Effect of Finite Velocity

By Takuichi Hirano (Tokyo Institute of Technology)

Electric Dipole

<< Calculus`VectorAnalysis`

SetCoordinates[Cartesian[x, y, z]]

r[x_, y_, 
          z_] := (Sqrt[(x^2) + (y^2) + (z^2)]);
ϕ[x_, y_, z_] := 
        (q/r)[x, y - d/2, z] + ((-q)/r)[x, y + d/2, z];
e[x_, y_] := 
        Drop[-Grad[ϕ[x, y, 
                0]], -1];
f[d_, x_, y_] = e[x, y];

<< Graphics`PlotField`

q = 1. ;
d = 1. ;
charges[
          d_] := {AbsoluteThickness[2], {{Red, Disk[{0, d/2}, 0.2]}, 
            Circle[{0, d/2}, 0.2]}, 
{{Blue, 
              Disk[{0, -d/2}, 0.2]}}, 
          Circle[{0, -d/2}, 0.2]};
\(g[d_] := 
      PlotVectorField[
        f[d, x, y], {x, \(-5\), 5}, {y, \(-5\), 
          5}, 
ImageSize -> {288, 
            288}, 
PlotRange -> {{\(-5\), 5}, {\(-5\), 
              5}}, 
PlotPoints -> 
          19, 
ScaleFunction -> \((#\^0.2 &)\), 
ScaleFactor -> 
          2, 
Epilog -> {charges[
              d]}]\)
g[d]

Electric Dipole

Map[g[#] &, 
      Table[0.5*
          Sin[x], {x, π/7, π/7 + 2*π - 0.001, π/
            8}]]