Permalink
Switch branches/tags
Nothing to show
Find file Copy path
Fetching contributors…
Cannot retrieve contributors at this time
11067 lines (10973 sloc) 570 KB
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 11.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 158, 7]
NotebookDataLength[ 572618, 11058]
NotebookOptionsPosition[ 568723, 10940]
NotebookOutlinePosition[ 569134, 10956]
CellTagsIndexPosition[ 569091, 10953]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell["Let\[CloseCurlyQuote]s examine the electrostatic vector field \
function.", "Text",
CellFrame->{{0, 0}, {0, 0.5}},
CellGroupingRules->{"GroupTogetherGrouping", 0},
CellChangeTimes->{{3.6893448078512926`*^9, 3.689344868525245*^9}}],
Cell[TextData[Cell[BoxData[
FormBox[GridBox[{
{""}
},
GridBoxItemSize->{"Columns" -> {{
Scaled[0.96]}}}], TraditionalForm]]]], "Text",
CellChangeTimes->{{3.689344912065056*^9, 3.689344916502315*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"F", "[",
RowBox[{"x_", ",", " ", "y_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "1"}], "]"}], "*", "x"}], " ", "+", " ", "\n",
" ",
RowBox[{
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "2"}], "]"}], "*", "y"}]}]}], ";"}],
" "}], "\n",
RowBox[{"VectorPlot", "[",
RowBox[{
RowBox[{"F", "[",
RowBox[{"i", ",", " ", "j"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"i", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ",
RowBox[{"{",
RowBox[{"j", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{
"PlotLabel", " ", "->", " ", "\n", " ", "\"\<2D Position Vector\>\""}]}],
"]"}]}], "Input",
CellChangeTimes->{{3.688892187141012*^9, 3.688892203515355*^9}, {
3.6888923547025914`*^9, 3.6888923897316675`*^9}, {3.6888924812089567`*^9,
3.688892522773132*^9}, {3.688892603065627*^9, 3.6888926241044397`*^9}, {
3.6893443414257035`*^9, 3.6893443428947496`*^9}, {3.689345014859291*^9,
3.6893450697442164`*^9}, {3.689345110946555*^9, 3.689345368574374*^9}, {
3.689345495094056*^9, 3.689345505686316*^9}, {3.689345542029546*^9,
3.6893456471204443`*^9}, 3.689356436628965*^9}],
Cell[BoxData[
GraphicsBox[{{},
{GrayLevel[0],
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.9285714285714286}, \
{-1.0714285714285714`, -1.0714285714285714`}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.7959183673469389}, \
{-1.0714285714285714`, -0.9183673469387756}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.6632653061224492}, \
{-1.0714285714285714`, -0.7653061224489797}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.5306122448979593}, \
{-1.0714285714285714`, -0.6122448979591838}}]},
{Arrowheads[{{0.03529105076134966, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.39795918367346955`}, \
{-1.0714285714285714`, -0.45918367346938793`}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.2653061224489798}, \
{-1.0714285714285714`, -0.30612244897959207`}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.13265306122449}, \
{-1.0714285714285714`, -0.15306122448979614`}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-0.9285714285714286, -2.061842760018148*^-16}, \
{-1.0714285714285714`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.13265306122448958`}, {-1.0714285714285714`, 0.15306122448979567`}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.2653061224489794}, {-1.0714285714285714`, 0.30612244897959157`}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.39795918367346916`}, {-1.0714285714285714`, 0.4591836734693875}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.530612244897959}, {-1.0714285714285714`, 0.6122448979591835}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.6632653061224487}, {-1.0714285714285714`, 0.7653061224489792}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.7959183673469384}, {-1.0714285714285714`, 0.9183673469387751}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.9285714285714282}, {-1.0714285714285714`, 1.071428571428571}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.9285714285714286}, \
{-0.9183673469387756, -1.0714285714285714`}}]},
{Arrowheads[{{0.039320301634514, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.7959183673469389}, \
{-0.9183673469387756, -0.9183673469387756}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.6632653061224492}, \
{-0.9183673469387756, -0.7653061224489797}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.5306122448979593}, \
{-0.9183673469387755, -0.6122448979591838}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.39795918367346955`}, \
{-0.9183673469387755, -0.45918367346938793`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.2653061224489798}, \
{-0.9183673469387756, -0.30612244897959207`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.13265306122449}, \
{-0.9183673469387756, -0.15306122448979614`}}]},
{Arrowheads[{{0.027803651924065337`, 1.}}],
ArrowBox[{{-0.7959183673469389, -2.061842760018148*^-16}, \
{-0.9183673469387756, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.13265306122448958`}, {-0.9183673469387756, 0.15306122448979567`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.2653061224489794}, {-0.9183673469387756, 0.3061224489795916}}]},
{Arrowheads[{{0.03108542786247645, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.39795918367346916`}, {-0.9183673469387756, 0.4591836734693875}}]},
{Arrowheads[{{0.03341583088579019, 1.}}],
ArrowBox[{{-0.7959183673469389, 0.530612244897959}, {-0.9183673469387756,
0.6122448979591835}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.6632653061224487}, {-0.9183673469387756, 0.7653061224489792}}]},
{Arrowheads[{{0.03932030163451398, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.7959183673469384}, {-0.9183673469387756, 0.9183673469387751}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.9285714285714282}, {-0.9183673469387756, 1.071428571428571}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.9285714285714286}, \
{-0.7653061224489797, -1.0714285714285714`}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.7959183673469389}, \
{-0.7653061224489797, -0.9183673469387756}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.6632653061224492}, \
{-0.7653061224489797, -0.7653061224489797}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.5306122448979593}, \
{-0.7653061224489797, -0.6122448979591838}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.39795918367346955`}, \
{-0.7653061224489797, -0.45918367346938793`}}]},
{Arrowheads[{{0.02495454130854903, 1.}}],
ArrowBox[{{-0.663265306122449, -0.2653061224489798}, \
{-0.7653061224489797, -0.30612244897959207`}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.13265306122449}, \
{-0.7653061224489797, -0.15306122448979614`}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-0.6632653061224492, -2.061842760018148*^-16}, \
{-0.7653061224489797, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.13265306122448958`}, {-0.7653061224489797, 0.15306122448979567`}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.2653061224489794}, {-0.7653061224489797, 0.30612244897959157`}}]},
{Arrowheads[{{0.027020292811707983`, 1.}}],
ArrowBox[{{-0.663265306122449,
0.39795918367346916`}, {-0.7653061224489797, 0.4591836734693875}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.6632653061224492, 0.530612244897959}, {-0.7653061224489797,
0.6122448979591835}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.6632653061224487}, {-0.7653061224489797, 0.7653061224489792}}]},
{Arrowheads[{{0.03619224390482541, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.7959183673469384}, {-0.7653061224489797, 0.9183673469387751}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.9285714285714282}, {-0.7653061224489797, 1.071428571428571}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.9285714285714286}, \
{-0.6122448979591838, -1.0714285714285714`}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.7959183673469389}, \
{-0.6122448979591838, -0.9183673469387755}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.6632653061224492}, \
{-0.6122448979591838, -0.7653061224489797}}]},
{Arrowheads[{{0.026213534423009357`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.5306122448979593}, \
{-0.6122448979591839, -0.6122448979591839}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.39795918367346955`}, \
{-0.6122448979591838, -0.45918367346938793`}}]},
{Arrowheads[{{0.020723618574984323`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.2653061224489798}, \
{-0.6122448979591839, -0.30612244897959207`}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.13265306122449}, \
{-0.6122448979591838, -0.15306122448979614`}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-0.5306122448979593, -2.061842760018148*^-16}, \
{-0.6122448979591838, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.13265306122448958`}, {-0.6122448979591838, 0.15306122448979567`}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.2653061224489794}, {-0.6122448979591838, 0.30612244897959157`}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.39795918367346916`}, {-0.6122448979591838, 0.4591836734693875}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{-0.5306122448979593, 0.530612244897959}, {-0.6122448979591838,
0.6122448979591835}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.6632653061224487}, {-0.6122448979591838, 0.7653061224489792}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.7959183673469384}, {-0.6122448979591838, 0.9183673469387751}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.9285714285714282}, {-0.6122448979591838, 1.071428571428571}}]},
{Arrowheads[{{0.03529105076134966, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.9285714285714286}, \
{-0.45918367346938793`, -1.0714285714285714`}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.7959183673469389}, \
{-0.45918367346938793`, -0.9183673469387755}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.6632653061224492}, \
{-0.45918367346938793`, -0.7653061224489797}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.5306122448979593}, \
{-0.45918367346938793`, -0.6122448979591838}}]},
{Arrowheads[{{0.019660150817257, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.39795918367346955`}, \
{-0.45918367346938793`, -0.45918367346938793`}}]},
{Arrowheads[{{0.0167079154428951, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.2653061224489798}, \
{-0.45918367346938793`, -0.30612244897959207`}}]},
{Arrowheads[{{0.014653811225094899`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.13265306122449}, \
{-0.45918367346938793`, -0.15306122448979614`}}]},
{Arrowheads[{{0.013901825962032668`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -2.061842760018148*^-16}, \
{-0.45918367346938793`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.014653811225094897`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.13265306122448958`}, {-0.45918367346938793`, 0.15306122448979567`}}]},
{Arrowheads[{{0.016707915442895085`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.2653061224489794}, {-0.45918367346938793`, 0.30612244897959157`}}]},
{Arrowheads[{{0.01966015081725699, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.39795918367346916`}, {-0.45918367346938793`, 0.4591836734693875}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.530612244897959}, {-0.45918367346938793`, 0.6122448979591835}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.6632653061224487}, {-0.45918367346938793`, 0.7653061224489792}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.7959183673469384}, {-0.45918367346938793`, 0.9183673469387751}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{-0.3979591836734696,
0.9285714285714282}, {-0.45918367346938793`, 1.071428571428571}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.9285714285714286}, \
{-0.30612244897959207`, -1.0714285714285714`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.7959183673469389}, \
{-0.30612244897959207`, -0.9183673469387756}}]},
