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Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}}, {{ Hold[$CellContext`option$$], 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}}, { Hold[ Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = {600., {197., 203.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`fno$292142$$ = False, $CellContext`option$292143$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`fno$$ = 9, $CellContext`option$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`fno$$, $CellContext`fno$292142$$, False], Hold[$CellContext`option$$, $CellContext`option$292143$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`fp$, $CellContext`EE$, $CellContext`uv$, \ $CellContext`xdata$, $CellContext`dx$, $CellContext`ydata$, $CellContext`dy$, \ $CellContext`Eavedata$, $CellContext`urange$, $CellContext`vrange$, \ $CellContext`x1$, $CellContext`x2$, $CellContext`y1$, $CellContext`y2$}, \ $CellContext`f[ Pattern[$CellContext`z$, Blank[]]] = Switch[$CellContext`fno$$, 1, E^$CellContext`z$, 2, Sin[$CellContext`z$], 3, Sin[$CellContext`z$], 4, $CellContext`z$^2, 5, I Cot[$CellContext`z$], 6, (E^$CellContext`z$ + 1)^Rational[1, 2], 7, JacobiSN[$CellContext`z$, 0.5], 8, JacobiCN[$CellContext`z$, 0.2], 9, ($CellContext`z$ + 1 + E^$CellContext`z$)/Pi, 10, (E^$CellContext`z$ + 1)^Rational[1, 2] + (1/2) Log[((E^$CellContext`z$ + 1)^Rational[1, 2] - 1)/((E^$CellContext`z$ + 1)^Rational[1, 2] + 1)]]; $CellContext`fp$[ Pattern[$CellContext`z, Blank[]]] = Derivative[1][$CellContext`f][$CellContext`z]; $CellContext`EE$[ Pattern[$CellContext`z$, Blank[]]] := 1/Abs[ $CellContext`fp$[$CellContext`z$]]; $CellContext`uv$[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Block[{$CellContext`i = $CellContext`f[$CellContext`x + I $CellContext`y]}, { Re[$CellContext`i], Im[$CellContext`i]}]; {$CellContext`xdata$, $CellContext`dx$, \ $CellContext`ydata$, $CellContext`dy$} = Switch[$CellContext`fno$$, 1, {{{-1, 1}, {-0.7, 1}, {0, 1}}, 0.1, {{0, 2 Pi}}, Pi/24}, 2, {{{0, 2 Pi}}, Pi/24, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.1}, 3, {{{-(Pi/2), Pi/2}, {-(5 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Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}, ControlPlacement -> 1}, {{$CellContext`option$$, 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}, ControlPlacement -> 2}, Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]}, "Options" :> { TrackedSymbols :> {$CellContext`fno$$, $CellContext`option$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{643., {250., 255.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->1053691804] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "ManipulateCaptionSection"], Cell[TextData[{ "A conformal mapping ", Cell[BoxData[ FormBox["f", TraditionalForm]], "InlineMath"], " produces a complex function of a complex variable, ", Cell[BoxData[ FormBox[ RowBox[{"w", "=", RowBox[{"f", "(", "z", ")"}]}], TraditionalForm]], "InlineMath"], ", so that the analytical function ", Cell[BoxData[ FormBox["f", TraditionalForm]], "InlineMath"], " maps the complex ", Cell[BoxData[ FormBox["z", TraditionalForm]], "InlineMath"], " plane into the complex ", Cell[BoxData[ FormBox["w", TraditionalForm]], "InlineMath"], " plane. This technique is useful for calculating two-dimensional electric \ fields: the curve in the ", Cell[BoxData[ FormBox["w", TraditionalForm]], "InlineMath"], " plane where either ", Cell[BoxData[ FormBox[ RowBox[{"Re", "[", "z", "]"}], TraditionalForm]], "InlineMath"], " or ", Cell[BoxData[ FormBox[ RowBox[{"Im", "[", "z", "]"}], TraditionalForm]], "InlineMath"], " is constant corresponds to either an equipotential line or electric flux. \ This Demonstration shows 10 examples of electrostatic fields often \ encountered in high voltage applications. The electric field is shown in the ", Cell[BoxData[ FormBox["u", TraditionalForm]], "InlineMath"], "-", Cell[BoxData[ FormBox["v", TraditionalForm]], "InlineMath"], " plane (or the ", Cell[BoxData[ FormBox["w", TraditionalForm]], "InlineMath"], " plane, where ", Cell[BoxData[ FormBox[ RowBox[{"w", "=", RowBox[{"u", "+", RowBox[{"i", " ", "v"}]}]}], TraditionalForm]], "InlineMath"], "). The electrodes correspond to either ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"x", "=", SubscriptBox["x", "1"]}], ",", SubscriptBox["x", "2"]}], TraditionalForm]], "InlineMath"], " or ", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"y", "=", SubscriptBox["y", "1"]}], ",", SubscriptBox["y", "2"]}], TraditionalForm]], "InlineMath"], ", where ", Cell[BoxData[ FormBox[ RowBox[{"z", "=", RowBox[{"x", "+", RowBox[{"i", " ", "y"}]}]}], TraditionalForm]], "InlineMath"], " (", Cell[BoxData[ FormBox[ RowBox[{"x", ",", "y", ",", "u", ",", RowBox[{"v", "\[Element]", "\[DoubleStruckCapitalR]"}]}], TraditionalForm]], "InlineMath"], "). 