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"Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["relative permittivities", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Epsilon]r$$], 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{ Hold[$CellContext`\[Epsilon]rsp$$], 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, Typeset`size$$ = {515., {201., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Epsilon]r$149056$$ = 0, $CellContext`\[Epsilon]rsp$149057$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = 5}, "ControllerVariables" :> { Hold[$CellContext`\[Epsilon]r$$, $CellContext`\[Epsilon]r$149056$$, 0], Hold[$CellContext`\[Epsilon]rsp$$, \ $CellContext`\[Epsilon]rsp$149057$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`Eo$ = 1, $CellContext`a$ = 1, $CellContext`Emax$ = 3, $CellContext`Ev$}, If[$CellContext`\[Epsilon]rsp$$ == Infinity, $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, {0, 0}, { 3 $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ \ $CellContext`z$/($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2), $CellContext`Eo$ + $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/($CellContext`r$^2 + \ $CellContext`z$^2)^(5/2)}], $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, { 0, 3 $CellContext`\[Epsilon]r$$ $CellContext`Eo$/( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$)}, \ {-(3 ($CellContext`\[Epsilon]r$$ - $CellContext`\[Epsilon]rsp$$) \ $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ $CellContext`z$/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2))), $CellContext`Eo$ - ($CellContext`\[Epsilon]r$$ - \ $CellContext`\[Epsilon]rsp$$) $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/2))}]]; Pane[ Row[{ Show[ ParametricPlot[{$CellContext`r, $CellContext`z}, \ {$CellContext`r, -3, 3}, {$CellContext`z, -3, 3}, ColorFunctionScaling -> False, Mesh -> {80, 80}, MeshStyle -> None, ColorFunction -> Function[{$CellContext`X$, $CellContext`Y$, $CellContext`r$, \ $CellContext`z$}, $CellContext`huefunc[Norm[ $CellContext`Ev$[$CellContext`r$, \ $CellContext`z$]]/$CellContext`Emax$]], Axes -> None], VectorPlot[ Block[{$CellContext`vec = $CellContext`Ev$[$CellContext`r, \ $CellContext`z]}, If[$CellContext`vec == {0, 0}, {0, 0}, $CellContext`vec/ Norm[$CellContext`vec]]], {$CellContext`r, -3.2, 2.8}, {$CellContext`z, -3.2, 2.8}, VectorPoints -> {16, 16}, VectorScale -> 0.03, VectorStyle -> Black], Graphics[{Black, Thickness[0.01], Circle[{0, 0}, $CellContext`a$]}], Frame -> True, LabelStyle -> 14, FrameLabel -> { Row[{ Style["r", Italic], " / ", Style["a", Italic]}], Row[{ Style["z", Italic], " / ", Style["a", Italic]}], None, None}, ImageSize -> 420, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}], Spacer[5], DensityPlot[$CellContext`y/ 3, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 3}, PlotRange -> {{0, 1}, {0, 3}}, ColorFunctionScaling -> False, AspectRatio -> 10, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Style[ Row[{"|", Style["E", Italic], "| / ", Subscript[ Style["E", Italic], " 0"], Spacer[10]}], 14], ImagePadding -> {{30, 10}, {Automatic, Automatic}}, ImageSize -> {90, 230}]}]]], "Specifications" :> { Style[ "relative permittivities", Bold], {{$CellContext`\[Epsilon]r$$, 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{$CellContext`\[Epsilon]rsp$$, 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, "Options" :> { TrackedSymbols :> {$CellContext`\[Epsilon]r$$, \ $CellContext`\[Epsilon]rsp$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{558., {263., 269.