{Arrowheads[{{0.02495454130854903, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.663265306122449}, \
{-0.30612244897959207`, -0.7653061224489797}}]},
{Arrowheads[{{0.020723618574984323`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.5306122448979593}, \
{-0.30612244897959207`, -0.6122448979591839}}]},
{Arrowheads[{{0.0167079154428951, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.39795918367346955`}, \
{-0.30612244897959207`, -0.45918367346938793`}}]},
{Arrowheads[{{0.013106767211504678`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.2653061224489798}, \
{-0.30612244897959207`, -0.30612244897959207`}}]},
{Arrowheads[{{0.010361809287492162`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.13265306122449}, \
{-0.30612244897959207`, -0.15306122448979614`}}]},
{Arrowheads[{{0.009267883974688454, 1.}}],
ArrowBox[{{-0.2653061224489798, -2.061842760018148*^-16}, \
{-0.30612244897959207`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.010361809287492156`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.13265306122448958`}, {-0.30612244897959207`, 0.15306122448979567`}}]},
{Arrowheads[{{0.01310676721150466, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.2653061224489794}, {-0.30612244897959207`, 0.30612244897959157`}}]},
{Arrowheads[{{0.016707915442895092`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.39795918367346916`}, {-0.30612244897959207`, 0.4591836734693875}}]},
{Arrowheads[{{0.0207236185749843, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.530612244897959}, {-0.30612244897959207`, 0.6122448979591835}}]},
{Arrowheads[{{0.024954541308549006`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.6632653061224487}, {-0.30612244897959207`, 0.7653061224489792}}]},
{Arrowheads[{{0.029307622450189773`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.7959183673469384}, {-0.30612244897959207`, 0.9183673469387751}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.9285714285714282}, {-0.30612244897959207`, 1.071428571428571}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.13265306122449, -0.9285714285714286}, \
{-0.15306122448979614`, -1.0714285714285714`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.7959183673469389}, \
{-0.15306122448979614`, -0.9183673469387756}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.6632653061224492}, \
{-0.15306122448979614`, -0.7653061224489797}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.13265306122449, -0.5306122448979593}, \
{-0.15306122448979614`, -0.6122448979591838}}]},
{Arrowheads[{{0.014653811225094899`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.39795918367346955`}, \
{-0.15306122448979614`, -0.45918367346938793`}}]},
{Arrowheads[{{0.010361809287492162`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.2653061224489798}, \
{-0.15306122448979614`, -0.30612244897959207`}}]},
{Arrowheads[{{0.006553383605752339, 1.}}],
ArrowBox[{{-0.13265306122449, -0.13265306122449}, \
{-0.15306122448979614`, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344227, 1.}}],
ArrowBox[{{-0.13265306122449, -2.061842760018148*^-16}, \
{-0.15306122448979614`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.00655338360575233, 1.}}],
ArrowBox[{{-0.13265306122449,
0.13265306122448958`}, {-0.15306122448979614`, 0.15306122448979567`}}]},
{Arrowheads[{{0.010361809287492139`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.2653061224489794}, {-0.15306122448979614`, 0.30612244897959157`}}]},
{Arrowheads[{{0.014653811225094886`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.39795918367346916`}, {-0.15306122448979614`, 0.4591836734693875}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.13265306122449, 0.530612244897959}, {-0.15306122448979614`,
0.6122448979591835}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.6632653061224487}, {-0.15306122448979614`, 0.7653061224489792}}]},
{Arrowheads[{{0.02818716868819308, 1.}}],
ArrowBox[{{-0.13265306122449,
0.7959183673469384}, {-0.15306122448979614`, 0.9183673469387751}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.13265306122449,
0.9285714285714282}, {-0.15306122448979614`, 1.071428571428571}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.9285714285714286}, \
{-2.379049338482478*^-16, -1.0714285714285714`}}]},
{Arrowheads[{{0.027803651924065337`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.7959183673469389}, \
{-2.379049338482478*^-16, -0.9183673469387756}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.6632653061224492}, \
{-2.379049338482478*^-16, -0.7653061224489797}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.5306122448979593}, \
{-2.379049338482478*^-16, -0.6122448979591838}}]},
{Arrowheads[{{0.013901825962032668`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.39795918367346955`}, \
{-2.379049338482478*^-16, -0.45918367346938793`}}]},
{Arrowheads[{{0.009267883974688454, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.2653061224489798}, \
{-2.379049338482478*^-16, -0.30612244897959207`}}]},
{Arrowheads[{{0.004633941987344227, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.13265306122449}, \
{-2.379049338482478*^-16, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344214, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.13265306122448958`}, {-2.379049338482478*^-16,
0.15306122448979567`}}]},
{Arrowheads[{{0.009267883974688428, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.2653061224489794}, {-2.379049338482478*^-16, 0.30612244897959157`}}]},
{Arrowheads[{{0.013901825962032655`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.39795918367346916`}, {-2.379049338482478*^-16, 0.4591836734693875}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.530612244897959}, {-2.379049338482478*^-16, 0.6122448979591835}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.6632653061224487}, {-2.379049338482478*^-16, 0.7653061224489792}}]},
{Arrowheads[{{0.02780365192406531, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.7959183673469384}, {-2.379049338482478*^-16, 0.9183673469387751}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.9285714285714282}, {-2.379049338482478*^-16, 1.071428571428571}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.9285714285714286}, {
0.15306122448979567`, -1.0714285714285714`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.7959183673469389}, {
0.15306122448979567`, -0.9183673469387756}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.6632653061224492}, {
0.15306122448979567`, -0.7653061224489797}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.5306122448979593}, {
0.15306122448979567`, -0.6122448979591838}}]},
{Arrowheads[{{0.014653811225094897`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.39795918367346955`}, {
0.15306122448979567`, -0.45918367346938793`}}]},
{Arrowheads[{{0.010361809287492156`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.2653061224489798}, {
0.15306122448979567`, -0.30612244897959207`}}]},
{Arrowheads[{{0.00655338360575233, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.13265306122449}, {
0.15306122448979567`, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344214, 1.}}],
ArrowBox[{{0.13265306122448958`, -2.061842760018148*^-16}, {
0.15306122448979567`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.006553383605752321, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.13265306122448958`}, {
0.15306122448979567`, 0.15306122448979567`}}]},
{Arrowheads[{{0.010361809287492144`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.2653061224489794}, {
0.15306122448979567`, 0.3061224489795916}}]},
{Arrowheads[{{0.014653811225094883`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.39795918367346916`}, {
0.15306122448979567`, 0.4591836734693875}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.530612244897959}, {
0.15306122448979567`, 0.6122448979591835}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.6632653061224487}, {
0.15306122448979567`, 0.7653061224489792}}]},
{Arrowheads[{{0.028187168688193077`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.7959183673469384}, {
0.15306122448979567`, 0.9183673469387751}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.9285714285714282}, {
0.15306122448979567`, 1.071428571428571}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.2653061224489794, -0.9285714285714286}, {
0.30612244897959157`, -1.0714285714285714`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.7959183673469389}, {
0.3061224489795916, -0.9183673469387756}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.2653061224489794, -0.6632653061224492}, {
0.30612244897959157`, -0.7653061224489797}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.2653061224489794, -0.5306122448979593}, {
0.30612244897959157`, -0.6122448979591838}}]},
{Arrowheads[{{0.016707915442895085`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.39795918367346955`}, {
0.30612244897959157`, -0.45918367346938793`}}]},
{Arrowheads[{{0.01310676721150466, 1.}}],
ArrowBox[{{0.2653061224489794, -0.2653061224489798}, {
0.30612244897959157`, -0.30612244897959207`}}]},
{Arrowheads[{{0.010361809287492139`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.13265306122449}, {
0.30612244897959157`, -0.15306122448979614`}}]},
{Arrowheads[{{0.009267883974688428, 1.}}],
ArrowBox[{{0.2653061224489794, -2.061842760018148*^-16}, {
0.30612244897959157`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.010361809287492144`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.13265306122448958`}, {
0.3061224489795916, 0.15306122448979567`}}]},
{Arrowheads[{{0.013106767211504642`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.2653061224489794}, {
0.30612244897959157`, 0.30612244897959157`}}]},
{Arrowheads[{{0.016707915442895075`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.39795918367346916`}, {
0.30612244897959157`, 0.4591836734693875}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.2653061224489794, 0.530612244897959}, {0.30612244897959157`,
0.6122448979591835}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.2653061224489794, 0.6632653061224487}, {
0.30612244897959157`, 0.7653061224489792}}]},
{Arrowheads[{{0.029307622450189766`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.7959183673469384}, {
0.30612244897959157`, 0.9183673469387751}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.2653061224489794, 0.9285714285714282}, {
0.30612244897959157`, 1.071428571428571}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.9285714285714286}, {
0.4591836734693875, -1.0714285714285714`}}]},
{Arrowheads[{{0.03108542786247645, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.7959183673469389}, {
0.4591836734693875, -0.9183673469387756}}]},
{Arrowheads[{{0.027020292811707983`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.663265306122449}, {
0.4591836734693875, -0.7653061224489797}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.5306122448979593}, {
0.4591836734693875, -0.6122448979591838}}]},
{Arrowheads[{{0.01966015081725699, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.39795918367346955`}, {
0.4591836734693875, -0.45918367346938793`}}]},
{Arrowheads[{{0.016707915442895092`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.2653061224489798}, {
0.4591836734693875, -0.30612244897959207`}}]},
{Arrowheads[{{0.014653811225094886`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.13265306122449}, {
0.4591836734693875, -0.15306122448979614`}}]},
{Arrowheads[{{0.013901825962032655`, 1.}}],
ArrowBox[{{0.39795918367346916`, -2.061842760018148*^-16}, {
0.4591836734693875, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.014653811225094883`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.13265306122448958`}, {
0.4591836734693875, 0.15306122448979567`}}]},
{Arrowheads[{{0.016707915442895075`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.2653061224489794}, {
0.4591836734693875, 0.30612244897959157`}}]},
{Arrowheads[{{0.01966015081725698, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.39795918367346916`}, {
