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(* http://www.wolfram.com/cdf *)

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(*************************************************************************)
(*                                                                       *)
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(*  Wolfram Research, Inc.                                               *)
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    ColorFunction->RGBColor],
   ImageSize->{1714, 38},
   PlotRange->{{0, 1714}, {0, 38}}],
  Alignment->Left,
  BaseStyle->{"Hyperlink", "DemonstrationHeader"},
  ButtonData->{
    URL["http://demonstrations.wolfram.com"], None},
  ButtonNote->"http://demonstrations.wolfram.com"]], "DemonstrationHeader"],

Cell["Electric Field around a Charged Ring", "DemoTitle"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`a$$ = 1, $CellContext`r$$ = 
    2, $CellContext`scale$$ = 2, $CellContext`showFieldLines$$ = 
    False, $CellContext`showVectorField$$ = 
    False, $CellContext`vectorPoints$$ = 4, $CellContext`z$$ = 
    2, $CellContext`\[Phi]\[Phi]$$ = 0, Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{
      Hold[
       Spacer[210]], Manipulate`Dump`ThisIsNotAControl}, {{
       Hold[$CellContext`r$$], 2, "test charge r"}, 0.001, 4, 0.001}, {{
       Hold[$CellContext`\[Phi]\[Phi]$$], 0, "test charge \[Theta]"}, -3.1416,
       3.1416, 0.0001}, {{
       Hold[$CellContext`z$$], 2, "test charge z"}, -4, 4, 0.001}, {{
       Hold[$CellContext`scale$$], 2, "arrow scale"}, 0.1, 10, 0.001}, {{
       Hold[$CellContext`a$$], 1, "ring radius"}, 0.01, 3, 0.001}, {{
       Hold[$CellContext`showFieldLines$$], False, "field lines"}, {
      False, True}}, {{
       Hold[$CellContext`showVectorField$$], False, "vector field"}, {
      False, True}}, {{
       Hold[$CellContext`vectorPoints$$], 4, "vector lattice size"}, 2, 10, 
      2}}, Typeset`size$$ = Automatic, Typeset`update$$ = 0, 
    Typeset`initDone$$, Typeset`skipInitDone$$ = 
    False, $CellContext`r$19179$$ = 0, $CellContext`\[Phi]\[Phi]$19180$$ = 
    0, $CellContext`z$19181$$ = 0, $CellContext`scale$19182$$ = 
    0, $CellContext`a$19183$$ = 0, $CellContext`showFieldLines$19184$$ = 
    False, $CellContext`showVectorField$19185$$ = 
    False, $CellContext`vectorPoints$19186$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`a$$ = 1, $CellContext`r$$ = 
        2, $CellContext`scale$$ = 2, $CellContext`showFieldLines$$ = 
        False, $CellContext`showVectorField$$ = 
        False, $CellContext`vectorPoints$$ = 4, $CellContext`z$$ = 
        2, $CellContext`\[Phi]\[Phi]$$ = 0}, "ControllerVariables" :> {
        Hold[$CellContext`r$$, $CellContext`r$19179$$, 0], 
        Hold[$CellContext`\[Phi]\[Phi]$$, $CellContext`\[Phi]\[Phi]$19180$$, 
         0], 
        Hold[$CellContext`z$$, $CellContext`z$19181$$, 0], 
        Hold[$CellContext`scale$$, $CellContext`scale$19182$$, 0], 
        Hold[$CellContext`a$$, $CellContext`a$19183$$, 0], 
        Hold[$CellContext`showFieldLines$$, \
$CellContext`showFieldLines$19184$$, False], 
        Hold[$CellContext`showVectorField$$, \
$CellContext`showVectorField$19185$$, False], 
        Hold[$CellContext`vectorPoints$$, $CellContext`vectorPoints$19186$$, 
         0]}, "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> Show[{
         ParametricPlot3D[{($CellContext`a$$ + 0.2 Cos[$CellContext`\[Phi]]) 
           Cos[$CellContext`\[Theta]], ($CellContext`a$$ + 
            0.2 Cos[$CellContext`\[Phi]]) Sin[$CellContext`\[Theta]], 0.2 
           Sin[$CellContext`\[Phi]]}, {$CellContext`\[Phi], 0, 2 
           Pi}, {$CellContext`\[Theta], 0, 2 Pi}, PlotRange -> 5, Mesh -> 
          None, PerformanceGoal -> "Quality", PlotStyle -> Red, Ticks -> 
          None], 
         Graphics3D[{
           AbsolutePointSize[5], Black, 
           Dynamic[
            
