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2, $CellContext`i == 1], 100., True, RandomReal[{0, 100}]], {$CellContext`i, $CellContext`size$$/ 2}, {$CellContext`j, $CellContext`size$$}], \ $CellContext`step$$], {$CellContext`size$$, $CellContext`size$$}], Table[{$CellContext`size$$ - $CellContext`n + 1, $CellContext`n}, {$CellContext`n, $CellContext`size$$/ 2}]], 200. -> 100.]}, $CellContext`plateoctave + Reverse[ Map[Reverse, Transpose[$CellContext`plateoctave]]]]; With[{$CellContext`platepart$ = If[$CellContext`resize$$, ArrayFlatten[ ({{ Reverse[#], Transpose[#]}, {#, Map[Reverse, #]}}& )[ PadRight[$CellContext`platequarter$, {$CellContext`size$$, \ $CellContext`size$$}, ""]]], $CellContext`platequarter$]}, Grid[{{ ArrayPlot[$CellContext`platepart$, ImageSize -> {250, 250}, Mesh -> If[$CellContext`resize$$, 2, 1] {{0, $CellContext`size$$}, { 0, $CellContext`size$$}}], ListPlot3D[ Flatten[ MapIndexed[{ Apply[Sequence, #2], #/100}& , $CellContext`platepart$, {2}], 1], RegionFunction -> If[$CellContext`resize$$, Not[ And[ 3 ($CellContext`size$$/2) + 1 >= # >= $CellContext`size$$/ 2, $CellContext`size$$/2 <= #2 <= 3 ($CellContext`size$$/2) + 1]]& , Or[# >= $CellContext`size$$/2 + 1, #2 < $CellContext`size$$/ 2]& ], ImageSize -> {250, 250}, PerformanceGoal -> "Quality", Ticks -> None, PlotRangePadding -> 0]}}]]], "Specifications" :> {{{$CellContext`size$$, 20, "grid size"}, 10, 40, 2, Appearance -> "Labeled"}, {{$CellContext`step$$, 2}, 0, 20, 1, Appearance -> "Labeled"}, {{$CellContext`resize$$, False, "complete plate"}, { True, False}}, {$CellContext`seed$$, 1000, 2000, 1}}, "Options" :> {}, "DefaultOptions" :> {ControllerLinking -> True}], ImageSizeCache->{554., {220., 225.}}, SingleEvaluation->True], Deinitialization:>None, DynamicModuleValues:>{}, Initialization:>({$CellContext`rm = CompiledFunction[{ Blank[Integer], { Blank[Real], 2}}, {{2, 0, 0}, {3, 2, 0}, {3, 2, 1}}, {2, 10, 6, 0, 3}, {{1, 5}, {46, 0, 1}, {7, 1, 2}, {7, 2, 3}, {15, 0, 2, 2}, {15, 0, 3, 1}, {94, 260, 3, 0, 2, 3, 0, 1, 3, 0, 3}, {15, 1, 0, 2}, {21, 2, 3, 2}, {7, -1, 2}, {15, 0, 2, 3}, {18, 2, 3, 2}, {28, 2, 2}, {7, 1, 3}, {4, 84}, {11, 0, 5}, {7, 1, 6}, {4, 80}, {7, 1, 7}, {7, 2, 8}, {15, 0, 7, 2}, {15, 0, 8, 3}, {94, 260, 3, 0, 2, 3, 0, 3, 3, 0, 1}, {15, 1, 0, 2}, {21, 2, 1, 2}, {23, 6, 7}, {7, 1, 8}, {15, 0, 7, 1}, {15, 0, 8, 3}, {18, 2, 1, 3, 2}, {15, 0, 3, 1}, {39, 2, 1, 0}, { 3, 0, 62}, {7, 1, 7}, {7, 2, 8}, {15, 0, 7, 2}, {15, 0, 8, 1}, {94, 260, 3, 0, 2, 3, 0, 1, 3, 0, 3}, {15, 1, 0, 2}, {21, 2, 3, 2}, {23, 6, 7}, {7, 1, 8}, {15, 0, 7, 3}, {15, 0, 8, 1}, {18, 2, 3, 1, 2}, { 15, 0, 3, 3}, {34, 3, 2, 0, 1}, {3, 1, 5}, {7, 1, 7}, {17, 3, 7, 8}, {11, 8, 7}, {4, 4}, {7, -1, 7}, {17, 3, 7, 9}, {11, 9, 7}, {70, 1, 0, 7, 0, 6, 0, 2}, {7, 1, 7}, {17, 3, 7, 8}, {70, 1, 0, 8, 0, 6, 0, 3}, {7, 1, 8}, {7, 2, 7}, {15, 0, 8, 1}, {15, 0, 7, 4}, {94, 260, 3, 0, 1, 3, 0, 4, 3, 0, 5}, {15, 1, 0, 1}, {21, 1, 5, 1}, {23, 6, 8}, {7, 1, 7}, {15, 0, 8, 5}, {15, 0, 7, 4}, {18, 1, 5, 4, 1}, {15, 0, 3, 5}, {34, 5, 1, 0, 1}, {3, 1, 5}, {7, 1, 8}, {17, 6, 8, 7}, { 11, 7, 8}, {4, 4}, {7, -1, 8}, {17, 6, 8, 9}, {11, 9, 8}, {70, 1, 0, 3, 0, 8, 0, 1}, {33, 6, 0, 1}, {3, 1, 3}, {11, 6, 8}, {4, 4}, {7, 1, 8}, {17, 6, 8, 7}, {11, 7, 8}, {70, 1, 0, 3, 0, 8, 0, 5}, {67, 2, 3, 1, 5, 3, 2}, {55, Mean, 3, 1, 2, 3, 0, 2}, {12, 2, 1}, {4, 3}, { 8, 0., 3}, {12, 3, 1}, {71, 1, 0, 3, 0, 6, 0, 1}, {5, 6, 5, -79}, { 5, 3, 2, -83}, {2}}, Function[{$CellContext`size, $CellContext`grid}, Module[{$CellContext`plate = $CellContext`grid}, Do[Part[$CellContext`plate, $CellContext`a, $CellContext`b] = If[$CellContext`a >= $CellContext`size/2 - $CellContext`b + 1, Mean[{ Part[$CellContext`plate, If[$CellContext`a == $CellContext`size/2 - $CellContext`b + 1, $CellContext`a + 1, $CellContext`a - 1], $CellContext`b], Part[$CellContext`plate, $CellContext`a + 1, $CellContext`b], Part[$CellContext`plate, $CellContext`a, If[$CellContext`a == $CellContext`size/2 - $CellContext`b + 1, $CellContext`b + 1, $CellContext`b - 1]], Part[$CellContext`plate, 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inclina\[CCedilla]\[ATilde]o do segmento com respeito ao eixo x \[EAcute] \ tal que\n\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"cos", " ", "\[Theta]"}], " ", "=", FractionBox[ RowBox[{ SubscriptBox["x", "f"], "-", SubscriptBox["x", "i"]}], "L"]}], TraditionalForm]]], "\n\t", Cell[BoxData[ FormBox[ RowBox[{ RowBox[{"sen", " ", "\[Theta]"}], " ", "=", FractionBox[ RowBox[{ SubscriptBox["y", "f"], "-", SubscriptBox["y", "i"]}], "L"]}], TraditionalForm]]], "\n\nO segmento de lado L que come\[CCedilla]a no ponto inicial e termina no \ ponto final pode ent\[ATilde]o ser definido como dado pelas coordenadas:\n\n\t\ ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["x", "s"], "=", RowBox[{ RowBox[{"cos", " ", "\[Theta]", " ", "*", RowBox[{"(", RowBox[{"x", "-", SubscriptBox["x", "m"]}], ")"}]}], " ", "+", " ", RowBox[{"sen", " ", "\[Theta]", " ", "*", " ", RowBox[{"(", RowBox[{"y", "-", SubscriptBox["y", "m"]}], ")"}], " "}]}]}], TraditionalForm]]], "\t\[LongRightArrow] ", Cell[BoxData[ 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Trata-se de uma solu\[CCedilla]\ \[ATilde]o para ", StyleBox["um certo", FontSlant->"Italic"], " problema, mas um problema distinto do de duas tiras que for\[CCedilla]amos \ estarem em potenciais iguais.\n\nO fato surpreendente \[EAcute] que, se \ observarmos nessa nova solu\[CCedilla]\[ATilde]o a linha imagin\[AAcute]ria \ que une as extremidades dos dois fios (em 3D isso seria uma nova tira unindo \ as arestas das duas tiras originais), o potencial ao longo dessa linha imagin\ \[AAcute]ria \[EAcute] justamente ", Cell[BoxData[ FormBox[ RowBox[{ SubscriptBox["\[CurlyPhi]", "0"], "=", "1"}], TraditionalForm]]], "!\n\nPodemos ver isso pelo gr\[AAcute]fico abaixo, no qual plotamos a soma \ do potencial do fio A (ao longo do eixo x) e do fio C (a ", Cell[BoxData[ FormBox[ SuperscriptBox["60", "o"], TraditionalForm]]], ") como fun\[CCedilla]\[ATilde]o de x, e ressaltamos a linha de \ equipotencial \[CurlyPhi]=1." }], "Subsection", CellChangeTimes->{{3.5859083119080276`*^9, 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De fato, \ juntando segmentos como fizemos acima podemos encontrar as solu\[CCedilla]\ \[OTilde]es para ", StyleBox["tubos com se\[CCedilla]\[OTilde]es poligonais arbitr\[AAcute]rias.", FontWeight->"Bold"], "\n\nMas vamos nos ater ao tubo triangular, mostrado acima. Dentro do tubo \ triangular o potencial \[EAcute] constante, e fora do tubo o campo \[EAcute] \ diferente de zero -- de fato, o campo el\[EAcute]trico vai ser \ particularmente forte nas pontas do tri\[AHat]ngulo.\n\nEsse campo \ el\[EAcute]trico \[EAcute] dado por ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox[ OverscriptBox[ StyleBox["E", FontWeight->"Bold"], "\[RightVector]"], FontWeight->"Bold"], "=", RowBox[{"-", RowBox[{ StyleBox[ OverscriptBox[ StyleBox["\[Del]", FontWeight->"Bold"], "\[RightVector]"], FontWeight->"Bold"], StyleBox["\[CurlyPhi]", FontWeight->"Plain"]}]}]}], TraditionalForm]], FormatType->"TraditionalForm"], " . 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