0.4591836734693875, 0.4591836734693875}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.530612244897959}, {0.4591836734693875,
0.6122448979591835}}]},
{Arrowheads[{{0.02702029281170796, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.6632653061224487}, {
0.4591836734693875, 0.7653061224489792}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.7959183673469384}, {
0.4591836734693875, 0.9183673469387751}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.9285714285714282}, {
0.4591836734693875, 1.071428571428571}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.530612244897959, -0.9285714285714286}, {
0.6122448979591835, -1.0714285714285714`}}]},
{Arrowheads[{{0.03341583088579019, 1.}}],
ArrowBox[{{0.530612244897959, -0.7959183673469389}, {
0.6122448979591835, -0.9183673469387756}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.530612244897959, -0.6632653061224492}, {
0.6122448979591835, -0.7653061224489797}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{0.530612244897959, -0.5306122448979593}, {
0.6122448979591835, -0.6122448979591838}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{0.530612244897959, -0.39795918367346955`}, {
0.6122448979591835, -0.45918367346938793`}}]},
{Arrowheads[{{0.0207236185749843, 1.}}],
ArrowBox[{{0.530612244897959, -0.2653061224489798}, {
0.6122448979591835, -0.30612244897959207`}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{0.530612244897959, -0.13265306122449}, {
0.6122448979591835, -0.15306122448979614`}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{0.530612244897959, -2.061842760018148*^-16}, {
0.6122448979591835, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.530612244897959, 0.13265306122448958`}, {0.6122448979591835,
0.15306122448979567`}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.530612244897959, 0.2653061224489794}, {0.6122448979591835,
0.30612244897959157`}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.530612244897959, 0.39795918367346916`}, {0.6122448979591835,
0.4591836734693875}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{0.530612244897959, 0.530612244897959}, {0.6122448979591835,
0.6122448979591835}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.530612244897959, 0.6632653061224487}, {0.6122448979591835,
0.7653061224489792}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.530612244897959, 0.7959183673469384}, {0.6122448979591835,
0.9183673469387751}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.530612244897959, 0.9285714285714282}, {0.6122448979591835,
1.071428571428571}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.9285714285714286}, {
0.7653061224489792, -1.0714285714285714`}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.7959183673469389}, {
0.7653061224489792, -0.9183673469387756}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.6632653061224492}, {
0.7653061224489792, -0.7653061224489797}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.5306122448979593}, {
0.7653061224489792, -0.6122448979591838}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{0.6632653061224487, -0.39795918367346955`}, {
0.7653061224489792, -0.45918367346938793`}}]},
{Arrowheads[{{0.024954541308549006`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.2653061224489798}, {
0.7653061224489792, -0.30612244897959207`}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.13265306122449}, {
0.7653061224489792, -0.15306122448979614`}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{0.6632653061224487, -2.061842760018148*^-16}, {
0.7653061224489792, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.6632653061224487, 0.13265306122448958`}, {
0.7653061224489792, 0.15306122448979567`}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.6632653061224487, 0.2653061224489794}, {0.7653061224489792,
0.30612244897959157`}}]},
{Arrowheads[{{0.02702029281170796, 1.}}],
ArrowBox[{{0.6632653061224487, 0.39795918367346916`}, {
0.7653061224489792, 0.4591836734693875}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.530612244897959}, {0.7653061224489792,
0.6122448979591835}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.6632653061224487}, {0.7653061224489792,
0.7653061224489792}}]},
{Arrowheads[{{0.03619224390482543, 1.}}],
ArrowBox[{{0.6632653061224487, 0.7959183673469384}, {0.7653061224489793,
0.9183673469387751}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.9285714285714282}, {0.7653061224489792,
1.071428571428571}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.7959183673469384, -0.9285714285714286}, {
0.9183673469387751, -1.0714285714285714`}}]},
{Arrowheads[{{0.03932030163451398, 1.}}],
ArrowBox[{{0.7959183673469384, -0.7959183673469389}, {
0.9183673469387751, -0.9183673469387756}}]},
{Arrowheads[{{0.03619224390482541, 1.}}],
ArrowBox[{{0.7959183673469384, -0.6632653061224492}, {
0.9183673469387751, -0.7653061224489797}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.7959183673469384, -0.5306122448979593}, {
0.9183673469387751, -0.6122448979591838}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.7959183673469384, -0.39795918367346955`}, {
0.9183673469387751, -0.45918367346938793`}}]},
{Arrowheads[{{0.029307622450189773`, 1.}}],
ArrowBox[{{0.7959183673469384, -0.2653061224489798}, {
0.9183673469387751, -0.30612244897959207`}}]},
{Arrowheads[{{0.02818716868819308, 1.}}],
ArrowBox[{{0.7959183673469384, -0.13265306122449}, {
0.9183673469387751, -0.15306122448979614`}}]},
{Arrowheads[{{0.02780365192406531, 1.}}],
ArrowBox[{{0.7959183673469384, -2.061842760018148*^-16}, {
0.9183673469387751, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.028187168688193077`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.13265306122448958`}, {
0.9183673469387751, 0.15306122448979567`}}]},
{Arrowheads[{{0.029307622450189766`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.2653061224489794}, {0.9183673469387751,
0.30612244897959157`}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.7959183673469384, 0.39795918367346916`}, {
0.9183673469387751, 0.4591836734693875}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.530612244897959}, {0.9183673469387751,
0.6122448979591835}}]},
{Arrowheads[{{0.03619224390482543, 1.}}],
ArrowBox[{{0.7959183673469384, 0.6632653061224487}, {0.9183673469387751,
0.7653061224489793}}]},
{Arrowheads[{{0.03932030163451396, 1.}}],
ArrowBox[{{0.7959183673469384, 0.7959183673469384}, {0.9183673469387751,
0.9183673469387751}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.7959183673469384, 0.9285714285714282}, {0.9183673469387751,
1.071428571428571}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, -0.9285714285714286}, {
1.071428571428571, -1.0714285714285714`}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{0.9285714285714282, -0.7959183673469389}, {
1.071428571428571, -0.9183673469387756}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.6632653061224492}, {
1.071428571428571, -0.7653061224489797}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.9285714285714282, -0.5306122448979593}, {
1.071428571428571, -0.6122448979591838}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.3979591836734696}, {
1.071428571428571, -0.45918367346938793`}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.2653061224489798}, {
1.071428571428571, -0.30612244897959207`}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.9285714285714282, -0.13265306122449}, {
1.071428571428571, -0.15306122448979614`}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{0.9285714285714282, -2.061842760018148*^-16}, {
1.071428571428571, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.9285714285714282, 0.13265306122448958`}, {1.071428571428571,
0.15306122448979567`}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.9285714285714282, 0.2653061224489794}, {1.071428571428571,
0.30612244897959157`}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.9285714285714282, 0.39795918367346916`}, {1.071428571428571,
0.4591836734693875}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.9285714285714282, 0.530612244897959}, {1.071428571428571,
0.6122448979591835}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.9285714285714282, 0.6632653061224487}, {1.071428571428571,
0.7653061224489792}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.9285714285714282, 0.7959183673469384}, {1.071428571428571,
0.9183673469387751}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, 0.9285714285714282}, {1.071428571428571,
1.071428571428571}}]}}},
AspectRatio->1,
AxesStyle->GrayLevel[0],
BaseStyle->{FontFamily -> "Times"},
DisplayFunction->Identity,
Frame->True,
FrameStyle->GrayLevel[0],
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotLabel->FormBox["\"2D Position Vector\"", TraditionalForm],
PlotRange->{{-1.101015254455221, 1.101015254455221}, {-1.101015254455221,
1.101015254455221}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.02],
Scaled[0.02]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{
3.68934522325099*^9, {3.689345277559744*^9, 3.6893453151340647`*^9}, {
3.6893453569653025`*^9, 3.689345371825616*^9}, {3.689345509751195*^9,
3.6893456631028028`*^9}, 3.6893564366942196`*^9, {3.68941463064072*^9,
3.689414640592829*^9}}]
}, Open ]],
Cell[BoxData[
RowBox[{
RowBox[{"G", "[",
RowBox[{"x_", ",", " ", "y_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"-", "\[ImaginaryI]y"}], " ", "+", " ", "\[ImaginaryJ]x"}],
")"}], "/",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{"x", "^", "2"}], " ", "+", " ",
RowBox[{"y", "^", "2"}]}], "]"}]}]}]], "Text",
CellChangeTimes->{
3.689345126959575*^9, 3.68934522942475*^9, {3.689345426044791*^9,
3.6893454732012887`*^9}, 3.689345527329298*^9, {3.6893457596500196`*^9,
3.689345762921658*^9}, 3.6893564367183332`*^9},
FormatType->"InputForm"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"VectorPlot", "[",
RowBox[{
RowBox[{"G", "[",
RowBox[{"i", ",", " ", "j"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"i", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ",
RowBox[{"{",
RowBox[{"j", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{
"PlotLabel", " ", "->", " ", "\n", " ",
"\"\<Tangential to Origin Vector Field\>\""}]}], "]"}]], "Input",
CellChangeTimes->{{3.6888925693335943`*^9, 3.6888925836321383`*^9}, {
3.6888926385020933`*^9, 3.688892737329537*^9}, {3.688892777296649*^9,
3.6888928055423822`*^9}, {3.6888930160846415`*^9,
3.6888932490725403`*^9}, {3.6888932836768503`*^9,
3.6888933077317247`*^9}, {3.68889400372309*^9, 3.6888940680358195`*^9}, {
3.6888942983433123`*^9, 3.6888943008740807`*^9}, {3.68934572682747*^9,
3.6893457434395123`*^9}, 3.6893564367383375`*^9},
FormatType->"InputForm"],
Cell[BoxData[
FormBox[
GraphicsBox[{{},
{GrayLevel[0],
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-1.0714285714285714`, -0.9285714285714286}, \
{-0.9285714285714286, -1.0714285714285714`}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{-1.0657398561869176`, -0.7804463582581201}, \
{-0.9342601438130825, -0.9338393560275943}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-1.0587139240376275`, -0.6320862206330358}, \
{-0.9412860759623723, -0.7964852079383931}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{-1.050117601103259, -0.4837227694978687}, \
{-0.9498823988967412, -0.6591343733592746}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-1.0397918581807968`, -0.33572375948290284`}, \
{-0.9602081418192032, -0.5214190976599548}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-1.027751024638779, -0.18858569947855952`}, \
{-0.972248975361221, -0.3828428719500123}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-1.0142857142857142`, -0.04285714285714309}, \
{-0.9857142857142858, -0.24285714285714305`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-1., 0.10101525445522085`}, {-1., -0.10101525445522129`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.9857142857142858,
