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Cell[CellGroupData[{
Cell["Campo El\[EAcute]trico", "Title",
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 " O campo el\[EAcute]trico \[EAcute] uma grandeza vetorial que descreve a \
for\[CCedilla]a el\[EAcute]trica que uma carga el\[EAcute]trica experimenta \
em um determinado ponto do espa\[CCedilla]o . O estudo do campo \
el\[EAcute]trico teve in\[IAcute]cio no s\[EAcute]culo XVIII, com as \
descobertas de Benjamin Franklin e Charles Coulomb . Desde ent\[ATilde]o, \
diversos f\[IAcute]sicos t\[EHat]m contribu\[IAcute]do para o desenvolvimento \
da eletrost\[AAcute]tica e do campo el\[EAcute]trico . O objetivo deste \
trabalho \[EAcute] apresentar tr\[EHat]s demonstra\[CCedilla]\[OTilde]es do ",
 StyleBox["Wolfram",
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 " sobre o tema do campo el\[EAcute]trico . As \
demonstra\[CCedilla]\[OTilde]es apresentadas buscam ilustrar as caracter\
\[IAcute]sticas do campo el\[EAcute]trico em diferentes situa\[CCedilla]\
\[OTilde]es . O desenvolvimento do trabalho busca contextualizar o tema, \
destacando conceitos fundamentais do campo el\[EAcute]trico .\n\n"
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Cell["\<\
O campo el\[EAcute]trico \[EAcute] uma grandeza vetorial que descreve a for\
\[CCedilla]a el\[EAcute]trica que uma carga el\[EAcute]trica experimenta em \
um determinado ponto do espa\[CCedilla]o . Ele \[EAcute] definido como a for\
\[CCedilla]a el\[EAcute]trica por unidade de carga e \[EAcute] denotado por E \
. O campo el\[EAcute]trico \[EAcute] uma grandeza vetorial, o que significa \
que ele possui m\[OAcute]dulo, dire\[CCedilla]\[ATilde]o e sentido . Aqui est\
\[ATilde]o algumas das mais famosas defini\[CCedilla]\[OTilde]es matem\
\[AAcute]ticas de campo el\[EAcute]trico :
  
  \
\>", "Text",
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Cell["\<\
Outro t\[OAcute]pico importante para n\[OAcute]s ser\[AAcute] as linhas de \
campo . Representamos todo campo vetorial, como \[EAcute] o caso do campo el\
\[EAcute]trico por meio de linhas de campo . Definimos tais mecanismos como \
linhas de for\[CCedilla]a que s\[ATilde]o linhas imagin\[AAcute]rias, podendo \
ser retas ou curvas, cuja tangente em qualquer ponto, fornece a dire\
\[CCedilla]\[ATilde]o e o sentido do vetor campo el\[EAcute]trico . Essas \
ferramentas n\[ATilde]o nos fornecem diretamente a intensidade do campo el\
\[EAcute]trico, mas em regi\[OTilde]es de maior intensidade de campo el\
\[EAcute]trico elas s\[ATilde]o mais densas, assim como em s\[ATilde]o menos \
densas numa regi\[ATilde]o onde o campo el\[EAcute]trico tem menor \
intensidade . Observamos seu comportamento como sendo da seguinte forma :\
\>", "Text",
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Acima observamos uma part\[IAcute]cula eletrizada com carga positiva (I) e \
com carga negativa (II) . Sempre iremos observar esse comportamento das \
linhas de afastamento das cargas positivas e aproximam - se das negativas . \
Outro ponto \[EAcute] que elas nunca se cruzam, pois se isso ocorresse no \
ponto de cruzamento voc\[EHat] teria dois vetores campo el\[EAcute]trico .
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A primeira demonstra\[CCedilla]\[ATilde]o apresentada pelo Wolfram \[EAcute] \
\"Campos El\[EAcute]tricos para 3 Cargas pontuais\" . Nesta demonstra\
\[CCedilla]\[ATilde]o, \[EAcute] poss\[IAcute]vel visualizar o campo el\
\[EAcute]trico gerado por tr\[EHat]s cargas pontuais . A demonstra\[CCedilla]\
\[ATilde]o ilustra como o campo el\[EAcute]trico \[EAcute] influenciado pela \
posi\[CCedilla]\[ATilde]o e magnitude das cargas . \[CapitalEAcute] poss\
\[IAcute]vel notar que as linhas de campo el\[EAcute]trico se estendem \
infinitamente no espa\[CCedilla]o, o que significa que o campo \
el\[EAcute]trico \[EAcute] uma grandeza que pode ser observada em qualquer \
ponto do espa\[CCedilla]o . \[CapitalEAcute] poss\[IAcute]vel ajustar as posi\
\[CCedilla]\[OTilde]es e cargas das tr\[EHat]s part\[IAcute]culas e ver como \
o campo el\[EAcute]trico resultante se comporta em diferentes regi\[OTilde]es \
do espa\[CCedilla]o .