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The parameters are shown on the right. The calculated electric fields are \ shown by color, normalized to the average field ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["E", "ave"], "=", RowBox[{"|", RowBox[{ SubscriptBox["x", "1"], "-", SubscriptBox["x", "2"]}], "|", RowBox[{"/", "g"}]}]}], TraditionalForm]], "InlineMath"], " or ", Cell[BoxData[ FormBox[ RowBox[{"|", RowBox[{ SubscriptBox["y", "1"], "-", SubscriptBox["y", "2"]}], "|", RowBox[{"/", "g"}]}], TraditionalForm]], "InlineMath"], ", where ", Cell[BoxData[ FormBox["g", TraditionalForm]], "InlineMath"], " is the smallest distance between two electrodes. If you select option 1, \ the local field is high in the vicinity of sharp electrode edges. When \ selecting option 2 or 3, the values are reduced owing to blunted edge \ conditions. The white lines indicate the flux line and the dashed lines are \ the equipotential lines for constant ", Cell[BoxData[ FormBox["x", TraditionalForm]], "InlineMath"], " or constant ", Cell[BoxData[ FormBox["y", TraditionalForm]], "InlineMath"], ". Those two families of curves are orthogonal." }], "ManipulateCaption", CellChangeTimes->{ 3.564247809191179*^9, {3.5642479588825827`*^9, 3.5642479589535894`*^9}, { 3.56632010441123*^9, 3.566320127384328*^9}, {3.5663201955314093`*^9, 3.566320262105858*^9}, {3.566320315401762*^9, 3.566320324850191*^9}, { 3.5663745585786*^9, 3.5663745614022045`*^9}, {3.5663746010106745`*^9, 3.566374606408284*^9}, {3.5663746585123754`*^9, 3.566374800410225*^9}, { 3.566619945676256*^9, 3.566619972645006*^9}, {3.566620006082506*^9, 3.566620065191881*^9}, {3.566620131270006*^9, 3.566620187332506*^9}, { 3.566620274457506*^9, 3.566620283676256*^9}, {3.566620316363756*^9, 3.566620408129381*^9}, {3.566632810598075*^9, 3.566632815590084*^9}, { 3.566632980917765*^9, 3.566632980948965*^9}, {3.5678933691602488`*^9, 3.567893477461545*^9}, {3.5678935245110083`*^9, 3.567893583493779*^9}, { 3.567893791734124*^9, 3.5678937931596947`*^9}, {3.5679143978725147`*^9, 3.567914401429321*^9}, {3.5679587372037487`*^9, 3.567958737427206*^9}, { 3.567958767980932*^9, 3.56795877006022*^9}, 3.5679594183691874`*^9, { 3.567959561639433*^9, 3.5679596124775677`*^9}, {3.567961368651864*^9, 3.56796137155352*^9}}, CellID->435651577] }, Open ]], Cell[CellGroupData[{ Cell["", "ThumbnailSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`fno$$ = 9, $CellContext`option$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fno$$], 9, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}}, {{ Hold[$CellContext`option$$], 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}}, { Hold[ Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`fno$292197$$ = False, $CellContext`option$292198$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`fno$$ = 9, $CellContext`option$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`fno$$, $CellContext`fno$292197$$, False], Hold[$CellContext`option$$, $CellContext`option$292198$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`fp$, $CellContext`EE$, $CellContext`uv$, \ $CellContext`xdata$, $CellContext`dx$, $CellContext`ydata$, $CellContext`dy$, \ $CellContext`Eavedata$, $CellContext`urange$, $CellContext`vrange$, \ $CellContext`x1$, $CellContext`x2$, $CellContext`y1$, $CellContext`y2$}, \ $CellContext`f[ Pattern[$CellContext`z$, Blank[]]] = Switch[$CellContext`fno$$, 1, E^$CellContext`z$, 2, Sin[$CellContext`z$], 3, Sin[$CellContext`z$], 4, $CellContext`z$^2, 5, I Cot[$CellContext`z$], 6, (E^$CellContext`z$ + 1)^Rational[1, 2], 7, JacobiSN[$CellContext`z$, 0.5], 8, JacobiCN[$CellContext`z$, 0.2], 9, ($CellContext`z$ + 1 + E^$CellContext`z$)/Pi, 10, (E^$CellContext`z$ + 1)^Rational[1, 2] + (1/2) Log[((E^$CellContext`z$ + 1)^Rational[1, 2] - 1)/((E^$CellContext`z$ + 1)^Rational[1, 2] + 1)]]; $CellContext`fp$[ Pattern[$CellContext`z, Blank[]]] = Derivative[1][$CellContext`f][$CellContext`z]; $CellContext`EE$[ Pattern[$CellContext`z$, Blank[]]] := 1/Abs[ $CellContext`fp$[$CellContext`z$]]; $CellContext`uv$[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Block[{$CellContext`i = $CellContext`f[$CellContext`x + I $CellContext`y]}, { Re[$CellContext`i], Im[$CellContext`i]}]; {$CellContext`xdata$, $CellContext`dx$, \ $CellContext`ydata$, $CellContext`dy$} = Switch[$CellContext`fno$$, 1, {{{-1, 1}, {-0.7, 1}, {0, 1}}, 0.1, {{0, 2 Pi}}, Pi/24}, 2, {{{0, 2 Pi}}, Pi/24, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.1}, 3, {{{-(Pi/2), Pi/2}, {-(5 Pi/12), 5 Pi/12}, {-(2 Pi/6), 2 Pi/6}}, Pi/24, {{-1.5, 1.5}}, 0.1}, 4, {{{-1.2, 1.2}}, 0.05, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.05}, 5, {{{-(Pi/2), Pi/2}}, Pi/24, {{-1, 1}, {-0.8, 0.8}, {-0.5, 0.5}}, 0.1}, 6, {{{-1.2, 2}, {-0.8, 2}, {-0.4, 2}}, 0.2, {{-Pi, Pi}}, Pi/ 18}, 7, {{{-1.854, 1.854}, {-1.483, 1.483}, {-0.927, 0.927}}, 0.1854, {{-1.854, 1.854}}, 0.1854}, 8, {{{-3.319, 0}}, 0.16596, {{0, 2.257}, {0, 2.031}, {0.226, 2.257}}, 0.11285}, 9, {{{-8, 2.5}}, 0.25, {{-Pi, Pi}, {-(2 Pi/3), 2 Pi/3}, {-(Pi/2), Pi/2}}, Pi/12}, 10, {{{-4, 3}}, 0.2, {{0, 3.139}, {0, 2.877}, {0, 2.354}}, 0.261538}]; $CellContext`Eavedata$ = Switch[$CellContext`fno$$, 1, {{2.35, 0.851}, {2.222, 0.765}, {1.718, 0.582}}, 2, {{0.543, 1.841}, {0.538, 1.673}, {0.498, 1.406}}, 3, {{2., 1.571}, {1.932, 1.355}, {1.732, 1.209}}, 4, {{1., 1.