Infinitesimal Dipole

By Takuichi Hirano (Tokyo Institute of Technology)

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<<Graphics`Colors` ;

<<Graphics`Arrow` ;

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c = 3 * 10^8 ;

ă0 = 1 ;

k0 = (2 ƒÎ)/ƒÉ0 ;

h = ă0/4 ;

Electric Field

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

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

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

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

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

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

Overscript[r,^] . Overscript[z,^] = Cos[Į] ;

Overscript[Į,^] . Overscript[z,^] = Sin[Į] ;

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

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er[r_, Į_, t_] := 2 Cos[Į] (Cos[k0 (c t - r)]/(k0 * r)^2 + Sin[k0 (c t - r)]/(k0 * r)^3) ;

etheta[r_, Į_, t_] := Sin[Į] (Cos[k0 (c t - r)]/(k0 * r)^2 - (1/(k0 * r) - 1/(k0 * r)^3) Sin[k0 (c t - r)]) ;

ex[r_, Į_, \[CurlyPhi]_, t_] := Sin[Į] Cos[\[CurlyPhi]] er[r, Į, t] + Cos[Į] Cos[\[CurlyPhi]] etheta[r, Į, t] ;

ey[r_, Į_, \[CurlyPhi]_, t_] := Sin[Į] Sin[\[CurlyPhi]] er[r, Į, t] + Cos[Į] Sin[\[CurlyPhi]] etheta[r, Į, t] ;

ez[r_, Į_, \[CurlyPhi]_, t_] := Cos[Į] er[r, Į, t] + Sin[Į] etheta[r, Į, t] ;

energy[x_, y_, z_, t_] := Module[{r = (x^2 + y^2 + z^2)^(1/2), Į = ArcCos[z/(x^2 + y^2 + z^2 ... 2)], \[CurlyPhi] = ArcCos[x/(x^2 + y^2)^(1/2)]}, 
ex[r, Į, \[CurlyPhi], t]^2 + ey[r, Į, \[CurlyPhi], t]^2 + ez[r, Į, \[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, (ƒÎ/(c k0)) - 0.001 * (ƒÎ/(c k0)), (ƒÎ/(c k0))/8}]

[Graphics:HTMLFiles/index_23.gif]

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{- DensityGraphics -, - DensityGraphics -, - DensityGraphics -, - DensityGraphics -, - DensityGraphics -, - DensityGraphics -, - DensityGraphics -, - DensityGraphics -}


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