            Point[{$CellContext`r$$ 
              Cos[$CellContext`\[Phi]\[Phi]$$], $CellContext`r$$ 
              Sin[$CellContext`\[Phi]\[Phi]$$], $CellContext`z$$}]], 
           Dynamic[
            
            Arrow[{{$CellContext`r$$ 
               Cos[$CellContext`\[Phi]\[Phi]$$], $CellContext`r$$ 
               Sin[$CellContext`\[Phi]\[Phi]$$], $CellContext`z$$}, \
{$CellContext`r$$ Cos[$CellContext`\[Phi]\[Phi]$$], $CellContext`r$$ 
                Sin[$CellContext`\[Phi]\[Phi]$$], $CellContext`z$$} + \
$CellContext`scale$$ \
$CellContext`ringChargeFieldComponentsPolar[$CellContext`a$$, \
{$CellContext`r$$, $CellContext`\[Phi]\[Phi]$$, $CellContext`z$$}]}]]}], 
         Graphics3D[
          If[$CellContext`showFieldLines$$, {Blue, 
            Line[
             Flatten[
              Map[$CellContext`fieldLineData3D[#, $CellContext`a$$, 4]& , 
               Range[(-11) (Pi/12), Pi, Pi/12]], 1]]}, {Black}], PlotRange -> 
          5], 
         If[$CellContext`showVectorField$$, 
          VectorPlot3D[
           $CellContext`ringChargeFieldComponents[$CellContext`a$$, \
{$CellContext`xx, $CellContext`yy, $CellContext`zz}], {$CellContext`xx, -4, 
            4}, {$CellContext`yy, -4, 4}, {$CellContext`zz, -4, 4}, 
           VectorPoints -> $CellContext`vectorPoints$$, VectorStyle -> {
             Darker[Green], 
             Arrowheads[Medium]}], 
          Graphics3D[{Black}]]}, Boxed -> False, ImageSize -> {400, 400}, 
        BoxStyle -> Directive[
          GrayLevel[0.8]], SphericalRegion -> True, Axes -> None], 
      "Specifications" :> {
        Spacer[
        210], {{$CellContext`r$$, 2, "test charge r"}, 0.001, 4, 0.001, 
         Appearance -> "Labeled", ImageSize -> 
         Tiny}, {{$CellContext`\[Phi]\[Phi]$$, 0, 
          "test charge \[Theta]"}, -3.1416, 3.1416, 0.0001, Appearance -> 
         "Labeled", ImageSize -> 
         Tiny}, {{$CellContext`z$$, 2, "test charge z"}, -4, 4, 0.001, 
         Appearance -> "Labeled", ImageSize -> 
         Tiny}, {{$CellContext`scale$$, 2, "arrow scale"}, 0.1, 10, 0.001, 
         Appearance -> "Labeled", ImageSize -> 
         Tiny}, {{$CellContext`a$$, 1, "ring radius"}, 0.01, 3, 0.001, 
         Appearance -> "Labeled", ImageSize -> 
         Tiny}, {{$CellContext`showFieldLines$$, False, "field lines"}, {
         False, True}}, 
        Delimiter, {{$CellContext`showVectorField$$, False, "vector field"}, {
         False, True}}, {{$CellContext`vectorPoints$$, 4, 
          "vector lattice size"}, 2, 10, 2, Appearance -> "Labeled", 
         ImageSize -> Tiny}}, 
      "Options" :> {
       ControlPlacement -> Left, SynchronousInitialization -> False, 
        AutorunSequencing -> {1, 2, 6, 7}}, 
      "DefaultOptions" :> {ControllerLinking -> True}],
     ImageSizeCache->{485., {103., 108.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>(({
       Attributes[PlotRange] = {
         ReadProtected}, $CellContext`ringChargeFieldComponentsPolar[
          PatternTest[
           Pattern[$CellContext`a, 
            Blank[]], NumericQ], {
           PatternTest[
            Pattern[$CellContext`r, 
             Blank[]], NumericQ], 
           PatternTest[
            Pattern[$CellContext`\[Phi], 
             Blank[]], NumericQ], 
           PatternTest[
            Pattern[$CellContext`z, 
             Blank[]], NumericQ]}] := 
        With[{$CellContext`rcfc = \
$CellContext`ringChargeFieldComponents[$CellContext`a, {$CellContext`r, \
$CellContext`z}]}, {
          Part[$CellContext`rcfc, 1] Cos[$CellContext`\[Phi]], 
           Part[$CellContext`rcfc, 1] Sin[$CellContext`\[Phi]], 
           