0.2428571428571426}, {-1.0142857142857142`, 0.04285714285714265}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.972248975361221, 0.3828428719500119}, {-1.027751024638779,
0.18858569947855908`}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9602081418192032,
0.5214190976599542}, {-1.0397918581807968`, 0.3357237594829024}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.9498823988967412, 0.659134373359274}, {-1.050117601103259,
0.48372276949786824`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.9412860759623725,
0.7964852079383926}, {-1.0587139240376275`, 0.6320862206330353}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{-0.9342601438130825,
0.9338393560275938}, {-1.0657398561869176`, 0.7804463582581197}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.9285714285714286,
1.071428571428571}, {-1.0714285714285714`, 0.928571428571428}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.9338393560275943, -0.9342601438130825}, \
{-0.7804463582581203, -1.0657398561869176`}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.7857142857142858}, \
{-0.7857142857142858, -0.9285714285714286}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.9218112471732276, -0.63668364624927}, \
{-0.7924744671124868, -0.7918877823221588}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.9131760386109098, -0.48737879922649274`}, \
{-0.8011096756748046, -0.6554783436306505}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9023182522881198, -0.33822063828090365`}, \
{-0.8119674619975946, -0.5189222188619538}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.8890866853928542, -0.18988280096429494`}, \
{-0.8251990288928601, -0.3815457704642769}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.8737496626776886, -0.043216309648155135`}, \
{-0.8405360516080258, -0.24249797606613105`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.8571428571428572,
0.10101525445522085`}, {-0.8571428571428572, -0.10101525445522129`}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.8405360516080259,
0.2424979760661306}, {-0.8737496626776885, 0.04321630964815466}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.8251990288928602,
0.38154577046427646`}, {-0.8890866853928542, 0.1898828009642945}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.8119674619975946,
0.5189222188619534}, {-0.9023182522881197, 0.3382206382809032}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.8011096756748046, 0.65547834363065}, {-0.9131760386109098,
0.4873787992264923}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.7924744671124868,
0.7918877823221584}, {-0.9218112471732275, 0.6366836462492694}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.7857142857142858,
0.9285714285714282}, {-0.9285714285714286, 0.7857142857142853}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{-0.7804463582581201,
1.0657398561869171`}, {-0.9338393560275943, 0.9342601438130821}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.7964852079383931, -0.9412860759623725}, \
{-0.6320862206330358, -1.0587139240376275`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.7918877823221588, -0.7924744671124868}, \
{-0.63668364624927, -0.9218112471732276}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.7857142857142858, -0.642857142857143}, \
{-0.642857142857143, -0.7857142857142858}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{-0.777389443471341, -0.4925489099465384}, \
{-0.6511819851000877, -0.6503082329106049}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.7662576339363572, -0.3419515624870242}, \
{-0.6623137946350716, -0.5151912946558334}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.7518018379599208, -0.1919239765287698}, \
{-0.6767695906115079, -0.37950459489980204`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.7340964355794726, -0.043803536388352174`}, \
{-0.6944749929919561, -0.24191074932593393`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.7142857142857144,
0.10101525445522085`}, {-0.7142857142857143, -0.10101525445522129`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.6944749929919563,
0.24191074932593354`}, {-0.7340964355794726, 0.0438035363883517}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.676769590611508,
0.3795045948998016}, {-0.7518018379599208, 0.19192397652876936`}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{-0.6623137946350717,
0.515191294655833}, {-0.7662576339363572, 0.34195156248702363`}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.6511819851000878,
0.6503082329106045}, {-0.777389443471341, 0.4925489099465379}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.642857142857143,
0.7857142857142854}, {-0.7857142857142858, 0.6428571428571426}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.63668364624927, 0.9218112471732272}, {-0.7918877823221588,
0.7924744671124864}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.6320862206330358,
1.058713924037627}, {-0.7964852079383931, 0.941286075962372}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.6591343733592745, -0.9498823988967412}, \
{-0.4837227694978687, -1.0501176011032587`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.6554783436306505, -0.8011096756748046}, \
{-0.48737879922649274`, -0.9131760386109098}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{-0.6503082329106049, -0.6511819851000878}, \
{-0.4925489099465384, -0.7773894434713411}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.642857142857143, -0.5000000000000002}, \
{-0.5000000000000002, -0.642857142857143}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.6320377241017042, -0.3477592250072519}, \
{-0.5108194187554389, -0.5093836321356057}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.6166039665738342, -0.1953634954237608}, \
{-0.526253176283309, -0.37606507600481104`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.5959283693060728, -0.04485795134713805}, \
{-0.5469287735510704, -0.2408563343671481}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.5714285714285716,
0.10101525445522085`}, {-0.5714285714285715, -0.10101525445522129`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.5469287735510704,
0.24085633436714768`}, {-0.5959283693060728, 0.044857951347137576`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.5262531762833091,
0.37606507600481065`}, {-0.6166039665738342, 0.19536349542376033`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.510819418755439,
0.5093836321356052}, {-0.6320377241017042, 0.3477592250072515}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.5000000000000002,
0.6428571428571426}, {-0.642857142857143, 0.4999999999999997}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.49254890994653844`,
0.7773894434713406}, {-0.6503082329106048, 0.6511819851000873}}]},
{Arrowheads[{{0.04587368524026629, 1.}}],
ArrowBox[{{-0.4873787992264928,
0.9131760386109093}, {-0.6554783436306504, 0.8011096756748042}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.48372276949786874`,
1.0501176011032585`}, {-0.6591343733592745, 0.9498823988967406}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.5214190976599546, -0.9602081418192031}, \
{-0.33572375948290284`, -1.039791858180797}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.5189222188619539, -0.8119674619975946}, \
{-0.33822063828090365`, -0.9023182522881198}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.5151912946558334, -0.6623137946350717}, \
{-0.3419515624870242, -0.7662576339363573}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.5093836321356056, -0.510819418755439}, \
{-0.3477592250072519, -0.6320377241017043}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{-0.5000000000000002, -0.3571428571428573}, \
{-0.3571428571428573, -0.5000000000000002}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.48460461003948135`, -0.20166451351220704`}, \
{-0.3725382471033762, -0.3697640579163648}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.4605152568214258, -0.047025658107152105`}, \
{-0.39662760032143174`, -0.238688627607134}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.4285714285714288,
0.10101525445522085`}, {-0.4285714285714287, -0.10101525445522129`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.39662760032143185`,
0.2386886276071336}, {-0.4605152568214257, 0.04702565810715165}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.37253824710337624`,
0.36976405791636435`}, {-0.48460461003948124`, 0.2016645135122066}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.3571428571428574,
0.4999999999999998}, {-0.5000000000000001, 0.3571428571428568}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.3477592250072519,
0.6320377241017039}, {-0.5093836321356056, 0.5108194187554386}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.3419515624870242,
0.7662576339363568}, {-0.5151912946558334, 0.6623137946350712}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.33822063828090365`,
0.9023182522881193}, {-0.5189222188619539, 0.8119674619975942}}]},
{Arrowheads[{{0.04587368524026628, 1.}}],
ArrowBox[{{-0.3357237594829029,
1.0397918581807963`}, {-0.5214190976599546, 0.9602081418192028}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.3828428719500123, -0.972248975361221}, \
{-0.18858569947855952`, -1.0277510246387789`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.3815457704642769, -0.8251990288928602}, \
{-0.18988280096429494`, -0.8890866853928543}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.37950459489980204`, -0.676769590611508}, \
{-0.1919239765287698, -0.751801837959921}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.37606507600481104`, -0.526253176283309}, \
{-0.1953634954237608, -0.6166039665738342}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.3697640579163648, -0.3725382471033762}, \
{-0.20166451351220704`, -0.4846046100394814}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.3571428571428573, -0.2142857142857145}, \
{-0.2142857142857145, -0.3571428571428573}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.3308896808595485, -0.05250635256661797}, \
{-0.24053889056902333`, -0.23320793314766813`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.285714285714286,
0.10101525445522085`}, {-0.2857142857142858, -0.10101525445522129`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.24053889056902344`,
0.2332079331476678}, {-0.3308896808595484, 0.05250635256661747}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.21428571428571455`,
0.357142857142857}, {-0.3571428571428573, 0.214285714285714}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.2016645135122071,
0.48460461003948097`}, {-0.36976405791636474`,
0.37253824710337574`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.1953634954237608,
0.6166039665738338}, {-0.37606507600481104`, 0.5262531762833086}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{-0.19192397652876983`,
0.7518018379599205}, {-0.37950459489980204`, 0.6767695906115074}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{-0.18988280096429494`,
0.8890866853928538}, {-0.3815457704642769, 0.8251990288928597}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.18858569947855952`,
1.0277510246387787`}, {-0.3828428719500123, 0.9722489753612206}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.24285714285714305`, -0.9857142857142857}, \
{-0.04285714285714309, -1.0142857142857145`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.242497976066131, -0.8405360516080258}, \
{-0.043216309648155135`, -0.8737496626776886}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.24191074932593398`, -0.6944749929919563}, \
{-0.043803536388352174`, -0.7340964355794727}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{-0.2408563343671481, -0.5469287735510704}, \
{-0.04485795134713805, -0.5959283693060728}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.23868862760713405`, -0.39662760032143174`}, \
{-0.047025658107152105`, -0.4605152568214258}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.2332079331476682, -0.24053889056902333`}, \