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->53034239] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "ManipulateCaptionSection"], Cell[TextData[{ "This Demonstration shows the electric field in and around a spherical \ dielectric in a uniform external electric field. The spatial distribution of \ field intensity and direction are indicated by colors and arrows, \ respectively. You can vary the relative permittivity of the sphere and the \ surrounding medium. In the graphics, the radial and axial lengths are \ normalized to the sphere radius ", Cell[BoxData[ FormBox["a", TraditionalForm]], "InlineMath"], ", and the field intensity magnitude is given relative to the applied field ", Cell[BoxData[ FormBox[ SubscriptBox["E", "0"], TraditionalForm]], "InlineMath"], "." }], "ManipulateCaption", CellChangeTimes->{ 3.564827935992903*^9, {3.564872388572002*^9, 3.564872431378477*^9}, { 3.564872463701734*^9, 3.5648725043398056`*^9}, {3.5648725547122936`*^9, 3.5648725984079704`*^9}, {3.564872642556048*^9, 3.564872730524603*^9}, { 3.5648727993831234`*^9, 3.5648728887244806`*^9}, {3.564872943808177*^9, 3.5648729542289953`*^9}, {3.5648729899842587`*^9, 3.5648730919460373`*^9}, {3.5648731311645064`*^9, 3.56487319021061*^9}, { 3.564873245933908*^9, 3.5648732543267226`*^9}, {3.5648732946059933`*^9, 3.5648733137160273`*^9}, {3.564873399843778*^9, 3.564873450372267*^9}, { 3.5648735038023605`*^9, 3.5648735516788445`*^9}, {3.564873583580901*^9, 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Style["relative permittivities", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Epsilon]r$$], 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{ Hold[$CellContext`\[Epsilon]rsp$$], 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, Typeset`size$$ = {515., {201., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Epsilon]r$149111$$ = 0, $CellContext`\[Epsilon]rsp$149112$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = 5}, "ControllerVariables" :> { Hold[$CellContext`\[Epsilon]r$$, $CellContext`\[Epsilon]r$149111$$, 0], Hold[$CellContext`\[Epsilon]rsp$$, \ $CellContext`\[Epsilon]rsp$149112$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`Eo$ = 1, $CellContext`a$ = 1, $CellContext`Emax$ = 3, $CellContext`Ev$}, If[$CellContext`\[Epsilon]rsp$$ == Infinity, $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, {0, 0}, { 3 $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ \ $CellContext`z$/($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2), $CellContext`Eo$ + $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/($CellContext`r$^2 + \ $CellContext`z$^2)^(5/2)}], $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, { 0, 3 $CellContext`\[Epsilon]r$$ $CellContext`Eo$/( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$)}, \ {-(3 ($CellContext`\[Epsilon]r$$ - $CellContext`\[Epsilon]rsp$$) \ $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ $CellContext`z$/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2))), $CellContext`Eo$ - ($CellContext`\[Epsilon]r$$ - \ $CellContext`\[Epsilon]rsp$$) $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/2))}]]; Pane[ Row[{ Show[ ParametricPlot[{$CellContext`r, $CellContext`z}, \ {$CellContext`r, -3, 3}, {$CellContext`z, -3, 3}, ColorFunctionScaling -> False, Mesh -> {80, 80}, MeshStyle -> None, ColorFunction -> Function[{$CellContext`X$, $CellContext`Y$, $CellContext`r$, \ $CellContext`z$}, $CellContext`huefunc[Norm[ $CellContext`Ev$[$CellContext`r$, \ $CellContext`z$]]/$CellContext`Emax$]], Axes -> None], VectorPlot[ Block[{$CellContext`vec = $CellContext`Ev$[$CellContext`r, \ $CellContext`z]}, If[$CellContext`vec == {0, 0}, {0, 0}, $CellContext`vec/ Norm[$CellContext`vec]]], {$CellContext`r, -3.2, 2.8}, {$CellContext`z, -3.2, 2.8}, VectorPoints -> {16, 16}, VectorScale -> 0.03, VectorStyle -> Black], Graphics[{Black, Thickness[0.01], Circle[{0, 0}, $CellContext`a$]}], Frame -> True, LabelStyle -> 14, FrameLabel -> { Row[{ Style["r", Italic], " / ", Style["a", Italic]}], Row[{ Style["z", Italic], " / ", Style["a", Italic]}], None, None}, ImageSize -> 420, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}], Spacer[5], DensityPlot[$CellContext`y/ 3, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 3}, PlotRange -> {{0, 1}, {0, 3}}, ColorFunctionScaling -> False, AspectRatio -> 10, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Style[ Row[{"|", Style["E", Italic], "| / ", Subscript[ Style["E", Italic], " 0"], Spacer[10]}], 14], ImagePadding -> {{30, 10}, {Automatic, Automatic}}, ImageSize -> {90, 230}]}]]], "Specifications" :> { Style[ "relative permittivities", Bold], {{$CellContext`\[Epsilon]r$$, 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{$CellContext`\[Epsilon]rsp$$, 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, "Options" :> { TrackedSymbols :> {$CellContext`\[Epsilon]r$$, \ $CellContext`\[Epsilon]rsp$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{558., {263., 269.