           Part[$CellContext`rcfc, 
            2]}], $CellContext`ringChargeFieldComponents[
          PatternTest[
           Pattern[$CellContext`a, 
            Blank[]], NumericQ], {
           PatternTest[
            Pattern[$CellContext`r, 
             Blank[]], NumericQ], 
           PatternTest[
            Pattern[$CellContext`z, 
             Blank[]], NumericQ]}] := 
        Module[{$CellContext`\[Phi], $CellContext`mainExpression, \
$CellContext`denominator, $CellContext`int1, $CellContext`int2}, \
$CellContext`mainExpression = $CellContext`a^2 + $CellContext`r^2 + \
$CellContext`z^2 - ((2 $CellContext`a) $CellContext`r) 
            Cos[$CellContext`\[Phi]]; $CellContext`denominator = \
$CellContext`mainExpression 
            Sqrt[$CellContext`mainExpression]; $CellContext`int1 = 
           NIntegrate[
            1/$CellContext`denominator, {$CellContext`\[Phi], 0, 2 
              Pi}]; $CellContext`int2 = 
           NIntegrate[
            Cos[$CellContext`\[Phi]]/$CellContext`denominator, {$CellContext`\
\[Phi], 0, 2 
              Pi}]; {$CellContext`int1 $CellContext`r - $CellContext`int2 \
$CellContext`a, $CellContext`int1 $CellContext`z}], \
$CellContext`ringChargeFieldComponents[
          PatternTest[
           Pattern[$CellContext`a, 
            Blank[]], NumericQ], {
           PatternTest[
            Pattern[$CellContext`x, 
             Blank[]], NumericQ], 
           PatternTest[
            Pattern[$CellContext`y, 
             Blank[]], NumericQ], 
           PatternTest[
            Pattern[$CellContext`z, 
             Blank[]], NumericQ]}] := 
        With[{$CellContext`\[Phi] = 
           ArcTan[$CellContext`x, $CellContext`y], $CellContext`rcfc = \
$CellContext`ringChargeFieldComponents[$CellContext`a, {
              Sqrt[$CellContext`x^2 + $CellContext`y^2], $CellContext`z}]}, {
          Part[$CellContext`rcfc, 1] Cos[$CellContext`\[Phi]], 
           Part[$CellContext`rcfc, 1] Sin[$CellContext`\[Phi]], 
           Part[$CellContext`rcfc, 2]}], $CellContext`fieldLineData3D[
          Pattern[$CellContext`\[Theta], 
           Blank[]], 
          Pattern[$CellContext`r, 
           Blank[]], 
          Pattern[$CellContext`R, 
           Blank[]]] := Table[
          $CellContext`fieldLineData[$CellContext`\[Theta], {$CellContext`r, \
$CellContext`\[Phi]}, $CellContext`R], {$CellContext`\[Phi], 0, 2 Pi - Pi/3, 
           Pi/3}], $CellContext`fieldLineData[0] = CompressedData["
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         "], $CellContext`fieldLineData[Pi] = CompressedData["
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         "], $CellContext`fieldLineData[
          Pattern[$CellContext`\[Theta], 
           Blank[]], {
           Pattern[$CellContext`r, 
            Blank[]], 
           Pattern[$CellContext`\[Phi], 
            Blank[]]}, 
          Pattern[$CellContext`R, 
           Blank[]]] := ReplaceAll[
          $CellContext`fieldLineData[$CellContext`\[Theta], $CellContext`r, \
$CellContext`R], {
            Pattern[$CellContext`\[Rho], 
             Blank[]], 
            Pattern[$CellContext`\[Zeta], 
             Blank[]]} :> {$CellContext`\[Rho] 
            Cos[$CellContext`\[Phi]], $CellContext`\[Rho] 
            Sin[$CellContext`\[Phi]], $CellContext`\[Zeta]}], \
$CellContext`fieldLineData[
          Pattern[$CellContext`\[Theta], 
           Blank[]], 
          Pattern[$CellContext`r, 
           Blank[]], 
          Pattern[$CellContext`R, 
           