\
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          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) (($CellContext`x - \
$CellContext`v $CellContext`t)/(($CellContext`x - $CellContext`v \
$CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Ey[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) \
($CellContext`y/(($CellContext`x - $CellContext`v $CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Ez[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) \
($CellContext`z/(($CellContext`x - $CellContext`v $CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Bx[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = 0; $CellContext`By[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           
           Blank[]]] = (-($CellContext`v/$CellContext`c^2)) \
$CellContext`Ez[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]; $CellContext`Bz[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = 
        Plus[$CellContext`v/$CellContext`c^2] $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]; \
$CellContext`ue[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (Subscript[$CellContext`\[Epsilon], 0]/
          2) ($CellContext`Ex[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2 + $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2 + \
$CellContext`Ez[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2); $CellContext`ub[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = ((Subscript[$CellContext`\[Epsilon], 0]/
           2) $CellContext`c^2) ($CellContext`Bx[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2 + \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2 + $CellContext`Bz[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2); \
$CellContext`u[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           
           Blank[]]] = $CellContext`ue[$CellContext`t, $CellContext`x, \
$CellContext`y, $CellContext`z, $CellContext`v] + \
$CellContext`ub[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]; $CellContext`Sx[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bz[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ez[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`Sy[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ez[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ex[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bz[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`Sz[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ex[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`ep[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Ex[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
          $CellContext`Ey[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]}; $CellContext`bp[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
          $CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]}; $CellContext`sp[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Sx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
          $CellContext`Sy[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]}; $CellContext`h = 50; Null}; 
     Typeset`initDone$$ = True),
    SynchronousInitialization->True,
    UndoTrackedVariables:>{Typeset`show$$, Typeset`bookmarkMode$$},
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Input",
 CellChangeTimes->{{3.896468206955614*^9, 
  3.8964682098837786`*^9}},ExpressionUUID->"481b7c62-18f0-46d1-9b8a-\
203d78a04a8d"],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`op$$ = $CellContext`ep, $CellContext`op1$$ \
= $CellContext`ub, $CellContext`t$$ = 
    6.272727272727272*^-8, $CellContext`v$$ = 
    2.2*^8, $CellContext`z$$ = -6.599999999999994, Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`op1$$], $CellContext`ue, 
       "contourplot"}, {$CellContext`ue -> 
       "electric energy density", $CellContext`ub -> 
       "magnetic energy density", $CellContext`Ez -> 
       Subscript["E", "z"], $CellContext`Bz -> 
       Subscript["B", "z"], $CellContext`Sz -> Subscript["S", "z"]}}, {{
       Hold[$CellContext`op$$], $CellContext`ep, 
       "vectorfield"}, {$CellContext`ep -> 
       "xy component of electric field ", $CellContext`bp -> 
       "xy component of magnetic field ", $CellContext`sp -> 
       "xy component of Poynting vector"}}, {{
       Hold[$CellContext`z$$], 10, "z position"}, -50, 50}, {{
       Hold[$CellContext`v$$], 100000000, "velocity"}, 100000000, 2.997*^8}, {{
       Hold[$CellContext`t$$], 0, "time"}, 
      Dynamic[-($CellContext`h/$CellContext`v$$)], 
      Dynamic[$CellContext`h/$CellContext`v$$]}}, Typeset`size$$ = {
    710., {183., 192.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = False}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`op$$ = $CellContext`ep, $CellContext`op1$$ = \
$CellContext`ue, $CellContext`t$$ = 0, $CellContext`v$$ = 
        100000000, $CellContext`z$$ = 10}, "ControllerVariables" :> {}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, 
      "Body" :> (
       If[$CellContext`z$$ < -$CellContext`h, $CellContext`z$$ = \
-$CellContext`h]; 
       If[$CellContext`z$$ > $CellContext`h, $CellContext`z$$ = \
$CellContext`h]; 
       If[$CellContext`t$$ < -($CellContext`h/$CellContext`v$$), \
$CellContext`t$$ = -($CellContext`h/$CellContext`v$$)]; 
       If[$CellContext`t$$ > $CellContext`h/$CellContext`v$$, \
$CellContext`t$$ = $CellContext`h/$CellContext`v$$]; GraphicsGrid[{{
           ContourPlot[10^20 Evaluate[
              $CellContext`op1$$[$CellContext`t$$, $CellContext`x, \
$CellContext`y, $CellContext`z$$, $CellContext`v$$]], {$CellContext`x, \
-$CellContext`h, $CellContext`h}, {$CellContext`y, -$CellContext`h, \
$CellContext`h}, AxesLabel -> Automatic, ImageSize -> {250, 250}], 
           VectorPlot[
            Evaluate[