{-0.05250635256661797, -0.3308896808595485}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.2142857142857145, -0.07142857142857165}, \
{-0.07142857142857165, -0.2142857142857145}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.14285714285714324`,
0.10101525445522085`}, {-0.14285714285714293`, \
-0.10101525445522129`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.07142857142857177,
0.21428571428571416`}, {-0.2142857142857144, 0.07142857142857109}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.05250635256661801,
0.3308896808595481}, {-0.23320793314766813`, 0.24053889056902283`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.047025658107152105`,
0.46051525682142536`}, {-0.238688627607134, 0.3966276003214313}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{-0.04485795134713805,
0.5959283693060725}, {-0.2408563343671481, 0.54692877355107}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.04380353638835216,
0.7340964355794722}, {-0.24191074932593398`, 0.6944749929919558}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.043216309648155135`,
0.8737496626776882}, {-0.24249797606613105`, 0.8405360516080255}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{-0.04285714285714308,
1.0142857142857138`}, {-0.2428571428571431, 0.9857142857142853}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -1.}, {0.10101525445522085`, -1.}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.8571428571428572}, {
0.10101525445522085`, -0.8571428571428572}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.7142857142857144}, {
0.10101525445522085`, -0.7142857142857145}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.5714285714285716}, {
0.10101525445522085`, -0.5714285714285717}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.4285714285714287}, {
0.10101525445522085`, -0.4285714285714288}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.28571428571428586`}, {
0.10101525445522085`, -0.28571428571428603`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.10101525445522129`, -0.1428571428571429}, {
0.10101525445522085`, -0.1428571428571432}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{-0.07142857142857165, 0.0714285714285712}, {
0.0714285714285712, -0.07142857142857165}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.1428571428571428}, {-0.10101525445522129`, 0.1428571428571425}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.28571428571428553`}, {-0.10101525445522129`,
0.28571428571428537`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.4285714285714284}, {-0.10101525445522129`, 0.42857142857142827`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.5714285714285712}, {-0.10101525445522129`, 0.5714285714285711}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.714285714285714}, {-0.10101525445522129`, 0.7142857142857139}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.8571428571428568}, {-0.10101525445522129`, 0.8571428571428568}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.10101525445522085`,
0.9999999999999996}, {-0.10101525445522129`, 0.9999999999999996}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.04285714285714265, -1.0142857142857142`}, {
0.2428571428571426, -0.9857142857142858}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.04321630964815466, -0.8737496626776885}, {
0.24249797606613055`, -0.8405360516080259}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{0.0438035363883517, -0.7340964355794726}, {
0.2419107493259336, -0.6944749929919563}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.044857951347137576`, -0.5959283693060728}, {
0.24085633436714768`, -0.5469287735510704}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.04702565810715165, -0.4605152568214257}, {
0.2386886276071336, -0.39662760032143185`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.05250635256661747, -0.3308896808595484}, {
0.23320793314766775`, -0.24053889056902344`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.07142857142857109, -0.21428571428571436`}, {
0.21428571428571416`, -0.07142857142857177}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.14285714285714246`, -0.10101525445522129`}, {
0.14285714285714277`, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.21428571428571405`, 0.0714285714285712}, {
0.0714285714285712, 0.21428571428571405`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.23320793314766775`, 0.24053889056902295`}, {
0.052506352566617495`, 0.330889680859548}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.2386886276071336, 0.39662760032143135`}, {
0.04702565810715165, 0.46051525682142525`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.24085633436714768`, 0.54692877355107}, {
0.044857951347137576`, 0.5959283693060724}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.24191074932593354`, 0.6944749929919558}, {
0.043803536388351716`, 0.7340964355794721}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.24249797606613055`, 0.8405360516080255}, {
0.04321630964815469, 0.873749662677688}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.2428571428571426, 0.9857142857142853}, {
0.04285714285714265, 1.0142857142857138`}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.18858569947855908`, -1.0277510246387789`}, {
0.3828428719500119, -0.9722489753612211}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.1898828009642945, -0.8890866853928542}, {
0.38154577046427646`, -0.8251990288928602}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.19192397652876936`, -0.7518018379599208}, {
0.3795045948998016, -0.676769590611508}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.19536349542376033`, -0.6166039665738341}, {
0.37606507600481065`, -0.526253176283309}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.2016645135122066, -0.4846046100394813}, {
0.36976405791636435`, -0.37253824710337624`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.214285714285714, -0.3571428571428573}, {
0.357142857142857, -0.21428571428571455`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.24053889056902283`, -0.23320793314766813`}, {
0.3308896808595481, -0.05250635256661801}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.2857142857142854, -0.10101525445522129`}, {
0.2857142857142856, 0.10101525445522085`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.330889680859548, 0.052506352566617495`}, {
0.24053889056902295`, 0.2332079331476678}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.3571428571428569, 0.21428571428571405`}, {
0.21428571428571405`, 0.3571428571428569}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.36976405791636435`, 0.37253824710337574`}, {
0.2016645135122066, 0.48460461003948085`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.3760650760048106, 0.5262531762833086}, {
0.19536349542376036`, 0.6166039665738337}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.3795045948998016, 0.6767695906115075}, {
0.19192397652876936`, 0.7518018379599204}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.38154577046427646`, 0.8251990288928598}, {
0.1898828009642945, 0.8890866853928537}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.3828428719500119, 0.9722489753612206}, {
0.18858569947855908`, 1.0277510246387787`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.3357237594829024, -1.0397918581807968`}, {
0.5214190976599543, -0.9602081418192032}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.3382206382809032, -0.9023182522881198}, {
0.5189222188619534, -0.8119674619975947}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.3419515624870237, -0.7662576339363572}, {
0.515191294655833, -0.6623137946350717}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.3477592250072514, -0.6320377241017042}, {
0.5093836321356052, -0.510819418755439}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.3571428571428569, -0.5000000000000001}, {
0.49999999999999983`, -0.35714285714285743`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.3725382471033757, -0.36976405791636474`}, {
0.4846046100394809, -0.2016645135122071}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.3966276003214313, -0.23868862760713405`}, {
0.46051525682142536`, -0.047025658107152105`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.42857142857142827`, -0.10101525445522129`}, {
0.4285714285714284, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.4605152568214253, 0.04702565810715165}, {
0.3966276003214314, 0.2386886276071336}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.4846046100394809, 0.2016645135122066}, {0.3725382471033758,
0.36976405791636435`}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{0.4999999999999998, 0.3571428571428569}, {0.3571428571428569,
0.4999999999999998}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{0.5093836321356052, 0.5108194187554386}, {0.3477592250072514,
0.6320377241017039}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.5151912946558329, 0.6623137946350712}, {
0.34195156248702374`, 0.7662576339363568}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.5189222188619534, 0.8119674619975942}, {0.3382206382809032,
0.9023182522881193}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.5214190976599542, 0.9602081418192028}, {0.3357237594829024,
1.0397918581807963`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.48372276949786824`, -1.0501176011032587`}, {
0.6591343733592742, -0.9498823988967412}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.4873787992264923, -0.9131760386109098}, {
0.65547834363065, -0.8011096756748046}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{0.4925489099465379, -0.777389443471341}, {
0.6503082329106045, -0.6511819851000878}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.4999999999999997, -0.642857142857143}, {
0.6428571428571426, -0.5000000000000002}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.5108194187554385, -0.5093836321356056}, {
0.6320377241017038, -0.347759225007252}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.5262531762833086, -0.37606507600481104`}, {
0.6166039665738338, -0.1953634954237608}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.5469287735510698, -0.2408563343671481}, {
0.5959283693060724, -0.04485795134713805}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.5714285714285712, -0.10101525445522129`}, {
0.5714285714285713, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.5959283693060724, 0.044857951347137576`}, {
0.54692877355107, 0.24085633436714768`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.6166039665738338, 0.19536349542376036`}, {
0.5262531762833087, 0.3760650760048106}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.6320377241017038, 0.3477592250072514}, {0.5108194187554386,
0.5093836321356052}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.6428571428571426, 0.4999999999999998}, {0.4999999999999998,
0.6428571428571426}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.6503082329106045, 0.6511819851000874}, {
0.49254890994653794`, 0.7773894434713405}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.65547834363065, 0.8011096756748042}, {0.4873787992264923,
0.9131760386109093}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.659134373359274, 0.9498823988967408}, {
0.48372276949786824`, 1.0501176011032582`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.6320862206330353, -1.0587139240376275`}, {
0.7964852079383926, -0.9412860759623723}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.6366836462492695, -0.9218112471732276}, {
0.7918877823221585, -0.7924744671124869}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.6428571428571426, -0.7857142857142858}, {
0.7857142857142854, -0.642857142857143}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.6511819851000873, -0.6503082329106048}, {
0.7773894434713406, -0.49254890994653844`}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.6623137946350711, -0.5151912946558334}, {
0.7662576339363567, -0.3419515624870242}}]},
{Arrowheads[{{0.04587368524026634, 1.}}],