}, { 0.99, 0.909}, {0.91, 0.769}}, 5, {{1.5232, 1.313}, {1.328, 1.205}, {0.924, 1.08}}, 6, {{1.756, 1.823}, {1.693, 1.654}, {1.604, 1.496}}, 7, {{2., 1.854}, {1.93, 1.537}, {1.531, 1.211}}, 8, {{2., 1.129}, {1.95, 1.042}, {1.797, 0.1129}}, 9, {{2., 3.141}, {1.334, 3.141}, {1., 3.141}}, 10, {{1.569, 1.999}, {1.437, 1.998}, {1.18, 1.994}}]; {$CellContext`urange$, $CellContext`vrange$} = Switch[$CellContext`fno$$, 1, {{-3, 3}, {-3, 3}}, 2, {{-1.6, 1.6}, {-1.6, 1.6}}, 3, {{-1.6, 1.6}, {-1.6, 1.6}}, 4, {{-1, 1}, {-1, 1}}, 5, {{-2.5, 2.5}, {-2.5, 2.5}}, 6, {{-1.2, 4}, {-2.6, 2.6}}, 7, {{-2, 2}, {-2, 2}}, 8, {{-2.5, 2.5}, {-0.25, 4.75}}, 9, {{-2, 2}, {-2, 2}}, 10, {{-1.5, 1.5}, {0, 3}}]; If[Length[$CellContext`xdata$] == 3, {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, $CellContext`option$$]; \ {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, 1], {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, 1]; {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, $CellContext`option$$]]; Pane[ Row[{ Show[ Graphics[ Table[{ $CellContext`huefunc[$CellContext`EE$[$CellContext`x + I $CellContext`y]/(2 Part[$CellContext`Eavedata$, $CellContext`option$$, 2])], Polygon[{ $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/2], $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/ 2]}]}, {$CellContext`x, $CellContext`x1$ + \ $CellContext`dx$/2, $CellContext`x2$ - $CellContext`dx$/ 2, $CellContext`dx$}, {$CellContext`y, $CellContext`y1$ + \ $CellContext`dy$/2, $CellContext`y2$ - $CellContext`dy$/ 2, $CellContext`dy$}]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White}, {White, Dashing[{0.02, 0.005}]}]]& , Table[(1 - $CellContext`t) {$CellContext`x1$, $CellContext`y} + \ $CellContext`t {$CellContext`x2$, $CellContext`y}, {$CellContext`y, \ $CellContext`y1$, $CellContext`y2$, $CellContext`dy$}]]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White, Dashing[{0.02, 0.005}]}, {White}]]& , Table[(1 - $CellContext`t) {$CellContext`x, $CellContext`y1$} + \ $CellContext`t {$CellContext`x, $CellContext`y2$}, {$CellContext`x, \ $CellContext`x1$, $CellContext`x2$, $CellContext`dx$}]]], If[Length[$CellContext`xdata$] == 3, ParametricPlot[{ $CellContext`uv$[$CellContext`x1$, $CellContext`y], $CellContext`uv$[$CellContext`x2$, $CellContext`y]}, \ {$CellContext`y, $CellContext`y1$, $CellContext`y2$}, PlotStyle -> {{Black, Thickness[0.01]}}], ParametricPlot[{ $CellContext`uv$[$CellContext`x, $CellContext`y1$], $CellContext`uv$[$CellContext`x, $CellContext`y2$]}, \ {$CellContext`x, $CellContext`x1$, $CellContext`x2$}, PlotStyle -> {{Black, Thickness[0.01]}}]], Frame -> True, FrameLabel -> {{ Style["v", Italic], None}, { Style["u", Italic], Row[{ Style["u", Italic], " + ", Style["i v", Italic], " = ", Style["f", Italic], "(", Style["x", Italic], " + ", Style["i y", Italic], ") "}]}}, PlotRangeClipping -> True, PlotRange -> {$CellContext`urange$, $CellContext`vrange$}, Epilog -> If[Length[$CellContext`xdata$] == 3, Table[ Inset[ Framed[ Style[ Subscript[ Style["x", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3] + {0, -0.2}, { Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}], Table[ Inset[ Framed[ Style[ Subscript[ Style["y", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[( 2 $CellContext`x1$ + $CellContext`x2$)/3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]] + {0, -0.2}, { Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}]], LabelStyle -> {FontSize -> 14}, ImageSize -> 350], Spacer[20], Column[{ Text[ Style[ Grid[{{"option", 1, 2, 3}, Join[{ Row[{ Subscript[ Style["x", Italic], 1], "/", Subscript[ Style["x", Italic], 2]}]}, Table[ If[Length[$CellContext`xdata$] == 3, Row[{ Part[$CellContext`xdata$, $CellContext`i, 1], "/", Part[$CellContext`xdata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{ Row[{ Subscript[ Style["y", Italic], 1], "/", Subscript[ Style["y", Italic], 2]}]}, Table[ If[Length[$CellContext`ydata$] == 3, Row[{ Part[$CellContext`ydata$, $CellContext`i, 1], "/", Part[$CellContext`ydata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{"gap"}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 1], 0.01], {$CellContext`i, 3}]], Join[{ Subscript[ Style[" E", Italic], "ave"]}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 2], 0.01], {$CellContext`i, 3}]]}, Frame -> All, Alignment -> Center], 14]], Spacer[100], DensityPlot[ 0.5 $CellContext`y, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 2}, PlotRange -> {{0, 1}, {0, 2}}, ColorFunctionScaling -> False, AspectRatio -> 12, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Column[{ Style["electric field", 14], Row[{ Style["E", Italic], "/", Subscript[ Style["E", Italic], "ave"]}]}, Center], ImageSize -> {75, 250}, ImagePadding -> {{30, 30}, {10, 10}}]}]}], ImageSize -> {600, 400}]], "Specifications" :> {{{$CellContext`fno$$, 9, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}, ControlPlacement -> 1}, {{$CellContext`option$$, 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}, ControlPlacement -> 2}, Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]}, "Options" :> { TrackedSymbols :> {$CellContext`fno$$, $CellContext`option$$}}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->1247996666] }, Open ]], Cell[CellGroupData[{ Cell["", "SnapshotsSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`fno$$ = 3, $CellContext`option$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fno$$], 3, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}}, {{ Hold[$CellContext`option$$], 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}}, { Hold[ Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`fno$292252$$ = False, $CellContext`option$292253$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`fno$$ = 