           Blank[]]] := ($CellContext`fieldLineData[$CellContext`\[Theta], \
$CellContext`r, $CellContext`R] = 
         Module[{$CellContext`truncated = 
            Select[$CellContext`r $CellContext`fieldLineData[$CellContext`\
\[Theta]], 
              Norm[#] < $CellContext`R& ], $CellContext`nTruncated, \
$CellContext`step, $CellContext`selected}, $CellContext`nTruncated = 
            Length[$CellContext`truncated]; $CellContext`step = 
            Ceiling[$CellContext`nTruncated/20]; $CellContext`selected = 
            Part[$CellContext`truncated, 
              Range[1, $CellContext`nTruncated, $CellContext`step]]; 
           Append[$CellContext`selected, $CellContext`R Normalize[
               Last[$CellContext`selected]]]])}; Typeset`initDone$$ = True); 
     ReleaseHold[
       HoldComplete[{$CellContext`ringChargeFieldComponents[
           PatternTest[
            Pattern[$CellContext`a, 
             Blank[]], NumericQ], {
            PatternTest[
             Pattern[$CellContext`r, 
              Blank[]], NumericQ], 
            PatternTest[
             Pattern[$CellContext`z, 
              Blank[]], NumericQ]}] := 
         Module[{$CellContext`\[Phi], $CellContext`mainExpression, \
$CellContext`denominator, $CellContext`int1, $CellContext`int2}, \
$CellContext`mainExpression = $CellContext`a^2 + $CellContext`r^2 + \
$CellContext`z^2 - 2 $CellContext`a $CellContext`r 
             Cos[$CellContext`\[Phi]]; $CellContext`denominator = \
$CellContext`mainExpression $CellContext`mainExpression^
              Rational[1, 2]; $CellContext`int1 = 
            NIntegrate[
             1/$CellContext`denominator, {$CellContext`\[Phi], 0, 2 
               Pi}]; $CellContext`int2 = 
            NIntegrate[
             Cos[$CellContext`\[Phi]]/$CellContext`denominator, \
{$CellContext`\[Phi], 0, 2 
               Pi}]; {$CellContext`int1 $CellContext`r - $CellContext`int2 \
$CellContext`a, $CellContext`int1 $CellContext`z}], \
$CellContext`ringChargeFieldComponents[
           PatternTest[
            Pattern[$CellContext`a, 
             Blank[]], NumericQ], {
            PatternTest[
             Pattern[$CellContext`x, 
              Blank[]], NumericQ], 
            PatternTest[
             Pattern[$CellContext`y, 
              Blank[]], NumericQ], 
            PatternTest[
             Pattern[$CellContext`z, 
              Blank[]], NumericQ]}] := 
         With[{$CellContext`\[Phi] = 
            ArcTan[$CellContext`x, $CellContext`y], $CellContext`rcfc = \
$CellContext`ringChargeFieldComponents[$CellContext`a, {($CellContext`x^2 + \
$CellContext`y^2)^Rational[1, 2], $CellContext`z}]}, {
           Part[$CellContext`rcfc, 1] Cos[$CellContext`\[Phi]], 
            Part[$CellContext`rcfc, 1] Sin[$CellContext`\[Phi]], 
            