ArrowBox[{{0.6767695906115074, -0.37950459489980204`}, {
0.7518018379599205, -0.19192397652876983`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.6944749929919557, -0.24191074932593398`}, {
0.7340964355794721, -0.04380353638835216}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.714285714285714, -0.10101525445522129`}, {
0.7142857142857141, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7340964355794721, 0.043803536388351716`}, {
0.6944749929919558, 0.24191074932593354`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7518018379599204, 0.19192397652876936`}, {
0.6767695906115075, 0.3795045948998016}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7662576339363567, 0.3419515624870237}, {0.6623137946350711,
0.5151912946558329}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7773894434713405, 0.49254890994653794`}, {
0.6511819851000874, 0.6503082329106045}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.7857142857142854, 0.6428571428571426}, {0.6428571428571426,
0.7857142857142854}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7918877823221584, 0.7924744671124864}, {0.6366836462492695,
0.9218112471732272}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{0.7964852079383926, 0.9412860759623719}, {0.6320862206330353,
1.0587139240376273`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7804463582581197, -1.0657398561869174`}, {
0.9338393560275938, -0.9342601438130825}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7857142857142854, -0.9285714285714286}, {
0.9285714285714283, -0.7857142857142858}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.7924744671124864, -0.7918877823221588}, {
0.9218112471732272, -0.63668364624927}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.8011096756748042, -0.6554783436306505}, {
0.9131760386109093, -0.4873787992264928}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.8119674619975942, -0.5189222188619539}, {
0.9023182522881193, -0.33822063828090365`}}]},
{Arrowheads[{{0.04587368524026633, 1.}}],
ArrowBox[{{0.8251990288928597, -0.3815457704642769}, {
0.8890866853928538, -0.18988280096429494`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{0.8405360516080254, -0.242497976066131}, {
0.873749662677688, -0.043216309648155135`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.8571428571428568, -0.10101525445522129`}, {
0.8571428571428568, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.873749662677688, 0.04321630964815469}, {0.8405360516080255,
0.2424979760661306}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.8890866853928537, 0.1898828009642945}, {0.8251990288928598,
0.38154577046427646`}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.9023182522881193, 0.3382206382809032}, {0.8119674619975942,
0.5189222188619534}}]},
{Arrowheads[{{0.045873685240266325`, 1.}}],
ArrowBox[{{0.9131760386109093, 0.4873787992264923}, {0.8011096756748042,
0.65547834363065}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.9218112471732272, 0.6366836462492695}, {0.7924744671124864,
0.7918877823221584}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, 0.7857142857142854}, {0.7857142857142854,
0.9285714285714282}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{0.9338393560275938, 0.9342601438130821}, {0.7804463582581197,
1.0657398561869171`}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, -1.0714285714285714`}, {
1.071428571428571, -0.9285714285714286}}]},
{Arrowheads[{{0.04587368524026629, 1.}}],
ArrowBox[{{0.9342601438130821, -0.9338393560275943}, {
1.065739856186917, -0.7804463582581203}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{0.9412860759623719, -0.7964852079383931}, {
1.0587139240376273`, -0.6320862206330358}}]},
{Arrowheads[{{0.04587368524026628, 1.}}],
ArrowBox[{{0.9498823988967408, -0.6591343733592745}, {
1.0501176011032582`, -0.48372276949786874`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.9602081418192027, -0.5214190976599546}, {
1.0397918581807966`, -0.3357237594829029}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{0.9722489753612206, -0.3828428719500123}, {
1.0277510246387784`, -0.18858569947855952`}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.9857142857142852, -0.24285714285714305`}, {
1.014285714285714, -0.04285714285714308}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{0.9999999999999996, -0.10101525445522129`}, {
0.9999999999999996, 0.10101525445522085`}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{1.0142857142857138`, 0.04285714285714265}, {
0.9857142857142852, 0.2428571428571426}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{1.0277510246387784`, 0.18858569947855908`}, {
0.9722489753612206, 0.3828428719500119}}]},
{Arrowheads[{{0.04587368524026631, 1.}}],
ArrowBox[{{1.0397918581807963`, 0.3357237594829024}, {
0.9602081418192027, 0.5214190976599542}}]},
{Arrowheads[{{0.045873685240266346`, 1.}}],
ArrowBox[{{1.0501176011032585`, 0.48372276949786824`}, {
0.9498823988967408, 0.6591343733592742}}]},
{Arrowheads[{{0.045873685240266304`, 1.}}],
ArrowBox[{{1.058713924037627, 0.6320862206330353}, {0.941286075962372,
0.7964852079383926}}]},
{Arrowheads[{{0.04587368524026632, 1.}}],
ArrowBox[{{1.065739856186917, 0.7804463582581197}, {0.9342601438130821,
0.9338393560275938}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{1.071428571428571, 0.9285714285714282}, {0.9285714285714282,
1.071428571428571}}]}}},
AspectRatio->1,
AxesStyle->GrayLevel[0],
BaseStyle->{FontFamily -> "Times"},
DisplayFunction->Identity,
Frame->True,
FrameStyle->GrayLevel[0],
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotLabel->FormBox[
"\"Tangential to Origin Vector Field\"", TraditionalForm],
PlotRange->{{-1.101015254455221, 1.101015254455221}, {-1.101015254455221,
1.101015254455221}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.02],
Scaled[0.02]}},
Ticks->{Automatic, Automatic}], TraditionalForm]], "Output",
CellChangeTimes->{{3.688893280409396*^9, 3.6888933086438174`*^9}, {
3.6888940063353157`*^9, 3.6888940694901466`*^9}, 3.6888943021857367`*^9,
3.689345232537166*^9, 3.6893454376063366`*^9, 3.6893454766101303`*^9,
3.6893455301913414`*^9, 3.6893457448642626`*^9, 3.6893564367809873`*^9,
3.689414648690304*^9}]
}, Open ]],
Cell["\<\
Now let\[CloseCurlyQuote]s look at the charge between two particles in free \
space in MKS units. This law of Physics was discovered by the French \
physicist Charles-Augustin de Coulomb (June 1736 \[Dash] 23 August 1806). He \
was best known for developing Coulomb\[CloseCurlyQuote]s law, the definition \
of the electrostatic force of attraction and repulsion, but also did \
important work on friction. The SI unit of electric charge, the coulomb, was \
named after him.\
\>", "Text",
CellChangeTimes->{{3.689346262459386*^9, 3.6893462726939225`*^9},
3.689697176771876*^9, {3.6929708826712155`*^9, 3.692970882678268*^9}}],
Cell["", "Text",
CellChangeTimes->{{3.689346262459386*^9, 3.6893462726939225`*^9},
3.689697176771876*^9}],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"CloudDeploy", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{
RowBox[{"forceCoulombs", "[",
RowBox[{"q1_", ",", "q2_", ",", "r_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"QuantityMagnitude", "[",
RowBox[{"(",
FractionBox[
RowBox[{"q1", "*", "q2"}],
RowBox[{"4", " ", "\[Pi]", " ", "freeSpacePermitivity", " ",
SuperscriptBox["r", "2"]}]], ")"}], "]"}], " ", "Coulombs"}]}], ";",
"\[IndentingNewLine]",
RowBox[{"Manipulate", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{
RowBox[{"r", "=",
RowBox[{"Sqrt", "[",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"r1", "[",
RowBox[{"[", "1", "]"}], "]"}], "-",
RowBox[{"r2", "[",
RowBox[{"[", "1", "]"}], "]"}]}], ")"}], "^", "2"}], " ", "+",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"r1", "[",
RowBox[{"[", "2", "]"}], "]"}], "-",
RowBox[{"r2", "[",
RowBox[{"[", "2", "]"}], "]"}]}], ")"}], "^", "2"}]}], "]"}]}],
";", "\[IndentingNewLine]",
RowBox[{"Grid", "[", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"Text", "[", "\"\<Coulombs Law\>\"", "]"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{"Show", "[", "\[IndentingNewLine]",
RowBox[{
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"\[Phi]", "[",
RowBox[{"q1", ",", "q2", ",",
RowBox[{"r1", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"r1", "[",
RowBox[{"[", "2", "]"}], "]"}], ",",
RowBox[{"r2", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"r2", "[",
RowBox[{"[", "2", "]"}], "]"}], ",", "x", ",", "y"}], "]"}],
",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"-", "2"}], ",", "2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",",
RowBox[{"Contours", "\[Rule]", "10"}], ",",
RowBox[{"ContourShading", "\[Rule]", "False"}], ",",
"\[IndentingNewLine]",
RowBox[{"Epilog", "\[Rule]",
RowBox[{"{", "\[IndentingNewLine]",
RowBox[{
RowBox[{"Inset", "[",
RowBox[{
RowBox[{"Graphics", "[",
RowBox[{"Text", "[",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Subscript", "[",
RowBox[{
RowBox[{"Style", "[",
RowBox[{"\"\<q\>\"", ",", "Italic"}], "]"}], ",", "1"}],
"]"}], ",", "24", ",", "Black"}], "]"}], "]"}], "]"}],
",",
RowBox[{"{",
RowBox[{
RowBox[{"r1", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{
RowBox[{"r1", "[",
RowBox[{"[", "2", "]"}], "]"}], "-", ".2"}]}], "}"}]}],
"]"}], ",",
RowBox[{"Inset", "[",
RowBox[{
RowBox[{"Graphics", "[",
RowBox[{"Text", "[",
RowBox[{"Style", "[",
RowBox[{
RowBox[{"Subscript", "[",
RowBox[{
RowBox[{"Style", "[",
RowBox[{"\"\<q\>\"", ",", "Italic"}], "]"}], ",", "2"}],
"]"}], ",", "24", ",", "Black"}], "]"}], "]"}], "]"}],
",",
RowBox[{"{",
RowBox[{
RowBox[{"r2", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{
RowBox[{"r2", "[",
RowBox[{"[", "2", "]"}], "]"}], "-", ".2"}]}], "}"}]}],
"]"}]}], "}"}]}]}], "\[IndentingNewLine]", "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"ContourPlot", "[",
RowBox[{
RowBox[{"\[Psi]", "[",
RowBox[{"q1", ",", "q2", ",",
RowBox[{"r1", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"r1", "[",
RowBox[{"[", "2", "]"}], "]"}], ",",
RowBox[{"r2", "[",
RowBox[{"[", "1", "]"}], "]"}], ",",
RowBox[{"r2", "[",
RowBox[{"[", "2", "]"}], "]"}], ",", "x", ",", "y"}], "]"}],
",",
RowBox[{"{",
RowBox[{"x", ",",
RowBox[{"-", "2"}], ",", "2"}], "}"}], ",",
RowBox[{"{",
RowBox[{"y", ",",
RowBox[{"-", "1.5"}], ",", "1.5"}], "}"}], ",",
RowBox[{"Contours", "\[Rule]", "12"}], ",",
RowBox[{"ContourStyle", "\[Rule]", "Red"}], ",",
RowBox[{"ContourShading", "\[Rule]", "False"}]}], "]"}], ",",
RowBox[{"AspectRatio", "\[Rule]",
RowBox[{"2", "/", "3"}]}], ",",
RowBox[{"ImageSize", "\[Rule]",
RowBox[{"{",
RowBox[{"575", ",", "350"}], "}"}]}]}], "]"}],
"\[IndentingNewLine]", "}"}], ",",
RowBox[{"{",
RowBox[{"InputField", "[",
RowBox[{
RowBox[{"forceCoulombs", "[",
RowBox[{"q1", ",", " ", "q2", ",", "r"}], "]"}], ",",
"\[IndentingNewLine]",
RowBox[{"FieldHint", "\[Rule]", "\"\<Coulombs\>\""}], ",",
"\[IndentingNewLine]",
RowBox[{"FieldSize", "\[Rule]", "20"}], ",",
"\[IndentingNewLine]",
RowBox[{"Enabled", "\[Rule]", "False"}]}], "]"}], "}"}]}],
"\[IndentingNewLine]", "}"}], "]"}]}], ",", "\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"q1", ",", "1", ",",
RowBox[{"\"\<Charge \>\"", " ",
RowBox[{"Subscript", "[",
RowBox[{"q", ",", "1"}], "]"}]}]}], "}"}], ",",
RowBox[{"-", "2"}], ",", "2", ",", ".1", ",",
RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"q2", ",",
RowBox[{"-", "1"}], ",",
RowBox[{"\"\<Charge \>\"", " ",
RowBox[{"Subscript", "[",
RowBox[{"q", ",", "2"}], "]"}]}]}], "}"}], ",",
RowBox[{"-", "2"}], ",", "2", ",", ".1", ",",
RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"r1", ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "1"}], ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "2"}], ",",
RowBox[{"-", "1.5"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"2", ",", "1.5"}], "}"}], ",", "Locator"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"{",
RowBox[{
RowBox[{"{",
