Animated Potential and Field in a Plane 
      Condensor with One Split Electrode

St. Rossegger,  B. Schnizer,

Institut fuer Theoretische Physik
		                           Technische Universitaet Graz
		                           A-8010 Graz, Austria, Europe
		                         Email: schnizer@itp.tu-graz.ac.at

2006-11-10

Needs["Graphics`ComplexMap`"]
Off[General::spell1]
Clear["sc*"]

scgd = 5;
scims = 
        700;
a = {};
step = 0.5;

\(For[i = 0, i < 15, 
          scgh = i; 
scf1[scWw_]\  = \ 
            Exp[scWw]\ ; 
scf2[sctt_]\  = \ 
            sctt/\((1\  - \ sctt)\)\ ; 
scf3[sctp_]\  = \ 
            scgd/π\ \((Log[
                    sctp]\  + \ \((1\  - \ scpa)\)^2/
                      scpa\ \((1/2\ \  - \ 
                        1/\((1\  + \ 
                              sctp)\))\))\)\ \ ; 
scf[
              scWw_]\  = \ 
            scf3[scf2[scf1[scWw]]]\  /. FindRoot[
                Log[scpa] + \(scpa\^2 - 1\)\/\(scpa\ 2\) - \(π\ scgh\)\/scgd, {scpa, 2}]; 
sccm = \ 
            CartesianMap[
              scf, {\(-20\), 5, 1}, {$MachineEpsilon, 
                Pi \((1 - $MachineEpsilon)\), π/15}, 
\ 
              ImageSize\  -> \ 
                scims, 
AxesLabel -> {"x [mm]", "y [mm]"}, PlotRange\  -> {20 {\(-1\), 1}, {\(-0.2\), scgd*2}}, 
              Epilog -> {Thickness[0.011], Hue[0], 
                  Line[{{\(-\ 20\)\ , scgd}, {\(-\ scgh\), 
                        scgd}}], 
Text["1 Volt", {\(-\ 
                          0.6\)\ *20, 1.2*10\ }], GrayLevel[0], 
                  Line[{{20, 0}, {\(-20\), 0}}], 
                  Line[{{20, scgd}, {scgh, 
                        scgd}}]}]; 
a = {a, 
              Sequence[sccm]}; 
i = i + step];\)

\(For[i = 15, i > 0, 
          scgh = i; 
scf1[scWw_]\  = \ 
            Exp[scWw]\ ; 
scf2[sctt_]\  = \ 
            sctt/\((1\  - \ sctt)\)\ ; 
scf3[sctp_]\  = \ 
            scgd/π\ \((Log[
                    sctp]\  + \ \((1\  - \ scpa)\)^2/
                      scpa\ \((1/2\ \  - \ 
                        1/\((1\  + \ 
                              sctp)\))\))\)\ \ ; 
scf[
              scWw_]\  = \ 
            scf3[scf2[scf1[scWw]]]\  /. FindRoot[
                Log[scpa] + \(scpa\^2 - 1\)\/\(scpa\ 2\) - \(π\ scgh\)\/scgd, {scpa, 2}]; 
sccm = \ 
            CartesianMap[
              scf, {\(-20\), 5, 1}, {$MachineEpsilon, 
                Pi \((1 - $MachineEpsilon)\), π/15}, 
\ 
              ImageSize\  -> \ 
                scims, 
AxesLabel -> {"x [mm]", "y [mm]"}, PlotRange\  -> {20 {\(-1\), 1}, {\(-0.2\), scgd*2}}, 
              Epilog -> {Thickness[0.011], Hue[0], 
                  Line[{{\(-\ 20\)\ , scgd}, {\(-\ scgh\), 
                        scgd}}], 
Text["1 Volt", {\(-\ 
                          0.6\)\ *20, 1.2*10\ }], GrayLevel[0], 
                  Line[{{20, 0}, {\(-20\), 0}}], 
                  Line[{{20, scgd}, {scgh, 
                        scgd}}]}]; 
a = {a, 
              Sequence[sccm]}; 
i = i - step];\)

For[i = 25,i > 5,cvw = i;
cvf[
                  cvWw_] = -(cvw/2) + ((scgd Log[((1 - (E^(cvWw + ((cvw π)/(2 scgd)))))/((E^cvWw) - (E^(((cvw π)/(2 scgd))))))])/π);
cvcm = CartesianMap[cvf,{-23, 80, 1},{$MachineEpsilon, π (1 - $MachineEpsilon), π /15},
 ImageSize  ->  scims ,
 PlotRange  -> {20 {-1, 1}, {-0.2, 
                          2  scgd }},
\(AxesLabel -> {"x [mm]", "y [mm]"}\),
Epilog -> {Thickness[
                          0.011], 
                        Line[2 {{-20, 0}, {20, 
                                0}}], 
Line[{{-20, 
                              scgd}, {0, scgd}}], 
                        Line[{{ 20, scgd}, {0, 
                              scgd}}], 
Hue[0], 
                        Line[{{-cvw, scgd}, {0, 
                              scgd}}], 
Text[
                          SequenceForm["Φ = ", 
                            cvV, " Volt"], {- 0.6 *20, 
                            1.2*10 }]}];
a = {a, Sequence[cvcm]};
i = i - 1.5*step];

For[i = 5,i < 25,cvw = i;
cvf[
                  cvWw_] = -(cvw/2) + ((scgd Log[((1 - (E^(cvWw + ((cvw π)/(2 scgd)))))/((E^cvWw) - (E^(((cvw π)/(2 scgd))))))])/π);
cvcm = CartesianMap[cvf,{-23, 80, 1},{$MachineEpsilon, π (1 - $MachineEpsilon), π /15},
 ImageSize  ->  scims ,
 PlotRange  -> {20 {-1, 1}, {-0.2, 
                          2  scgd }},
\(AxesLabel -> {"x [mm]", "y [mm]"}\),
Epilog -> {Thickness[
                          0.011], 
                        Line[2 {{-20, 0}, {20, 
                                0}}], 
Line[{{-20, 
                              scgd}, {0, scgd}}], 
                        Line[{{ 20, scgd}, {0, 
                              scgd}}], 
Hue[0], 
                        Line[{{-cvw, scgd}, {0, 
                              scgd}}], 
Text[
                          SequenceForm["Φ = ", 
                            cvV, " Volt"], {- 0.6 *20, 
                            1.2*10 }]}];
a = {a, Sequence[cvcm]};
i = i + 1.5*step];

SelectionMove[
        EvaluationNotebook[], After, 
        EvaluationCell];
SelectionMove[EvaluationNotebook[], Next, 
        CellGroup];
FrontEndTokenExecute["OpenCloseGroup"];
start /. zeit -> 0.1 // DisplayForm