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->140741368] }, Open ]], Cell[CellGroupData[{ Cell["", "SnapshotsSection"], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = 5, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["relative permittivities", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Epsilon]r$$], 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{ Hold[$CellContext`\[Epsilon]rsp$$], 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, Typeset`size$$ = {515., {201., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Epsilon]r$149166$$ = 0, $CellContext`\[Epsilon]rsp$149167$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = 5}, "ControllerVariables" :> { Hold[$CellContext`\[Epsilon]r$$, $CellContext`\[Epsilon]r$149166$$, 0], Hold[$CellContext`\[Epsilon]rsp$$, \ $CellContext`\[Epsilon]rsp$149167$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`Eo$ = 1, $CellContext`a$ = 1, $CellContext`Emax$ = 3, $CellContext`Ev$}, If[$CellContext`\[Epsilon]rsp$$ == Infinity, $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, {0, 0}, { 3 $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ \ $CellContext`z$/($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2), $CellContext`Eo$ + $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/($CellContext`r$^2 + \ $CellContext`z$^2)^(5/2)}], $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, { 0, 3 $CellContext`\[Epsilon]r$$ $CellContext`Eo$/( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$)}, \ {-(3 ($CellContext`\[Epsilon]r$$ - $CellContext`\[Epsilon]rsp$$) \ $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ $CellContext`z$/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2))), $CellContext`Eo$ - ($CellContext`\[Epsilon]r$$ - \ $CellContext`\[Epsilon]rsp$$) $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/2))}]]; Pane[ Row[{ Show[ ParametricPlot[{$CellContext`r, $CellContext`z}, \ {$CellContext`r, -3, 3}, {$CellContext`z, -3, 3}, ColorFunctionScaling -> False, Mesh -> {80, 80}, MeshStyle -> None, ColorFunction -> Function[{$CellContext`X$, $CellContext`Y$, $CellContext`r$, \ $CellContext`z$}, $CellContext`huefunc[Norm[ $CellContext`Ev$[$CellContext`r$, \ $CellContext`z$]]/$CellContext`Emax$]], Axes -> None], VectorPlot[ Block[{$CellContext`vec = $CellContext`Ev$[$CellContext`r, \ $CellContext`z]}, If[$CellContext`vec == {0, 0}, {0, 0}, $CellContext`vec/ Norm[$CellContext`vec]]], {$CellContext`r, -3.2, 2.8}, {$CellContext`z, -3.2, 2.8}, VectorPoints -> {16, 16}, VectorScale -> 0.03, VectorStyle -> Black], Graphics[{Black, Thickness[0.01], Circle[{0, 0}, $CellContext`a$]}], Frame -> True, LabelStyle -> 14, FrameLabel -> { Row[{ Style["r", Italic], " / ", Style["a", Italic]}], Row[{ Style["z", Italic], " / ", Style["a", Italic]}], None, None}, ImageSize -> 420, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}], Spacer[5], DensityPlot[$CellContext`y/ 3, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 3}, PlotRange -> {{0, 1}, {0, 3}}, ColorFunctionScaling -> False, AspectRatio -> 10, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Style[ Row[{"|", Style["E", Italic], "| / ", Subscript[ Style["E", Italic], " 0"], Spacer[10]}], 14], ImagePadding -> {{30, 10}, {Automatic, Automatic}}, ImageSize -> {90, 230}]}]]], "Specifications" :> { Style[ "relative permittivities", Bold], {{$CellContext`\[Epsilon]r$$, 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{$CellContext`\[Epsilon]rsp$$, 5, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, "Options" :> { TrackedSymbols :> {$CellContext`\[Epsilon]r$$, \ $CellContext`\[Epsilon]rsp$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{558., {263., 269.