Elektrický dipól

Elektrický dipól - jedná se o dvojici bodových nábojů, které se nacházejí ve vzájemné vzdálenosti (Overscript[l,  ->]) . Pro velikosti bodových nábojů platí |(Subscript[Q, 1])| = |(Subscript[Q, 2])| = 
          Q, kde (Subscript[Q, 1]) < 0 a (Subscript[Q, 2]) > 0.

Intenzita elektrického pole dipólu:

Needs["Graphics`PlotField`"]

DipoleE ... graf intenzity elektrického pole dipólu

DipoleE[potencial_, x_, y_] := 
        PlotGradientField[potencial, x, y, PlotPoints -> 30, 
          ScaleFunction -> (1 &), 
          Epilog -> {{Hue[0.95], Disk[{1, 0}, 0.1], GrayLevel[0], 
                Text[StyleForm["+", FontSize -> 24, 
                    FontWeight -> "Bold"], {1, 0}]}, {Hue[0.3], 
                Disk[{-1, 0}, 0.1], GrayLevel[0], 
                Text[StyleForm["-", FontSize -> 24, 
                    FontWeight -> "Bold"], {-1, 0}]}}];

potenciál dipólu:
	Q1 o souřadnicích [1,0] a naboji Q=1
	Q2  o souřadnicích [-1,0] a naboji Q=-1

dipole = 
      1/(Sqrt[(x + 1)^2 + y^2]) - 
        1/(Sqrt[(x - 1)^2 + y^2])

plot1 = 
        DipoleE[dipole, {x, -1.3, 1.3}, {y, -1.3, 1.3}];

Export["dipoleE.jpg", plot1, "JPEG", 
        ImageSize -> {640, 480}];

Ekvipotenciálové plochy dipólu:

DipoleV ... graf ekvipotenciálních ploch dipólu

DipoleV[potencial_, x_, y_] := 
        ContourPlot[potencial, x, y, ContourShading -> False,  
          ContourSmoothing -> True, PlotPoints -> 50, 
          Epilog -> {{Hue[0.95], Disk[{1, 0}, 0.1], GrayLevel[0], 
                Text[StyleForm["+", FontSize -> 24, 
                    FontWeight -> "Bold"], {1, 0}]}, {Hue[0.3], 
                Disk[{-1, 0}, 0.1], GrayLevel[0], 
                Text[StyleForm["-", FontSize -> 24, 
                    FontWeight -> "Bold"], {-1, 0}]}}];

plot2  = 
        DipoleV[dipole, {x, -1.3, 1.3}, {y, -1.3, 1.3}];

Export["dipoleV.jpg", plot2, "JPEG", 
        ImageSize -> {640, 480}];

DipoleE a DipoleV v jednom grafu

DiPictureEV = Show[plot1, plot2];

Export["dipoleEV.jpg", DiPictureEV, "JPEG", 
        ImageSize -> {640, 480}];

Postupné vykreslování siločar - vzdálený pohled na dipól

X[R_, θ_] := R Cos[θ];
Y[R_, θ_] := R Sin[θ];

Diq1 := 0;
Diq2 := 0;

    
For[
Diq1 = 0, 
Diq1 < 
          5, 
DiVector1[Diq1] = 
          Table[{X[Diq1 Sin[t]^2, t], Y[Diq1 Sin[t]^2, t]}, {t, 0, Pi, 
              Pi/50}], 
Diq1++
];

    
For[
Diq2 = 0, 
Diq2 < 
          5, 
DiVector2[Diq2] = 
          Table[{X[Diq2 Sin[t]^2, t], Y[Diq2 Sin[t]^2, t]}, {t, 2 Pi, 
              Pi, -Pi/
                50}], 
Diq2++
];

    
pomDiVector1 = DiVector1[1];
pomDiVector2 = DiVector2[1];

    
For[
DiPom1 = 1, 
DiPom1 < 
          5, 
pomDiVector1 = 
          Append[pomDiVector1, 
            DiVector1[
              DiPom1]], 
DiPom1++
];

    
For[
DiPom2 = 1, 
DiPom2 < 
          5, 
pomDiVector2 = 
          Append[pomDiVector2, 
            DiVector2[
              DiPom2]], 
DiPom2++
];

    
pomDiVector1 = Flatten[pomDiVector1];
pomDiVector2 = Flatten[pomDiVector2];

    
pomDiVector1 = 
        Partition[pomDiVector1, 2];
pomDiVector2 = Partition[pomDiVector2, 2];

DiPicture = 
        Show[
ListPlot[
Take[
              pomDiVector1, 
              Length[pomDiVector1]], 
PlotRange -> {{-1.2, 1.2}, {-2.8, 2.8}}, PlotJoined -> True, 
            Ticks -> None, 
            DisplayFunction -> 
              Identity
], 
ListPlot[
Take[pomDiVector2, 
              Length[pomDiVector1]], 
PlotRange -> {{-1.2, 1.2}, {-2.8, 2.8}}, PlotJoined -> True, 
            Ticks -> None, 
            DisplayFunction -> 
              Identity
], 
Graphics[
{Hue[0.95], Disk[{1/10, 0}, 0.06], 
              GrayLevel[
                0]}
], 
Graphics[
{Hue[0.3], Disk[{-1/10, 0}, 0.06], 
              GrayLevel[0]}
], 
          DisplayFunction -> $DisplayFunction
];

Export["dipole.jpg", DiPicture, "JPEG", 
        ImageSize -> {640, 480}];

DiMovie = 
Table[
Show[
ListPlot[
Take[pomDiVector1, 
                DiN], 
PlotRange -> {{-1.2, 
                    1.2}, {-2.8, 2.8}}, PlotJoined -> True, 
              Ticks -> None, 
              DisplayFunction -> 
                Identity
], 
ListPlot[
Take[pomDiVector2, 
                DiN], 
PlotRange -> {{-1.2, 
                    1.2}, {-2.8, 2.8}}, PlotJoined -> True, 
              Ticks -> None, 
              DisplayFunction -> 
                Identity
], 
Graphics[
{Hue[0.95], Disk[{1/10, 0}, 0.06], 
                GrayLevel[
                  0]}
], 
Graphics[
{Hue[0.3], Disk[{-1/10, 0}, 0.06], 
                GrayLevel[0]}
], 
            DisplayFunction -> $DisplayFunction
], {DiN, 1, Length[pomDiVector2], 2}
];

Export["dipole.avi",  DiMovie,  "AVI", 
        ImageSize -> {400, 300}];

Export["dipole.gif",  DiMovie,  "GIF", 
        ImageSize -> {640, 480}, 
        ConversionOptions -> {"Loop" -> True}];