3, $CellContext`option$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`fno$$, $CellContext`fno$292252$$, False], Hold[$CellContext`option$$, $CellContext`option$292253$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`fp$, $CellContext`EE$, $CellContext`uv$, \ $CellContext`xdata$, $CellContext`dx$, $CellContext`ydata$, $CellContext`dy$, \ $CellContext`Eavedata$, $CellContext`urange$, $CellContext`vrange$, \ $CellContext`x1$, $CellContext`x2$, $CellContext`y1$, $CellContext`y2$}, \ $CellContext`f[ Pattern[$CellContext`z$, Blank[]]] = Switch[$CellContext`fno$$, 1, E^$CellContext`z$, 2, Sin[$CellContext`z$], 3, Sin[$CellContext`z$], 4, $CellContext`z$^2, 5, I Cot[$CellContext`z$], 6, (E^$CellContext`z$ + 1)^Rational[1, 2], 7, JacobiSN[$CellContext`z$, 0.5], 8, JacobiCN[$CellContext`z$, 0.2], 9, ($CellContext`z$ + 1 + E^$CellContext`z$)/Pi, 10, (E^$CellContext`z$ + 1)^Rational[1, 2] + (1/2) Log[((E^$CellContext`z$ + 1)^Rational[1, 2] - 1)/((E^$CellContext`z$ + 1)^Rational[1, 2] + 1)]]; $CellContext`fp$[ Pattern[$CellContext`z, Blank[]]] = Derivative[1][$CellContext`f][$CellContext`z]; $CellContext`EE$[ Pattern[$CellContext`z$, Blank[]]] := 1/Abs[ $CellContext`fp$[$CellContext`z$]]; $CellContext`uv$[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Block[{$CellContext`i = $CellContext`f[$CellContext`x + I $CellContext`y]}, { Re[$CellContext`i], Im[$CellContext`i]}]; {$CellContext`xdata$, $CellContext`dx$, \ $CellContext`ydata$, $CellContext`dy$} = Switch[$CellContext`fno$$, 1, {{{-1, 1}, {-0.7, 1}, {0, 1}}, 0.1, {{0, 2 Pi}}, Pi/24}, 2, {{{0, 2 Pi}}, Pi/24, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.1}, 3, {{{-(Pi/2), Pi/2}, {-(5 Pi/12), 5 Pi/12}, {-(2 Pi/6), 2 Pi/6}}, Pi/24, {{-1.5, 1.5}}, 0.1}, 4, {{{-1.2, 1.2}}, 0.05, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.05}, 5, {{{-(Pi/2), Pi/2}}, Pi/24, {{-1, 1}, {-0.8, 0.8}, {-0.5, 0.5}}, 0.1}, 6, {{{-1.2, 2}, {-0.8, 2}, {-0.4, 2}}, 0.2, {{-Pi, Pi}}, Pi/ 18}, 7, {{{-1.854, 1.854}, {-1.483, 1.483}, {-0.927, 0.927}}, 0.1854, {{-1.854, 1.854}}, 0.1854}, 8, {{{-3.319, 0}}, 0.16596, {{0, 2.257}, {0, 2.031}, {0.226, 2.257}}, 0.11285}, 9, {{{-8, 2.5}}, 0.25, {{-Pi, Pi}, {-(2 Pi/3), 2 Pi/3}, {-(Pi/2), Pi/2}}, Pi/12}, 10, {{{-4, 3}}, 0.2, {{0, 3.139}, {0, 2.877}, {0, 2.354}}, 0.261538}]; $CellContext`Eavedata$ = Switch[$CellContext`fno$$, 1, {{2.35, 0.851}, {2.222, 0.765}, {1.718, 0.582}}, 2, {{0.543, 1.841}, {0.538, 1.673}, {0.498, 1.406}}, 3, {{2., 1.571}, {1.932, 1.355}, {1.732, 1.209}}, 4, {{1., 1.}, { 0.99, 0.909}, {0.91, 0.769}}, 5, {{1.5232, 1.313}, {1.328, 1.205}, {0.924, 1.08}}, 6, {{1.756, 1.823}, {1.693, 1.654}, {1.604, 1.496}}, 7, {{2., 1.854}, {1.93, 1.537}, {1.531, 1.211}}, 8, {{2., 1.129}, {1.95, 1.042}, {1.797, 0.1129}}, 9, {{2., 3.141}, {1.334, 3.141}, {1., 3.141}}, 10, {{1.569, 1.999}, {1.437, 1.998}, {1.18, 1.994}}]; {$CellContext`urange$, $CellContext`vrange$} = Switch[$CellContext`fno$$, 1, {{-3, 3}, {-3, 3}}, 2, {{-1.6, 1.6}, {-1.6, 1.6}}, 3, {{-1.6, 1.6}, {-1.6, 1.6}}, 4, {{-1, 1}, {-1, 1}}, 5, {{-2.5, 2.5}, {-2.5, 2.5}}, 6, {{-1.2, 4}, {-2.6, 2.6}}, 7, {{-2, 2}, {-2, 2}}, 8, {{-2.5, 2.5}, {-0.25, 4.75}}, 9, {{-2, 2}, {-2, 2}}, 10, {{-1.5, 1.5}, {0, 3}}]; If[Length[$CellContext`xdata$] == 3, {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, $CellContext`option$$]; \ {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, 1], {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, 1]; {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, $CellContext`option$$]]; Pane[ Row[{ Show[ Graphics[ Table[{ $CellContext`huefunc[$CellContext`EE$[$CellContext`x + I $CellContext`y]/(2 Part[$CellContext`Eavedata$, $CellContext`option$$, 2])], Polygon[{ $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/2], $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/ 2]}]}, {$CellContext`x, $CellContext`x1$ + \ $CellContext`dx$/2, $CellContext`x2$ - $CellContext`dx$/ 2, $CellContext`dx$}, {$CellContext`y, $CellContext`y1$ + \ $CellContext`dy$/2, $CellContext`y2$ - $CellContext`dy$/ 2, $CellContext`dy$}]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White}, {White, Dashing[{0.02, 0.005}]}]]& , Table[(1 - $CellContext`t) {$CellContext`x1$, $CellContext`y} + \ $CellContext`t {$CellContext`x2$, $CellContext`y}, {$CellContext`y, \ $CellContext`y1$, $CellContext`y2$, $CellContext`dy$}]]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White, Dashing[{0.02, 0.005}]}, {White}]]& , Table[(1 - $CellContext`t) {$CellContext`x, $CellContext`y1$} + \ $CellContext`t {$CellContext`x, $CellContext`y2$}, {$CellContext`x, \ $CellContext`x1$, $CellContext`x2$, $CellContext`dx$}]]], If[Length[$CellContext`xdata$] == 3, ParametricPlot[{ $CellContext`uv$[$CellContext`x1$, $CellContext`y], $CellContext`uv$[$CellContext`x2$, $CellContext`y]}, \ {$CellContext`y, $CellContext`y1$, $CellContext`y2$}, PlotStyle -> {{Black, Thickness[0.01]}}], ParametricPlot[{ $CellContext`uv$[$CellContext`x, $CellContext`y1$], $CellContext`uv$[$CellContext`x, $CellContext`y2$]}, \ {$CellContext`x, $CellContext`x1$, $CellContext`x2$}, PlotStyle -> {{Black, Thickness[0.01]}}]], Frame -> True, FrameLabel -> {{ Style["v", Italic], None}, { Style["u", Italic], Row[{ Style["u", Italic], " + ", Style["i v", Italic], " = ", Style["f", Italic], "(", Style["x", Italic], " + ", Style["i y", Italic], ") "}]}}, PlotRangeClipping -> True, PlotRange -> {$CellContext`urange$, $CellContext`vrange$}, Epilog -> If[Length[$CellContext`xdata$] == 3, Table[ Inset[ Framed[ Style[ Subscript[ Style["x", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3] + {0, -0.2}, { Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}], Table[ Inset[ Framed[ Style[ Subscript[ Style["y", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[( 2 $CellContext`x1$ + $CellContext`x2$)/3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]] + {0, -0.2}, { Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}]], LabelStyle -> {FontSize -> 14}, ImageSize -> 350], Spacer[20], Column[{ Text[ Style[ Grid[{{"option", 1, 2, 3}, Join[{ Row[{ Subscript[ Style["x", Italic], 1], "/", Subscript[ Style["x", Italic], 2]}]}, Table[ If[Length[$CellContext`xdata$] == 3, Row[{ Part[$CellContext`xdata$, $CellContext`i, 1], "/", Part[$CellContext`xdata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{ Row[{ Subscript[ Style["y", Italic], 1], "/", Subscript[ Style["y", Italic], 2]}]}, Table[ If[Length[$CellContext`ydata$] == 3, Row[{ Part[$CellContext`ydata$, $CellContext`i, 1], "/", Part[$CellContext`ydata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{"gap"}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 1], 0.01], {$CellContext`i, 3}]], Join[{ Subscript[ Style[" E", Italic], "ave"]}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 2], 0.01], {$CellContext`i, 3}]]}, Frame -> All, Alignment -> Center], 14]], Spacer[100], DensityPlot[ 0.5 $CellContext`y, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 2}, PlotRange -> {{0, 1}, {0, 2}}, ColorFunctionScaling -> False, AspectRatio -> 12, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Column[{ Style["electric field", 14], Row[{ Style["E", Italic], "/", Subscript[ Style["E", Italic], "ave"]}]}, Center], ImageSize -> {75, 250}, ImagePadding -> {{30, 30}, {10, 10}}]}]}], ImageSize -> {600, 400}]], "Specifications" :> {{{$CellContext`fno$$, 3, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}, ControlPlacement -> 1}, {{$CellContext`option$$, 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}, ControlPlacement -> 2}, Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]}, "Options" :> { TrackedSymbols :> {$CellContext`fno$$, $CellContext`option$$}}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->607185213], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`fno$$ = 9, $CellContext`option$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fno$$], 9, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}}, {{ Hold[$CellContext`option$$], 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}}, { Hold[ Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`fno$292307$$ = False, $CellContext`option$292308$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`fno$$ = 9, $CellContext`option$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`fno$$, $CellContext`fno$292307$$, False], Hold[$CellContext`option$$, $CellContext`option$292308$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`fp$, $CellContext`EE$, $CellContext`uv$, \ $CellContext`xdata$, $CellContext`dx$, $CellContext`ydata$, $CellContext`dy$, \ $CellContext`Eavedata$, $CellContext`urange$, $CellContext`vrange$, \ $CellContext`x1$, $CellContext`x2$, $CellContext`y1$, $CellContext`y2$}, \ $CellContext`f[ Pattern[$CellContext`z$, Blank[]]] = Switch[$CellContext`fno$$, 1, E^$CellContext`z$, 2, Sin[$CellContext`z$], 3, Sin[$CellContext`z$], 4, $CellContext`z$^2, 5, I Cot[$CellContext`z$], 6, (E^$CellContext`z$ + 1)^Rational[1, 2], 7, JacobiSN[$CellContext`z$, 0.5], 8, JacobiCN[$CellContext`z$, 0.2], 9, ($CellContext`z$ + 1 + E^$CellContext`z$)/Pi, 10, (E^$CellContext`z$ + 1)^Rational[1, 2] + (1/2) Log[((E^$CellContext`z$ + 1)^Rational[1, 2] - 1)/((E^$CellContext`z$ + 1)^Rational[1, 2] + 1)]]; $CellContext`fp$[ Pattern[$CellContext`z, Blank[]]] = Derivative[1][$CellContext`f][$CellContext`z]; $CellContext`EE$[ Pattern[$CellContext`z$, Blank[]]] := 1/Abs[ $CellContext`fp$[$CellContext`z$]]; $CellContext`uv$[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Block[{$CellContext`i = $CellContext`f[$CellContext`x + I $CellContext`y]}, { Re[$CellContext`i], Im[$CellContext`i]}]; {$CellContext`xdata$, $CellContext`dx$, \ $CellContext`ydata$, $CellContext`dy$} = Switch[$CellContext`fno$$, 1, {{{-1, 1}, {-0.7, 1}, {0, 1}}, 0.1, {{0, 2 Pi}}, Pi/24}, 2, {{{0, 2 Pi}}, Pi/24, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.1}, 3, {{{-(Pi/2), Pi/2}, {-(5 Pi/12), 5 Pi/12}, {-(2 Pi/6), 2 Pi/6}}, Pi/24, {{-1.5, 1.5}}, 0.1}, 4, {{{-1.2, 1.2}}, 0.05, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.05}, 5, {{{-(Pi/2), Pi/2}}, Pi/24, {{-1, 1}, {-0.8, 0.8}, {-0.5, 0.5}}, 0.1}, 6, {{{-1.2, 2}, {-0.8, 2}, {-0.4, 2}}, 0.2, {{-Pi, Pi}}, Pi/ 18}, 7, {{{-1.854, 1.854}, {-1.483, 1.483}, {-0.927, 0.927}}, 0.1854, {{-1.854, 1.854}}, 0.1854}, 8, {{{-3.319, 0}}, 0.16596, {{0, 2.257}, {0, 2.031}, {0.226, 2.257}}, 0.11285}, 9, {{{-8, 2.5}}, 0.25, {{-Pi, Pi}, {-(2 Pi/3), 2 Pi/3}, {-(Pi/2), Pi/2}}, Pi/12}, 10, {{{-4, 3}}, 0.2, {{0, 3.139}, {0, 2.877}, {0, 2.354}}, 0.261538}]; $CellContext`Eavedata$ = Switch[$CellContext`fno$$, 1, {{2.35, 0.851}, {2.222, 0.765}, {1.718, 0.582}}, 2, {{0.543, 1.841}, {0.538, 1.673}, {0.498, 1.406}}, 3, {{2., 1.571}, {1.932, 1.355}, {1.732, 1.209}}, 4, {{1., 1.