            Part[$CellContext`rcfc, 
             2]}], $CellContext`ringChargeFieldComponentsPolar[
           PatternTest[
            Pattern[$CellContext`a, 
             Blank[]], NumericQ], {
            PatternTest[
             Pattern[$CellContext`r, 
              Blank[]], NumericQ], 
            PatternTest[
             Pattern[$CellContext`\[Phi], 
              Blank[]], NumericQ], 
            PatternTest[
             Pattern[$CellContext`z, 
              Blank[]], NumericQ]}] := 
         With[{$CellContext`rcfc = \
$CellContext`ringChargeFieldComponents[$CellContext`a, {$CellContext`r, \
$CellContext`z}]}, {
           Part[$CellContext`rcfc, 1] Cos[$CellContext`\[Phi]], 
            Part[$CellContext`rcfc, 1] Sin[$CellContext`\[Phi]], 
            Part[$CellContext`rcfc, 2]}], $CellContext`fieldLineData[
           0] = CompressedData["
1:eJxd13usz3Ucx/HjuKaT5HbcLwdhMrNmKknS6eKWaGam0knNTK5RSVqpZNbM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           "]; Null, $CellContext`fieldLineData[Pi/2] = CompressedData["
1:eJx10j2sn2UZwOFDBZSCoHJQRG1BHers3NBN1nbuZAKruJaZmcUFV5g7McBC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           "]; Null, $CellContext`fieldLineData[Pi/12] = CompressedData["
1:eJwtWXdYTX8Yv6u99657bxFCUra8L0opKyUjShllFIki/YSsyIhIg0ghqWQk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           "]; Null, $CellContext`fieldLineData[5 (Pi/12)] = CompressedData["
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           "]; Null, 
         Do[$CellContext`fieldLineData[$CellContext`\[Theta]] = 
           Map[{-1, 1} #& , 
             $CellContext`fieldLineData[
             Pi - $CellContext`\[Theta]]], {$CellContext`\[Theta], 7 (Pi/12), 
            Pi, Pi/12}]; Null, 
         Do[$CellContext`fieldLineData[$CellContext`\[Theta]] = 
          Map[{1, -1} #& , 
            $CellContext`fieldLineData[-$CellContext`\[Theta]]], \
{$CellContext`\[Theta], (-11) (Pi/12), (-Pi)/12, Pi/
           12}], $CellContext`fieldLineData[
           Pattern[$CellContext`\[Theta], 
            Blank[]], 
           Pattern[$CellContext`r, 
            Blank[]], 
           Pattern[$CellContext`R, 
            
            Blank[]]] := ($CellContext`fieldLineData[$CellContext`\[Theta], \
$CellContext`r, $CellContext`R] = 
          Module[{$CellContext`truncated = 
             Select[$CellContext`r $CellContext`fieldLineData[$CellContext`\
\[Theta]], 
               Norm[#] < $CellContext`R& ], $CellContext`nTruncated, \
$CellContext`step, $CellContext`selected}, $CellContext`nTruncated = 
             Length[$CellContext`truncated]; $CellContext`step = 
             Ceiling[$CellContext`nTruncated/20]; $CellContext`selected = 
             Part[$CellContext`truncated, 
               Range[1, $CellContext`nTruncated, $CellContext`step]]; 
            Append[$CellContext`selected, $CellContext`R Normalize[
                Last[$CellContext`selected]]]]), $CellContext`fieldLineData[
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            Blank[]], {
            Pattern[$CellContext`r, 
             Blank[]], 
            Pattern[$CellContext`\[Phi], 
             Blank[]]}, 
           Pattern[$CellContext`R, 
            Blank[]]] := ReplaceAll[
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$CellContext`R], {
             Pattern[$CellContext`\[Rho], 
              Blank[]], 
             Pattern[$CellContext`\[Zeta], 
              Blank[]]} :> {$CellContext`\[Rho] 
             Cos[$CellContext`\[Phi]], $CellContext`\[Rho] 
             Sin[$CellContext`\[Phi]], $CellContext`\[Zeta]}], \
$CellContext`fieldLineData3D[
           Pattern[$CellContext`\[Theta], 
            Blank[]], 
           Pattern[$CellContext`r, 
            Blank[]], 
           Pattern[$CellContext`R, 
            Blank[]]] := Table[
           $CellContext`fieldLineData[$CellContext`\[Theta], {$CellContext`r, \
$CellContext`\[Phi]}, $CellContext`R], {$CellContext`\[Phi], 0, 2 Pi - Pi/3, 
            Pi/3}]}]]; Typeset`initDone$$ = True),
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This Demonstration shows the electric field around a uniformly charged ring, \
either as a force vector on a movable test particle, as a collection of field \
lines, or as a 3D vector field. The radius of the ring changes, becoming a \
point charge in the limit as the radius approaches zero. By default, the \
field lines and vector field views are switched off; switching on the latter, \
in particular, slows down the response time.\
\>", "ManipulateCaption"],

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