RowBox[{"r2", ",",
RowBox[{"{",
RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{
RowBox[{"-", "2"}], ",",
RowBox[{"-", "1.5"}]}], "}"}], ",",
RowBox[{"{",
RowBox[{"2", ",", "1.5"}], "}"}], ",", "Locator"}], "}"}], ",",
"\[IndentingNewLine]",
RowBox[{"TrackedSymbols", "\[RuleDelayed]",
RowBox[{"{",
RowBox[{"q1", ",", "q2", ",", "r1", ",", "r2"}], "}"}]}], ",",
RowBox[{"Initialization", "\[RuleDelayed]",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"\[Phi]", "[",
RowBox[{
"q1_", ",", "q2_", ",", "x1_", ",", "y1_", ",", "x2_", ",", "y2_",
",", "x_", ",", "y_"}], "]"}], ":=",
RowBox[{
FractionBox["q1",
RowBox[{" ",
RowBox[{
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x1"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y1"}], ")"}], "2"]}]], "+", ".0001",
" "}]}]], "+",
FractionBox["q2",
RowBox[{" ",
RowBox[{
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x2"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y2"}], ")"}], "2"]}]], "+",
".0001"}]}]]}]}], ";",
RowBox[{
RowBox[{"\[Psi]", "[",
RowBox[{
"q1_", ",", "q2_", ",", "x1_", ",", "y1_", ",", "x2_", ",", "y2_",
",", "x_", ",", "y_"}], "]"}], ":=",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"q1", " ",
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x2"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y2"}], ")"}], "2"]}]], " ",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"-",
RowBox[{"(",
RowBox[{"x", "-", "x1"}], ")"}]}], " ",
RowBox[{"(",
RowBox[{"x1", "-", "x2"}], ")"}]}], "-",
RowBox[{
RowBox[{"(",
RowBox[{"y", "-", "y1"}], ")"}], " ",
RowBox[{"(",
RowBox[{"y1", "-", "y2"}], ")"}]}]}], ")"}]}], "-",
RowBox[{"q2", " ",
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x1"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y1"}], ")"}], "2"]}]], " ",
RowBox[{"(",
RowBox[{
RowBox[{
RowBox[{"(",
RowBox[{"x", "-", "x2"}], ")"}], " ",
RowBox[{"(",
RowBox[{"x1", "-", "x2"}], ")"}]}], "+",
RowBox[{
RowBox[{"(",
RowBox[{"y", "-", "y2"}], ")"}], " ",
RowBox[{"(",
RowBox[{"y1", "-", "y2"}], ")"}]}]}], ")"}]}]}], ")"}], "/",
RowBox[{"(",
RowBox[{
RowBox[{
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x1"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y1"}], ")"}], "2"]}]], " ",
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x", "-", "x2"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y", "-", "y2"}], ")"}], "2"]}]], " ",
SqrtBox[
RowBox[{
SuperscriptBox[
RowBox[{"(",
RowBox[{"x1", "-", "x2"}], ")"}], "2"], "+",
SuperscriptBox[
RowBox[{"(",
RowBox[{"y1", "-", "y2"}], ")"}], "2"]}]]}], "+", ".0001"}],
")"}]}]}]}], ")"}]}]}], "]"}]}], ",",
RowBox[{"Permissions", "\[Rule]", "\"\<Public\>\""}]}], "]"}]], "Input",
CellChangeTimes->{
3.689694771253903*^9, {3.689694973089924*^9, 3.6896949960998816`*^9}, {
3.689695029875738*^9, 3.689695180685006*^9}, {3.6896952768764257`*^9,
3.689695282992777*^9}, {3.689695412467699*^9, 3.689695441320379*^9}, {
3.6896954975929775`*^9, 3.6896955495317364`*^9}, {3.689696597568408*^9,
3.6896966077267265`*^9}, {3.6896966461042953`*^9, 3.689696858756298*^9}, {
3.689696897193568*^9, 3.689697032371087*^9}, {3.6929708856076527`*^9,
3.6929709064135513`*^9}}],
Cell[BoxData[
InterpretationBox[
RowBox[{"CloudObject", "[",
TagBox[
ButtonBox[
PaneSelectorBox[{
False->"\<\"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-\
adb9-831a993984c5\"\>", True->
StyleBox["\<\"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-\
adb9-831a993984c5\"\>", "HyperlinkActive"]}, Dynamic[
CurrentValue["MouseOver"]],
BaseStyle->{"Hyperlink"},
FrameMargins->0,
ImageSize->Automatic],
BaseStyle->"Hyperlink",
ButtonData->{
URL[
"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-adb9-\
831a993984c5"], None},
ButtonNote->
"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-adb9-\
831a993984c5"],
Annotation[#,
"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-adb9-\
831a993984c5", "Hyperlink"]& ], "]"}],
CloudObject[
"https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-adb9-831a993984c5"],
SelectWithContents->True]], "Output",
CellChangeTimes->{
3.6896947722899046`*^9, {3.689695124812663*^9, 3.6896951575517035`*^9},
3.6896952858795123`*^9, 3.689695523106248*^9, 3.6896966091756897`*^9,
3.689696713513836*^9, 3.6896967977809663`*^9, 3.689696859900607*^9,
3.6896968989402122`*^9, 3.6896969348807993`*^9, 3.6896969660317993`*^9, {
3.689697017260708*^9, 3.689697033510372*^9}, 3.6929709088572507`*^9}]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"SetOptions", "[",
RowBox[{
RowBox[{
"CloudObject", "[",
"\"\<https://www.wolframcloud.com/objects/da99b6ea-9c81-4723-adb9-\
831a993984c5\>\"", "]"}], ",",
RowBox[{"Permissions", "\[Rule]", "\"\<Public\>\""}]}], "]"}]], "Input",
NumberMarks->False],
Cell[BoxData[
RowBox[{"{",
RowBox[{"Permissions", "\[Rule]", "\<\"Public\"\>"}], "}"}]], "Output",
CellChangeTimes->{3.6929709178420134`*^9}]
}, Open ]],
Cell["\<\
Due the principle of superposition electrostatic charges add vectorially. \
The electrostatic field is the force per unit charge. This is given by the \
following equation:\
\>", "Text",
CellChangeTimes->{{3.6908095308529596`*^9, 3.6908096565308266`*^9}, {
3.690809695104229*^9, 3.690809716949918*^9}}],
Cell[BoxData[
FormBox[
StyleBox[
RowBox[{
RowBox[{"E",
RowBox[{"(", "r", ")"}]}], "=",
RowBox[{
FractionBox[
RowBox[{"F",
RowBox[{"(", "r", ")"}]}],
SubscriptBox["q", "0"]], "=",
RowBox[{
FractionBox["1",
RowBox[{"4",
SubscriptBox["\[Pi]\[Epsilon]", "0"]}]],
FractionBox["q",
SuperscriptBox["r", "2"]],
OverscriptBox["u", "^"]}]}]}], "Equation"],
TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908095308529596`*^9, 3.6908096565308266`*^9}, {
3.690809695104229*^9, 3.6908097410321918`*^9}, {3.6908097840487566`*^9,
3.690809934629033*^9}, {3.6908099876492033`*^9, 3.6908100008173337`*^9}, {
3.690810038269661*^9, 3.690810069314843*^9}},
TextAlignment->Center],
Cell["This generalizes to: ", "Text",
CellChangeTimes->{{3.690809991382716*^9, 3.690809996104336*^9}, {
3.6908100267319613`*^9, 3.6908100267319613`*^9}, 3.6908102479220095`*^9}],
Cell[BoxData[
FormBox[
StyleBox[
RowBox[{
RowBox[{"E", "(", "r", ")"}], "=",
RowBox[{
FractionBox["1",
RowBox[{"4",
SubscriptBox["\[Pi]\[Epsilon]", "0"]}]],
RowBox[{
UnderoverscriptBox["\[Sum]",
RowBox[{"l", "=", "1"}], "n"],
RowBox[{
FractionBox[
SubscriptBox["q", "l"],
SuperscriptBox[
RowBox[{"\[LeftBracketingBar]",
RowBox[{"r", "-",
SubscriptBox["r", "l"]}], "\[RightBracketingBar]"}], "2"]],
SubscriptBox[
OverscriptBox["u", "^"], "l"]}]}]}]}], "Equation"],
TraditionalForm]], "Equation",
CellChangeTimes->{{3.690809991382716*^9, 3.690809996104336*^9}, {
3.6908100320290556`*^9, 3.690810032869291*^9}, {3.69081009590919*^9,
3.690810157581538*^9}, {3.690810192181367*^9, 3.6908102419217725`*^9}},
TextAlignment->Center],
Cell[TextData[{
"Where ",
Cell[BoxData[
FormBox[
SubscriptBox[
OverscriptBox["u", "^"], "l"], TraditionalForm]],
CellChangeTimes->{{3.690809991382716*^9, 3.690809996104336*^9}, {
3.6908100320290556`*^9, 3.690810032869291*^9}, {3.69081009590919*^9,
3.690810157581538*^9}, {3.690810192181367*^9, 3.6908102419217725`*^9}},
TextAlignment->Center],
" is the unit vector pointing from ",
Cell[BoxData[
FormBox[
SubscriptBox["r", "l"], TraditionalForm]],
CellChangeTimes->{{3.690809991382716*^9, 3.690809996104336*^9}, {
3.6908100320290556`*^9, 3.690810032869291*^9}, {3.69081009590919*^9,
3.690810157581538*^9}, {3.690810192181367*^9, 3.6908102419217725`*^9}},
TextAlignment->Center],
" to r and "
}], "Text",
CellChangeTimes->{{3.6908102503010254`*^9, 3.690810343035509*^9}}],
Cell[BoxData[
FormBox[
RowBox[{"r", "=",
RowBox[{
"\[DoubleStruckI]x", "+", "\[DoubleStruckJ]y", "+",
"\[DoubleStruckK]z"}]}], TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908102503010254`*^9, 3.690810355358116*^9}, {
3.690810396586199*^9, 3.690810428202073*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox[
RowBox[{
RowBox[{"produced", " ", "by", " ", "the", " ", "charges", " ",
SubscriptBox["q", "1"]}], ",", " ",
SubscriptBox["q", "2"], ",", " ", "...", ",", " ",
SubscriptBox["q", "n"]}], TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908102503010254`*^9, 3.690810355358116*^9}, {
3.690810396586199*^9, 3.690810524550413*^9}},
TextAlignment->Center],
Cell[TextData[{
"This just means the electrostatic field at r is the vector sum of the \
charges. Electromagnetism is a ",
StyleBox["field theory ",
FontSlant->"Italic"],
"and will play a part in our derivation of Maxwell\[CloseCurlyQuote]s \
equation in a future blog post."
}], "Text",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.6908107634196024`*^9}}],
Cell[TextData[{
"It is often convenient to treat the electrostatic charge as if it were \
continuous. Suppose we have a volume of space denoted by ",
StyleBox["\[CapitalDelta]V with a charge in this space of \[CapitalDelta]Q. \
Then we define the", "Equation"],
StyleBox[" average charge density ", "Equation",
FontSlant->"Italic"],
StyleBox["in \[CapitalDelta]V as", "Equation"]
}], "Text",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.690810993644679*^9}}],
Cell[BoxData[
FormBox[
RowBox[{
SubscriptBox[
OverscriptBox["\[Rho]", "_"],
StyleBox["\[CapitalDelta]V", "Equation"]], "\[Congruent]",
FractionBox[
StyleBox["\[CapitalDelta]Q", "Equation"],
RowBox[{" ",
StyleBox["\[CapitalDelta]V", "Equation"]}]]}],
TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.690811178202776*^9}},
TextAlignment->Center],
Cell["We now shrink the region around x, y, z by taking the limit.", "Text",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811252192766*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox[
RowBox[{
RowBox[{"\[Rho]", "(",
RowBox[{"x", ",", "y", ",", "z"}], ")"}], "\[Congruent]",
RowBox[{
UnderscriptBox[
RowBox[{
StyleBox["\[CapitalDelta]V", "Equation"],
OverscriptBox["\[RightArrow]", "lim"], "0", " "}],
RowBox[{
RowBox[{"about", " ", "x"}], ",", "y", ",", "z"}]],
FractionBox[
StyleBox["\[CapitalDelta]Q", "Equation"],
RowBox[{" ",
StyleBox["\[CapitalDelta]V", "Equation"]}]]}], "\[Congruent]",
RowBox[{
UnderscriptBox[
RowBox[{
StyleBox["\[CapitalDelta]V", "Equation"],
OverscriptBox["\[RightArrow]", "lim"], "0", " "}],
RowBox[{
RowBox[{"about", " ", "x"}], ",", "y", ",", "z"}]],
SubscriptBox[
OverscriptBox["\[Rho]", "_"],
StyleBox["\[CapitalDelta]V", "Equation"]]}]}],
TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.690811519889078*^9}, {3.690811586026474*^9, 3.690811617932277*^9}},
TextAlignment->Center],
Cell["\<\
This allows us to express the electric charge in some region V as the \
following triple integral:\
\>", "Text",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.690811519889078*^9}, {3.690811586026474*^9, 3.6908116984056005`*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox[
RowBox[{"Q", "=",
RowBox[{"\[Integral]",
RowBox[{"\[Integral]",
RowBox[{
SubscriptBox["\[Integral]", "V"],
RowBox[{
RowBox[{"\[Rho]", "(",
RowBox[{"x", ",", "y", ",", "z"}], ")"}], "dV"}]}]}]}]}],
TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.690811519889078*^9}, {3.690811586026474*^9, 3.6908118320638075`*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox[
StyleBox[
RowBox[{
"So", " ", "for", " ", "a", " ", "continuos", " ", "distribution", " ",
"of", " ", "charges", " ", "we", " ", "may", " ",
RowBox[{"write", ":"}]}], "Text"], TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.690811519889078*^9}, {3.690811586026474*^9, 3.690811893223456*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox[
RowBox[{
RowBox[{"E", "(", "r", ")"}], "=",
RowBox[{
FractionBox["1",
RowBox[{"4",
SubscriptBox["\[Pi]\[Epsilon]", "0"]}]],
RowBox[{"\[Integral]",
RowBox[{"\[Integral]",
RowBox[{
SubscriptBox["\[Integral]", "V"],
RowBox[{
FractionBox[
RowBox[{
RowBox[{"\[Rho]", "(",
RowBox[{"r", "'"}], ")"}],
RowBox[{
OverscriptBox["u", "^"], "(",
RowBox[{"r", "'"}], ")"}]}],
SuperscriptBox[
RowBox[{"\[LeftBracketingBar]",
RowBox[{"r", "-",
RowBox[{"r", "'"}]}], "\[RightBracketingBar]"}], "2"]],