}, { 0.99, 0.909}, {0.91, 0.769}}, 5, {{1.5232, 1.313}, {1.328, 1.205}, {0.924, 1.08}}, 6, {{1.756, 1.823}, {1.693, 1.654}, {1.604, 1.496}}, 7, {{2., 1.854}, {1.93, 1.537}, {1.531, 1.211}}, 8, {{2., 1.129}, {1.95, 1.042}, {1.797, 0.1129}}, 9, {{2., 3.141}, {1.334, 3.141}, {1., 3.141}}, 10, {{1.569, 1.999}, {1.437, 1.998}, {1.18, 1.994}}]; {$CellContext`urange$, $CellContext`vrange$} = Switch[$CellContext`fno$$, 1, {{-3, 3}, {-3, 3}}, 2, {{-1.6, 1.6}, {-1.6, 1.6}}, 3, {{-1.6, 1.6}, {-1.6, 1.6}}, 4, {{-1, 1}, {-1, 1}}, 5, {{-2.5, 2.5}, {-2.5, 2.5}}, 6, {{-1.2, 4}, {-2.6, 2.6}}, 7, {{-2, 2}, {-2, 2}}, 8, {{-2.5, 2.5}, {-0.25, 4.75}}, 9, {{-2, 2}, {-2, 2}}, 10, {{-1.5, 1.5}, {0, 3}}]; If[Length[$CellContext`xdata$] == 3, {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, $CellContext`option$$]; \ {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, 1], {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, 1]; {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, $CellContext`option$$]]; Pane[ Row[{ Show[ Graphics[ Table[{ $CellContext`huefunc[$CellContext`EE$[$CellContext`x + I $CellContext`y]/(2 Part[$CellContext`Eavedata$, $CellContext`option$$, 2])], Polygon[{ $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/2], $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/ 2]}]}, {$CellContext`x, $CellContext`x1$ + \ $CellContext`dx$/2, $CellContext`x2$ - $CellContext`dx$/ 2, $CellContext`dx$}, {$CellContext`y, $CellContext`y1$ + \ $CellContext`dy$/2, $CellContext`y2$ - $CellContext`dy$/ 2, $CellContext`dy$}]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White}, {White, Dashing[{0.02, 0.005}]}]]& , Table[(1 - $CellContext`t) {$CellContext`x1$, $CellContext`y} + \ $CellContext`t {$CellContext`x2$, $CellContext`y}, {$CellContext`y, \ $CellContext`y1$, $CellContext`y2$, $CellContext`dy$}]]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White, Dashing[{0.02, 0.005}]}, {White}]]& , Table[(1 - $CellContext`t) {$CellContext`x, $CellContext`y1$} + \ $CellContext`t {$CellContext`x, $CellContext`y2$}, {$CellContext`x, \ $CellContext`x1$, $CellContext`x2$, $CellContext`dx$}]]], If[Length[$CellContext`xdata$] == 3, ParametricPlot[{ $CellContext`uv$[$CellContext`x1$, $CellContext`y], $CellContext`uv$[$CellContext`x2$, $CellContext`y]}, \ {$CellContext`y, $CellContext`y1$, $CellContext`y2$}, PlotStyle -> {{Black, Thickness[0.01]}}], ParametricPlot[{ $CellContext`uv$[$CellContext`x, $CellContext`y1$], $CellContext`uv$[$CellContext`x, $CellContext`y2$]}, \ {$CellContext`x, $CellContext`x1$, $CellContext`x2$}, PlotStyle -> {{Black, Thickness[0.01]}}]], Frame -> True, FrameLabel -> {{ Style["v", Italic], None}, { Style["u", Italic], Row[{ Style["u", Italic], " + ", Style["i v", Italic], " = ", Style["f", Italic], "(", Style["x", Italic], " + ", Style["i y", Italic], ") "}]}}, PlotRangeClipping -> True, PlotRange -> {$CellContext`urange$, $CellContext`vrange$}, Epilog -> If[Length[$CellContext`xdata$] == 3, Table[ Inset[ Framed[ Style[ Subscript[ Style["x", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3] + {0, -0.2}, { Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}], Table[ Inset[ Framed[ Style[ Subscript[ Style["y", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 2] - 0.3 > Part[$CellContext`vrange$, 1], $CellContext`uv$[( 2 $CellContext`x1$ + $CellContext`x2$)/3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]] + {0, -0.2}, { Part[ $CellContext`uv$[(2 $CellContext`x1$ + $CellContext`x2$)/ 3, Part[{$CellContext`y1$, $CellContext`y2$}, \ $CellContext`i]], 1], Part[$CellContext`vrange$, 1] + 0.2}]], {$CellContext`i, 2}]], LabelStyle -> {FontSize -> 14}, ImageSize -> 350], Spacer[20], Column[{ Text[ Style[ Grid[{{"option", 1, 2, 3}, Join[{ Row[{ Subscript[ Style["x", Italic], 1], "/", Subscript[ Style["x", Italic], 2]}]}, Table[ If[Length[$CellContext`xdata$] == 3, Row[{ Part[$CellContext`xdata$, $CellContext`i, 1], "/", Part[$CellContext`xdata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{ Row[{ Subscript[ Style["y", Italic], 1], "/", Subscript[ Style["y", Italic], 2]}]}, Table[ If[Length[$CellContext`ydata$] == 3, Row[{ Part[$CellContext`ydata$, $CellContext`i, 1], "/", Part[$CellContext`ydata$, $CellContext`i, 2]}], "-"], {$CellContext`i, 3}]], Join[{"gap"}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 1], 0.01], {$CellContext`i, 3}]], Join[{ Subscript[ Style[" E", Italic], "ave"]}, Table[ Round[ Part[$CellContext`Eavedata$, $CellContext`i, 2], 0.01], {$CellContext`i, 3}]]}, Frame -> All, Alignment -> Center], 14]], Spacer[100], DensityPlot[ 0.5 $CellContext`y, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 2}, PlotRange -> {{0, 1}, {0, 2}}, ColorFunctionScaling -> False, AspectRatio -> 12, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Column[{ Style["electric field", 14], Row[{ Style["E", Italic], "/", Subscript[ Style["E", Italic], "ave"]}]}, Center], ImageSize -> {75, 250}, ImagePadding -> {{30, 30}, {10, 10}}]}]}], ImageSize -> {600, 400}]], "Specifications" :> {{{$CellContext`fno$$, 9, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}, ControlPlacement -> 1}, {{$CellContext`option$$, 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}, ControlPlacement -> 2}, Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]}, "Options" :> { TrackedSymbols :> {$CellContext`fno$$, $CellContext`option$$}}, "DefaultOptions" :> {ControllerLinking -> True}], SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->119584347], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`fno$$ = 10, $CellContext`option$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{{ Hold[$CellContext`fno$$], 10, Row[{ Style["f", Italic], "(", Style["z", Italic], ") = "}]}, {1 -> Row[{ Style[ Superscript["e", "z"], Italic], " (concentric circles)"}], 2 -> Row[{"sin(", Style["z", Italic], ") (ellipses)"}], 3 -> Row[{"sin(", Style["z", Italic], ") (hyperbolas)"}], 4 -> Row[{ Superscript[ Style["z", Italic], "2"], " (parabolas)"}], 5 -> Row[{ Style["i ", Italic], "cot(", Style["z", Italic], ") (bipolar circles)"}], 6 -> Row[{Row[{ Style[ Superscript["e", "-i w"], Italic], "+1"}]^Rational[1, 2], " (Cassinian ovals)"}], 7 -> Row[{"sn(", Style["z", Italic], ") (elliptical pairs\[LongDash]\[WarningSign] slow!)"}], 8 -> Row[{"cn(", Style["z", Italic], ") (blade to plate\[LongDash]\[WarningSign] slow!)"}], 9 -> Row[{"(", Style["z", Italic], " + 1 +", Style[ Superscript["e", "z"], Italic], ") / \[Pi] (Maxwell curves)"}], 10 -> Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], " + \!\(\*FractionBox[\(1\), \(2\)]\) ", "log(", Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "-1"}]/Row[{Row[{ Style[ Superscript["e", "z"], Italic], "+ 1"}]^Rational[1, 2], "+1"}], ") (square edge)"}]}}, {{ Hold[$CellContext`option$$], 1, "option"}, {1 -> 1, 2 -> 2, 3 -> 3}}, { Hold[ Row[{ Manipulate`Place[1], Spacer[30], Manipulate`Place[2]}]], Manipulate`Dump`ThisIsNotAControl}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`fno$292362$$ = False, $CellContext`option$292363$$ = False}, DynamicBox[Manipulate`ManipulateBoxes[ 2, StandardForm, "Variables" :> {$CellContext`fno$$ = 10, $CellContext`option$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`fno$$, $CellContext`fno$292362$$, False], Hold[$CellContext`option$$, $CellContext`option$292363$$, False]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`fp$, $CellContext`EE$, $CellContext`uv$, \ $CellContext`xdata$, $CellContext`dx$, $CellContext`ydata$, $CellContext`dy$, \ $CellContext`Eavedata$, $CellContext`urange$, $CellContext`vrange$, \ $CellContext`x1$, $CellContext`x2$, $CellContext`y1$, $CellContext`y2$}, \ $CellContext`f[ Pattern[$CellContext`z$, Blank[]]] = Switch[$CellContext`fno$$, 1, E^$CellContext`z$, 2, Sin[$CellContext`z$], 3, Sin[$CellContext`z$], 4, $CellContext`z$^2, 5, I Cot[$CellContext`z$], 6, (E^$CellContext`z$ + 1)^Rational[1, 2], 7, JacobiSN[$CellContext`z$, 0.5], 8, JacobiCN[$CellContext`z$, 0.2], 9, ($CellContext`z$ + 1 + E^$CellContext`z$)/Pi, 10, (E^$CellContext`z$ + 1)^Rational[1, 2] + (1/2) Log[((E^$CellContext`z$ + 1)^Rational[1, 2] - 1)/((E^$CellContext`z$ + 1)^Rational[1, 2] + 1)]]; $CellContext`fp$[ Pattern[$CellContext`z, Blank[]]] = Derivative[1][$CellContext`f][$CellContext`z]; $CellContext`EE$[ Pattern[$CellContext`z$, Blank[]]] := 1/Abs[ $CellContext`fp$[$CellContext`z$]]; $CellContext`uv$[ Pattern[$CellContext`x, Blank[]], Pattern[$CellContext`y, Blank[]]] := Block[{$CellContext`i = $CellContext`f[$CellContext`x + I $CellContext`y]}, { Re[$CellContext`i], Im[$CellContext`i]}]; {$CellContext`xdata$, $CellContext`dx$, \ $CellContext`ydata$, $CellContext`dy$} = Switch[$CellContext`fno$$, 1, {{{-1, 1}, {-0.7, 1}, {0, 1}}, 0.1, {{0, 2 Pi}}, Pi/24}, 2, {{{0, 2 Pi}}, Pi/24, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.1}, 3, {{{-(Pi/2), Pi/2}, {-(5 Pi/12), 5 Pi/12}, {-(2 Pi/6), 2 Pi/6}}, Pi/24, {{-1.5, 1.5}}, 0.1}, 4, {{{-1.2, 1.2}}, 0.05, {{0, 1}, {0.1, 1}, {0.3, 1}}, 0.05}, 5, {{{-(Pi/2), Pi/2}}, Pi/24, {{-1, 1}, {-0.8, 0.8}, {-0.5, 0.5}}, 0.1}, 6, {{{-1.2, 2}, {-0.8, 2}, {-0.4, 2}}, 0.2, {{-Pi, Pi}}, Pi/ 18}, 7, {{{-1.854, 1.854}, {-1.483, 1.483}, {-0.927, 0.927}}, 0.1854, {{-1.854, 1.854}}, 0.1854}, 8, {{{-3.319, 0}}, 0.16596, {{0, 2.257}, {0, 2.031}, {0.226, 2.257}}, 0.11285}, 9, {{{-8, 2.5}}, 0.25, {{-Pi, Pi}, {-(2 Pi/3), 2 Pi/3}, {-(Pi/2), Pi/2}}, Pi/12}, 10, {{{-4, 3}}, 0.2, {{0, 3.139}, {0, 2.877}, {0, 2.354}}, 0.261538}]; $CellContext`Eavedata$ = Switch[$CellContext`fno$$, 1, {{2.35, 0.851}, {2.222, 0.765}, {1.718, 0.582}}, 2, {{0.543, 1.841}, {0.538, 1.673}, {0.498, 1.406}}, 3, {{2., 1.571}, {1.932, 1.355}, {1.732, 1.209}}, 4, {{1., 1.}, { 0.99, 0.909}, {0.91, 0.769}}, 5, {{1.5232, 1.313}, {1.328, 1.205}, {0.924, 1.08}}, 6, {{1.756, 1.823}, {1.693, 1.654}, {1.604, 1.496}}, 7, {{2., 1.854}, {1.93, 1.537}, {1.531, 1.211}}, 8, {{2., 1.129}, {1.95, 1.042}, {1.797, 0.1129}}, 9, {{2., 3.141}, {1.334, 3.141}, {1., 3.141}}, 10, {{1.569, 1.999}, {1.437, 1.998}, {1.18, 1.994}}]; {$CellContext`urange$, $CellContext`vrange$} = Switch[$CellContext`fno$$, 1, {{-3, 3}, {-3, 3}}, 2, {{-1.6, 1.6}, {-1.6, 1.6}}, 3, {{-1.6, 1.6}, {-1.6, 1.6}}, 4, {{-1, 1}, {-1, 1}}, 5, {{-2.5, 2.5}, {-2.5, 2.5}}, 6, {{-1.2, 4}, {-2.6, 2.6}}, 7, {{-2, 2}, {-2, 2}}, 8, {{-2.5, 2.5}, {-0.25, 4.75}}, 9, {{-2, 2}, {-2, 2}}, 10, {{-1.5, 1.5}, {0, 3}}]; If[Length[$CellContext`xdata$] == 3, {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, $CellContext`option$$]; \ {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, 1], {$CellContext`x1$, $CellContext`x2$} = Part[$CellContext`xdata$, 1]; {$CellContext`y1$, $CellContext`y2$} = Part[$CellContext`ydata$, $CellContext`option$$]]; Pane[ Row[{ Show[ Graphics[ Table[{ $CellContext`huefunc[$CellContext`EE$[$CellContext`x + I $CellContext`y]/(2 Part[$CellContext`Eavedata$, $CellContext`option$$, 2])], Polygon[{ $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/2], $CellContext`uv$[$CellContext`x - $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y + $CellContext`dy$/2], $CellContext`uv$[$CellContext`x + $CellContext`dx$/ 2, $CellContext`y - $CellContext`dy$/ 2]}]}, {$CellContext`x, $CellContext`x1$ + \ $CellContext`dx$/2, $CellContext`x2$ - $CellContext`dx$/ 2, $CellContext`dx$}, {$CellContext`y, $CellContext`y1$ + \ $CellContext`dy$/2, $CellContext`y2$ - $CellContext`dy$/ 2, $CellContext`dy$}]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White}, {White, Dashing[{0.02, 0.005}]}]]& , Table[(1 - $CellContext`t) {$CellContext`x1$, $CellContext`y} + \ $CellContext`t {$CellContext`x2$, $CellContext`y}, {$CellContext`y, \ $CellContext`y1$, $CellContext`y2$, $CellContext`dy$}]]], Block[{$CellContext`i}, Map[ParametricPlot[ Evaluate[$CellContext`i = $CellContext`f[ First[#] + Last[#] I]; { Re[$CellContext`i], Im[$CellContext`i]}], {$CellContext`t, 0, 1}, PlotStyle -> If[Length[$CellContext`xdata$] == 3, {White, Dashing[{0.02, 0.005}]}, {White}]]& , Table[(1 - $CellContext`t) {$CellContext`x, $CellContext`y1$} + \ $CellContext`t {$CellContext`x, $CellContext`y2$}, {$CellContext`x, \ $CellContext`x1$, $CellContext`x2$, $CellContext`dx$}]]], If[Length[$CellContext`xdata$] == 3, ParametricPlot[{ $CellContext`uv$[$CellContext`x1$, $CellContext`y], $CellContext`uv$[$CellContext`x2$, $CellContext`y]}, \ {$CellContext`y, $CellContext`y1$, $CellContext`y2$}, PlotStyle -> {{Black, Thickness[0.01]}}], ParametricPlot[{ $CellContext`uv$[$CellContext`x, $CellContext`y1$], $CellContext`uv$[$CellContext`x, $CellContext`y2$]}, \ {$CellContext`x, $CellContext`x1$, $CellContext`x2$}, PlotStyle -> {{Black, Thickness[0.01]}}]], Frame -> True, FrameLabel -> {{ Style["v", Italic], None}, { Style["u", Italic], Row[{ Style["u", Italic], " + ", Style["i v", Italic], " = ", Style["f", Italic], "(", Style["x", Italic], " + ", Style["i y", Italic], ") "}]}}, PlotRangeClipping -> True, PlotRange -> {$CellContext`urange$, $CellContext`vrange$}, Epilog -> If[Length[$CellContext`xdata$] == 3, Table[ Inset[ Framed[ Style[ Subscript[ Style["x", Italic], Part[{"1", "2"}, $CellContext`i]], 14], Background -> LightYellow], If[Part[ $CellContext`uv$[ Part[{$CellContext`x1$, $CellContext`x2$}, \ $CellContext`i], (2 $CellContext`y1$ + $CellContext`y2$)/3], 2] - 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Therefore, its magnitude is given by\n", Cell[BoxData[ FormBox[ RowBox[{"E", "=", RowBox[{ RowBox[{"1", "/", SqrtBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", " ", FractionBox[ RowBox[{"\[PartialD]", "\[InvisibleSpace]", "u"}], RowBox[{"\[PartialD]", "\[InvisibleSpace]", "x"}]], ")"}], "2"], "+", SuperscriptBox[ RowBox[{"(", " ", FractionBox[ RowBox[{"\[PartialD]", "\[InvisibleSpace]", "v"}], RowBox[{"\[PartialD]", "x"}]], ")"}], "2"]}]]}], "=", RowBox[{ RowBox[{ RowBox[{"1", "/"}], "|", FractionBox[ RowBox[{"\[PartialD]", "\[InvisibleSpace]", RowBox[{"f", "(", RowBox[{"x", "+", RowBox[{"i", " ", "y"}]}], ")"}]}], RowBox[{"\[PartialD]", "x"}]], "|"}], "=", RowBox[{ RowBox[{"1", "/"}], "|", RowBox[{ RowBox[{"f", "'"}], RowBox[{"(", RowBox[{"x", "+", RowBox[{"i", " ", "y"}]}], ")"}]}], "|"}]}]}]}], TraditionalForm]], "InlineMath"], "." }], "DetailNotes", CellChangeTimes->{{3.5642479594346375`*^9, 3.564247959706665*^9}, { 3.565390325497376*^9, 3.5653903499259377`*^9}, {3.565390408259392*^9, 3.565390414311208*^9}, {3.566320389135441*^9, 3.566320466136079*^9}, { 3.5663755380585203`*^9, 3.566375547777337*^9}, {3.5663755866058054`*^9, 3.5663756219086676`*^9}, {3.566620766848131*^9, 3.566620766848131*^9}, { 3.566620808535631*^9, 3.566620905598131*^9}, {3.566620984629381*^9, 3.566621065348131*^9}, {3.567894048110691*^9, 3.567894217670372*^9}, { 3.567958856472205*^9, 3.567958872488304*^9}, 3.567959636450181*^9}, CellID->136793187], Cell[TextData[{ "The calculation is done for a limited number of ", Cell[BoxData[ FormBox["u", TraditionalForm]], "InlineMath"], " and ", Cell[BoxData[ FormBox["v", TraditionalForm]], "InlineMath"], " values to save time. Please be patient, particularly for ", Cell[BoxData[ FormBox[ RowBox[{"sn", StyleBox[" ", FontSlant->"Italic"], RowBox[{"(", "z", ")"}]}], TraditionalForm]], "InlineMath"], " and ", Cell[BoxData[ FormBox[ RowBox[{"cn", "(", "z", ")"}], TraditionalForm]], "InlineMath"], "." }], "DetailNotes", CellChangeTimes->{{3.564247831256385*^9, 3.5642478903943825`*^9}, { 3.566621140426256*^9, 3.566621189191881*^9}, {3.5666346082377787`*^9, 3.5666346096533813`*^9}, {3.5666346482098427`*^9, 3.566634669807079*^9}, { 3.5678942258712053`*^9, 3.5678942582824907`*^9}, {3.567959650290312*^9, 3.5679596506147137`*^9}}, CellID->217927333], Cell["References", "DetailNotes", CellID->61520609], Cell[TextData[{ "[1] H. Prinz, ", StyleBox["Hochspannungsfelder", FontSlant->"Italic"], ", M\[UDoubleDot]nchen: R. Oldenbourg Verlag, 1969." }], "DetailNotes", CellChangeTimes->{{3.565390425919299*^9, 3.565390433702302*^9}}, CellID->203214341], Cell[TextData[{ "[2] P. Moon and D. E. 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