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->1060676629], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = DirectedInfinity[1], Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["relative permittivities", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Epsilon]r$$], 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{ Hold[$CellContext`\[Epsilon]rsp$$], DirectedInfinity[1], Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, Typeset`size$$ = {515., {201., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Epsilon]r$149221$$ = 0, $CellContext`\[Epsilon]rsp$149222$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Epsilon]r$$ = 1, $CellContext`\[Epsilon]rsp$$ = DirectedInfinity[1]}, "ControllerVariables" :> { Hold[$CellContext`\[Epsilon]r$$, $CellContext`\[Epsilon]r$149221$$, 0], Hold[$CellContext`\[Epsilon]rsp$$, \ $CellContext`\[Epsilon]rsp$149222$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`Eo$ = 1, $CellContext`a$ = 1, $CellContext`Emax$ = 3, $CellContext`Ev$}, If[$CellContext`\[Epsilon]rsp$$ == Infinity, $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, {0, 0}, { 3 $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ \ $CellContext`z$/($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2), $CellContext`Eo$ + $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/($CellContext`r$^2 + \ $CellContext`z$^2)^(5/2)}], $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, { 0, 3 $CellContext`\[Epsilon]r$$ $CellContext`Eo$/( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$)}, \ {-(3 ($CellContext`\[Epsilon]r$$ - $CellContext`\[Epsilon]rsp$$) \ $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ $CellContext`z$/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2))), $CellContext`Eo$ - ($CellContext`\[Epsilon]r$$ - \ $CellContext`\[Epsilon]rsp$$) $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/2))}]]; Pane[ Row[{ Show[ ParametricPlot[{$CellContext`r, $CellContext`z}, \ {$CellContext`r, -3, 3}, {$CellContext`z, -3, 3}, ColorFunctionScaling -> False, Mesh -> {80, 80}, MeshStyle -> None, ColorFunction -> Function[{$CellContext`X$, $CellContext`Y$, $CellContext`r$, \ $CellContext`z$}, $CellContext`huefunc[Norm[ $CellContext`Ev$[$CellContext`r$, \ $CellContext`z$]]/$CellContext`Emax$]], Axes -> None], VectorPlot[ Block[{$CellContext`vec = $CellContext`Ev$[$CellContext`r, \ $CellContext`z]}, If[$CellContext`vec == {0, 0}, {0, 0}, $CellContext`vec/ Norm[$CellContext`vec]]], {$CellContext`r, -3.2, 2.8}, {$CellContext`z, -3.2, 2.8}, VectorPoints -> {16, 16}, VectorScale -> 0.03, VectorStyle -> Black], Graphics[{Black, Thickness[0.01], Circle[{0, 0}, $CellContext`a$]}], Frame -> True, LabelStyle -> 14, FrameLabel -> { Row[{ Style["r", Italic], " / ", Style["a", Italic]}], Row[{ Style["z", Italic], " / ", Style["a", Italic]}], None, None}, ImageSize -> 420, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}], Spacer[5], DensityPlot[$CellContext`y/ 3, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 3}, PlotRange -> {{0, 1}, {0, 3}}, ColorFunctionScaling -> False, AspectRatio -> 10, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Style[ Row[{"|", Style["E", Italic], "| / ", Subscript[ Style["E", Italic], " 0"], Spacer[10]}], 14], ImagePadding -> {{30, 10}, {Automatic, Automatic}}, ImageSize -> {90, 230}]}]]], "Specifications" :> { Style[ "relative permittivities", Bold], {{$CellContext`\[Epsilon]r$$, 1, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{$CellContext`\[Epsilon]rsp$$, DirectedInfinity[1], Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, "Options" :> { TrackedSymbols :> {$CellContext`\[Epsilon]r$$, \ $CellContext`\[Epsilon]rsp$$}}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{558., {263., 269.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>($CellContext`huefunc[ Pattern[$CellContext`x, Blank[]]] := Hue[ If[$CellContext`x > 1, 0., If[$CellContext`x < 0, 0.75, 0.75 (1 - $CellContext`x)]]]; Typeset`initDone$$ = True), SynchronousInitialization->True, UnsavedVariables:>{Typeset`initDone$$}, UntrackedVariables:>{Typeset`size$$}], "Manipulate", Deployed->True, StripOnInput->False], Manipulate`InterpretManipulate[1]]], "Output", CellID->530349856], Cell[BoxData[ TagBox[ StyleBox[ DynamicModuleBox[{$CellContext`\[Epsilon]r$$ = 50, $CellContext`\[Epsilon]rsp$$ = 1, Typeset`show$$ = True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = "\"untitled\"", Typeset`specs$$ = {{ Hold[ Style["relative permittivities", Bold]], Manipulate`Dump`ThisIsNotAControl}, {{ Hold[$CellContext`\[Epsilon]r$$], 50, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{ Hold[$CellContext`\[Epsilon]rsp$$], 1, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, DirectedInfinity[1]}}}, Typeset`size$$ = {515., {201., 206.