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Infinitesimal Dipole

By Takuichi Hirano (Tokyo Institute of Technology)

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Electric Field

$Overscript[r,^] . Overscript[x,^] = Sin[θ] Cos[\[CurlyPhi]] ;$

$Overscript[θ,^] . Overscript[x,^] = Cos[θ] Cos[\[CurlyPhi]] ;$

$Overscript[\[CurlyPhi],^] . Overscript[x,^] = Sin[\[CurlyPhi]] ;$

$Overscript[r,^] . Overscript[y,^] = Sin[θ] Sin[\[CurlyPhi]] ;$

$Overscript[θ,^] . Overscript[y,^] = Cos[θ] Sin[\[CurlyPhi]] ;$

$Overscript[\[CurlyPhi],^] . Overscript[y,^] = Cos[\[CurlyPhi]] ;$

$Overscript[\[CurlyPhi],^] . Overscript[z,^] = 0 ;$

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$ex[r_, θ_, \[CurlyPhi]_, t_] := Sin[θ] Cos[\[CurlyPhi]] er[r, θ, t] + Cos[θ] Cos[\[CurlyPhi]] etheta[r, θ, t] ;$

$ey[r_, θ_, \[CurlyPhi]_, t_] := Sin[θ] Sin[\[CurlyPhi]] er[r, θ, t] + Cos[θ] Sin[\[CurlyPhi]] etheta[r, θ, t] ;$

$ez[r_, θ_, \[CurlyPhi]_, t_] := Cos[θ] er[r, θ, t] + Sin[θ] etheta[r, θ, t] ;$

$energy[x_, y_, z_, t_] := Module[{r = (x^2 + y^2 + z^2)^(1/2), θ = ArcCos[z/(x^2 + y^2 + z^2 ... 2)], \[CurlyPhi] = ArcCos[x/(x^2 + y^2)^(1/2)]}, ex[r, θ, \[CurlyPhi], t]^2 + ey[r, θ, \[CurlyPhi], t]^2 + ez[r, θ, \[CurlyPhi], t]^2 ]$

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Table[DensityPlot[energy[0, x, y, t], {x, -2, 2}, {y, -2, 2}, ColorFunction -> (Hue[-0.7 * (# ... kness[2], Arrow[{0, -0.25}, {0, 0.25}]}], {t, 0, (π/(c k0)) - 0.001 * (π/(c k0)), (π/(c k0))/8}]

[Graphics:HTMLFiles/index_23.gif]

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Created by Mathematica (September 9, 2005)