used z=8 in my r' because that appears to be the total height the helix reaches.)
Animate[ParametricPlot3D[{Cos[t], Sin[t], t/4}, {t, 0, u},
ImageSize -> Small,
MeshFunctions -> {#4 &},
Mesh -> {{u}},
MeshStyle -> Red,
Method -> {"BoundaryOffset" -> False},
PlotRange -> {{-2, 2}, {-2, 2}, {0, 8}}] /.
Point -> (Sphere[#, 0.15] &), {u, 10^-8, 30}, AnimationRate -> 0.12]
Rvector = {-Cos[t], -Sin[t], 8 - t/4};
Rnorm = Norm[Rvector];
Vvector = {-Sin[t], Cos[t], 1/4};
Vnorm = Norm[Vvector];
Alpha = Rvector/Rnorm - Vvector;
a = {-Cos[t], -Sin[t], 0};
Evector =
Rnorm/(4*\[Pi] (Rvector.Alpha)^3) ((1 - Vnorm^2)*Alpha +
Cross[Rvector, Cross[Alpha, a]]);
Ex = Evector[[1]];
Ey = Evector[[2]];
Ez = Evector[[3]];
Animate[VectorPlot3D[{Ex, Ey, Ez}, {x, -5, 5}, {y, -5, 5}, {z, -5,
5}], {t, 10^-50, }]