}}, Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ = False, $CellContext`\[Epsilon]r$149276$$ = 0, $CellContext`\[Epsilon]rsp$149277$$ = 0}, DynamicBox[Manipulate`ManipulateBoxes[ 1, StandardForm, "Variables" :> {$CellContext`\[Epsilon]r$$ = 50, $CellContext`\[Epsilon]rsp$$ = 1}, "ControllerVariables" :> { Hold[$CellContext`\[Epsilon]r$$, $CellContext`\[Epsilon]r$149276$$, 0], Hold[$CellContext`\[Epsilon]rsp$$, \ $CellContext`\[Epsilon]rsp$149277$$, 0]}, "OtherVariables" :> { Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$, Typeset`skipInitDone$$}, "Body" :> Module[{$CellContext`Eo$ = 1, $CellContext`a$ = 1, $CellContext`Emax$ = 3, $CellContext`Ev$}, If[$CellContext`\[Epsilon]rsp$$ == Infinity, $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, {0, 0}, { 3 $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ \ $CellContext`z$/($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2), $CellContext`Eo$ + $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/($CellContext`r$^2 + \ $CellContext`z$^2)^(5/2)}], $CellContext`Ev$[ Pattern[$CellContext`r$, Blank[]], Pattern[$CellContext`z$, Blank[]]] := If[($CellContext`r$^2 + $CellContext`z$^2)^ Rational[1, 2] < $CellContext`a$, { 0, 3 $CellContext`\[Epsilon]r$$ $CellContext`Eo$/( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$)}, \ {-(3 ($CellContext`\[Epsilon]r$$ - $CellContext`\[Epsilon]rsp$$) \ $CellContext`a$^3 $CellContext`Eo$ $CellContext`r$ $CellContext`z$/(( 2 $CellContext`\[Epsilon]r$$ + $CellContext`\[Epsilon]rsp$$) \ ($CellContext`r$^2 + $CellContext`z$^2)^(5/ 2))), $CellContext`Eo$ - ($CellContext`\[Epsilon]r$$ - \ $CellContext`\[Epsilon]rsp$$) $CellContext`a$^3 $CellContext`Eo$ ( 2 $CellContext`z$^2 - $CellContext`r$^2)/(( 2 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Style["z", Italic], " / ", Style["a", Italic]}], None, None}, ImageSize -> 420, ImagePadding -> {{50, Automatic}, {Automatic, Automatic}}], Spacer[5], DensityPlot[$CellContext`y/ 3, {$CellContext`x, 0, 1}, {$CellContext`y, 0, 3}, PlotRange -> {{0, 1}, {0, 3}}, ColorFunctionScaling -> False, AspectRatio -> 10, ColorFunction -> $CellContext`huefunc, Frame -> True, FrameTicks -> {None, Automatic, None, Automatic}, Axes -> None, LabelStyle -> {FontSize -> 14}, PlotLabel -> Style[ Row[{"|", Style["E", Italic], "| / ", Subscript[ Style["E", Italic], " 0"], Spacer[10]}], 14], ImagePadding -> {{30, 10}, {Automatic, Automatic}}, ImageSize -> {90, 230}]}]]], "Specifications" :> { Style[ "relative permittivities", Bold], {{$CellContext`\[Epsilon]r$$, 50, Row[{" surrounding medium ", Subscript["\[Epsilon]", Style["r", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100}}, {{$CellContext`\[Epsilon]rsp$$, 1, Row[{" dielectric sphere ", Subscript["\[Epsilon]", Style["a", Italic]]}]}, {1, 2, 5, 10, 20, 50, 100, 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The field inside the sphere is uniform, its value being less than ", Cell[BoxData[ FormBox[ SubscriptBox["E", "0"], TraditionalForm]], "InlineMath"], " for ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[Epsilon]", "a"], ">", SubscriptBox["\[Epsilon]", "r"]}], TraditionalForm]], "InlineMath"], ". However, it is greater than ", Cell[BoxData[ FormBox[ SubscriptBox["E", "0"], TraditionalForm]], "InlineMath"], " for ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[Epsilon]", "a"], "<", SubscriptBox["\[Epsilon]", "r"]}], TraditionalForm]], "InlineMath"], ", as seen in snapshot 3. In the extreme case of ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[Epsilon]", "a"], RowBox[{"<<", " ", SubscriptBox["\[Epsilon]", "r"]}]}], TraditionalForm]], "InlineMath"], ", it tends to 1.5 ", Cell[BoxData[ FormBox[ SubscriptBox["E", "0"], TraditionalForm]], "InlineMath"], ". 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