             $CellContext`op$$[$CellContext`t$$, $CellContext`x, \
$CellContext`y, $CellContext`z$$, $CellContext`v$$]], {$CellContext`x, \
-$CellContext`h, $CellContext`h}, {$CellContext`y, -$CellContext`h, \
$CellContext`h}, VectorPoints -> 16, VectorScale -> Small, Frame -> False, 
            ImageSize -> {250, 250}]}}]), 
      "Specifications" :> {{{$CellContext`op1$$, $CellContext`ue, 
          "contourplot"}, {$CellContext`ue -> 
          "electric energy density", $CellContext`ub -> 
          "magnetic energy density", $CellContext`Ez -> 
          Subscript["E", "z"], $CellContext`Bz -> 
          Subscript["B", "z"], $CellContext`Sz -> 
          Subscript["S", "z"]}}, {{$CellContext`op$$, $CellContext`ep, 
          "vectorfield"}, {$CellContext`ep -> 
          "xy component of electric field ", $CellContext`bp -> 
          "xy component of magnetic field ", $CellContext`sp -> 
          "xy component of Poynting vector"}}, {{$CellContext`z$$, 10, 
          "z position"}, -$CellContext`h, $CellContext`h, Appearance -> 
         "Labeled", Exclusions -> 
         0}, {{$CellContext`v$$, 100000000, "velocity"}, 100000000, 2.997*^8, 
         Appearance -> "Labeled"}, {{$CellContext`t$$, 0, "time"}, 
         Dynamic[-($CellContext`h/$CellContext`v$$)], 
         Dynamic[$CellContext`h/$CellContext`v$$], Appearance -> "Labeled"}}, 
      "Options" :> {}, "DefaultOptions" :> {}],
     ImageSizeCache->{856., {367.76806640625, 379.23193359375}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    Initialization:>({$CellContext`q = 1.602177 10^(-19); $CellContext`c = 
        2.997924 10^8; 
       Subscript[$CellContext`\[Epsilon], 0] = 
        10^7/((4 Pi) $CellContext`c^2); $CellContext`\[Phi][
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) (
          1/(($CellContext`x - $CellContext`v $CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(1/2)); $CellContext`Ex[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) (($CellContext`x - \
$CellContext`v $CellContext`t)/(($CellContext`x - $CellContext`v \
$CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Ey[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) \
($CellContext`y/(($CellContext`x - $CellContext`v $CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Ez[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (($CellContext`q/((4 Pi) 
           Subscript[$CellContext`\[Epsilon], 0])) (1/Sqrt[
           1 - $CellContext`v^2/$CellContext`c^2])) \
($CellContext`z/(($CellContext`x - $CellContext`v $CellContext`t)^2/(
            1 - $CellContext`v^2/$CellContext`c^2) + $CellContext`y^2 + \
$CellContext`z^2)^(3/2)); $CellContext`Bx[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = 0; $CellContext`By[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           
           Blank[]]] = (-($CellContext`v/$CellContext`c^2)) \
$CellContext`Ez[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]; $CellContext`Bz[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = 
        Plus[$CellContext`v/$CellContext`c^2] $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]; \
$CellContext`ue[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (Subscript[$CellContext`\[Epsilon], 0]/
          2) ($CellContext`Ex[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2 + $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2 + \
$CellContext`Ez[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2); $CellContext`ub[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = ((Subscript[$CellContext`\[Epsilon], 0]/
           2) $CellContext`c^2) ($CellContext`Bx[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2 + \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]^2 + $CellContext`Bz[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v]^2); \
$CellContext`u[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           
           Blank[]]] = $CellContext`ue[$CellContext`t, $CellContext`x, \
$CellContext`y, $CellContext`z, $CellContext`v] + \
$CellContext`ub[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]; $CellContext`Sx[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bz[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ez[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`Sy[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ez[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ex[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bz[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`Sz[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = (
          Subscript[$CellContext`\[Epsilon], 
            0] $CellContext`c^2) ($CellContext`Ex[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v] - $CellContext`Ey[$CellContext`t, \
$CellContext`x, $CellContext`y, $CellContext`z, $CellContext`v] \
$CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]); $CellContext`ep[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Ex[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
          $CellContext`Ey[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]}; $CellContext`bp[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Bx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
          $CellContext`By[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v]}; $CellContext`sp[
          Pattern[$CellContext`t, 
           Blank[]], 
          Pattern[$CellContext`x, 
           Blank[]], 
          Pattern[$CellContext`y, 
           Blank[]], 
          Pattern[$CellContext`z, 
           Blank[]], 
          Pattern[$CellContext`v, 
           Blank[]]] = {
          $CellContext`Sx[$CellContext`t, $CellContext`x, $CellContext`y, \
$CellContext`z, $CellContext`v], 
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