"dV"}]}]}]}]}]}], TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.690811519889078*^9}, {3.690811586026474*^9, 3.6908119720972137`*^9}, {
3.690812003236891*^9, 3.690812021521064*^9}, {3.6908120700827265`*^9,
3.6908121824067373`*^9}},
TextAlignment->Center],
Cell[BoxData[
FormBox["", TraditionalForm]], "Equation",
CellChangeTimes->{{3.6908105415786734`*^9, 3.6908105863492427`*^9}, {
3.690810676005826*^9, 3.690810946607322*^9}, {3.6908109905020733`*^9,
3.6908110489542303`*^9}, {3.690811130556749*^9, 3.6908111781847286`*^9}, {
3.690811211841374*^9, 3.690811358462495*^9}, {3.690811394202344*^9,
3.6908115080239224`*^9}},
TextAlignment->Center],
Cell["Exercises I-1", "Text",
CellChangeTimes->{{3.6908122065888643`*^9, 3.6908122203082666`*^9}}],
Cell["(a)", "Text",
CellChangeTimes->{{3.6908122065888643`*^9, 3.6908122222840357`*^9}}],
Cell[BoxData[
RowBox[{"f", "=",
RowBox[{"\[ImaginaryI]x", "+", "\[ImaginaryJ]y"}]}]], "Input",
CellChangeTimes->{{3.6908122065888643`*^9, 3.6908122355186014`*^9}, {
3.6908122704469447`*^9, 3.6908122980949755`*^9}, 3.690812340656204*^9}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"Fa", "[",
RowBox[{"x_", ",", " ", "y_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "1"}], "]"}], "*", "x"}], " ", "+", " ", "\n",
" ",
RowBox[{
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "2"}], "]"}], "*", "y"}]}]}], ";"}],
" "}], "\n",
RowBox[{"VectorPlot", "[",
RowBox[{
RowBox[{"Fa", "[",
RowBox[{"i", ",", " ", "j"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"i", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ",
RowBox[{"{",
RowBox[{"j", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{
"PlotLabel", " ", "->", " ", "\n", " ", "\"\<2D Position Vector\>\""}]}],
"]"}]}], "Input",
CellChangeTimes->{
3.69081233685579*^9, {3.690812445313831*^9, 3.690812447704549*^9}, {
3.6908124943858624`*^9, 3.6908124977924557`*^9}}],
Cell[BoxData[
GraphicsBox[{{},
{RGBColor[0.0224, 0.43007999999999996`, 0.47488],
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.9285714285714286}, \
{-1.0714285714285714`, -1.0714285714285714`}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.7959183673469389}, \
{-1.0714285714285714`, -0.9183673469387756}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.6632653061224492}, \
{-1.0714285714285714`, -0.7653061224489797}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.5306122448979593}, \
{-1.0714285714285714`, -0.6122448979591838}}]},
{Arrowheads[{{0.03529105076134966, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.39795918367346955`}, \
{-1.0714285714285714`, -0.45918367346938793`}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.2653061224489798}, \
{-1.0714285714285714`, -0.30612244897959207`}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.9285714285714286, -0.13265306122449}, \
{-1.0714285714285714`, -0.15306122448979614`}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-0.9285714285714286, -2.061842760018148*^-16}, \
{-1.0714285714285714`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.13265306122448958`}, {-1.0714285714285714`, 0.15306122448979567`}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.2653061224489794}, {-1.0714285714285714`, 0.30612244897959157`}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.39795918367346916`}, {-1.0714285714285714`, 0.4591836734693875}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.530612244897959}, {-1.0714285714285714`, 0.6122448979591835}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.6632653061224487}, {-1.0714285714285714`, 0.7653061224489792}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.7959183673469384}, {-1.0714285714285714`, 0.9183673469387751}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{-0.9285714285714286,
0.9285714285714282}, {-1.0714285714285714`, 1.071428571428571}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.9285714285714286}, \
{-0.9183673469387756, -1.0714285714285714`}}]},
{Arrowheads[{{0.039320301634514, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.7959183673469389}, \
{-0.9183673469387756, -0.9183673469387756}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.6632653061224492}, \
{-0.9183673469387756, -0.7653061224489797}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.5306122448979593}, \
{-0.9183673469387755, -0.6122448979591838}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.39795918367346955`}, \
{-0.9183673469387755, -0.45918367346938793`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.2653061224489798}, \
{-0.9183673469387756, -0.30612244897959207`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.7959183673469389, -0.13265306122449}, \
{-0.9183673469387756, -0.15306122448979614`}}]},
{Arrowheads[{{0.027803651924065337`, 1.}}],
ArrowBox[{{-0.7959183673469389, -2.061842760018148*^-16}, \
{-0.9183673469387756, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.13265306122448958`}, {-0.9183673469387756, 0.15306122448979567`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.2653061224489794}, {-0.9183673469387756, 0.3061224489795916}}]},
{Arrowheads[{{0.03108542786247645, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.39795918367346916`}, {-0.9183673469387756, 0.4591836734693875}}]},
{Arrowheads[{{0.03341583088579019, 1.}}],
ArrowBox[{{-0.7959183673469389, 0.530612244897959}, {-0.9183673469387756,
0.6122448979591835}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.6632653061224487}, {-0.9183673469387756, 0.7653061224489792}}]},
{Arrowheads[{{0.03932030163451398, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.7959183673469384}, {-0.9183673469387756, 0.9183673469387751}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{-0.7959183673469389,
0.9285714285714282}, {-0.9183673469387756, 1.071428571428571}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.9285714285714286}, \
{-0.7653061224489797, -1.0714285714285714`}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.7959183673469389}, \
{-0.7653061224489797, -0.9183673469387756}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.6632653061224492}, \
{-0.7653061224489797, -0.7653061224489797}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.5306122448979593}, \
{-0.7653061224489797, -0.6122448979591838}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.39795918367346955`}, \
{-0.7653061224489797, -0.45918367346938793`}}]},
{Arrowheads[{{0.02495454130854903, 1.}}],
ArrowBox[{{-0.663265306122449, -0.2653061224489798}, \
{-0.7653061224489797, -0.30612244897959207`}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.6632653061224492, -0.13265306122449}, \
{-0.7653061224489797, -0.15306122448979614`}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-0.6632653061224492, -2.061842760018148*^-16}, \
{-0.7653061224489797, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.13265306122448958`}, {-0.7653061224489797, 0.15306122448979567`}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.2653061224489794}, {-0.7653061224489797, 0.30612244897959157`}}]},
{Arrowheads[{{0.027020292811707983`, 1.}}],
ArrowBox[{{-0.663265306122449,
0.39795918367346916`}, {-0.7653061224489797, 0.4591836734693875}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.6632653061224492, 0.530612244897959}, {-0.7653061224489797,
0.6122448979591835}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.6632653061224487}, {-0.7653061224489797, 0.7653061224489792}}]},
{Arrowheads[{{0.03619224390482541, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.7959183673469384}, {-0.7653061224489797, 0.9183673469387751}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{-0.6632653061224492,
0.9285714285714282}, {-0.7653061224489797, 1.071428571428571}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.9285714285714286}, \
{-0.6122448979591838, -1.0714285714285714`}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.7959183673469389}, \
{-0.6122448979591838, -0.9183673469387755}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.6632653061224492}, \
{-0.6122448979591838, -0.7653061224489797}}]},
{Arrowheads[{{0.026213534423009357`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.5306122448979593}, \
{-0.6122448979591839, -0.6122448979591839}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.39795918367346955`}, \
{-0.6122448979591838, -0.45918367346938793`}}]},
{Arrowheads[{{0.020723618574984323`, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.2653061224489798}, \
{-0.6122448979591839, -0.30612244897959207`}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.5306122448979593, -0.13265306122449}, \
{-0.6122448979591838, -0.15306122448979614`}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-0.5306122448979593, -2.061842760018148*^-16}, \
{-0.6122448979591838, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.13265306122448958`}, {-0.6122448979591838, 0.15306122448979567`}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.2653061224489794}, {-0.6122448979591838, 0.30612244897959157`}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.39795918367346916`}, {-0.6122448979591838, 0.4591836734693875}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{-0.5306122448979593, 0.530612244897959}, {-0.6122448979591838,
0.6122448979591835}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.6632653061224487}, {-0.6122448979591838, 0.7653061224489792}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.7959183673469384}, {-0.6122448979591838, 0.9183673469387751}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{-0.5306122448979593,
0.9285714285714282}, {-0.6122448979591838, 1.071428571428571}}]},
{Arrowheads[{{0.03529105076134966, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.9285714285714286}, \
{-0.45918367346938793`, -1.0714285714285714`}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.7959183673469389}, \
{-0.45918367346938793`, -0.9183673469387755}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.6632653061224492}, \
{-0.45918367346938793`, -0.7653061224489797}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.5306122448979593}, \
{-0.45918367346938793`, -0.6122448979591838}}]},
{Arrowheads[{{0.019660150817257, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.39795918367346955`}, \
{-0.45918367346938793`, -0.45918367346938793`}}]},
{Arrowheads[{{0.0167079154428951, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.2653061224489798}, \
{-0.45918367346938793`, -0.30612244897959207`}}]},
{Arrowheads[{{0.014653811225094899`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -0.13265306122449}, \
{-0.45918367346938793`, -0.15306122448979614`}}]},
{Arrowheads[{{0.013901825962032668`, 1.}}],
ArrowBox[{{-0.39795918367346955`, -2.061842760018148*^-16}, \
{-0.45918367346938793`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.014653811225094897`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.13265306122448958`}, {-0.45918367346938793`, 0.15306122448979567`}}]},
{Arrowheads[{{0.016707915442895085`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.2653061224489794}, {-0.45918367346938793`, 0.30612244897959157`}}]},
{Arrowheads[{{0.01966015081725699, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.39795918367346916`}, {-0.45918367346938793`, 0.4591836734693875}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.530612244897959}, {-0.45918367346938793`, 0.6122448979591835}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.6632653061224487}, {-0.45918367346938793`, 0.7653061224489792}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{-0.39795918367346955`,
0.7959183673469384}, {-0.45918367346938793`, 0.9183673469387751}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{-0.3979591836734696,
0.9285714285714282}, {-0.45918367346938793`, 1.071428571428571}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.9285714285714286}, \
{-0.30612244897959207`, -1.0714285714285714`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.7959183673469389}, \
{-0.30612244897959207`, -0.9183673469387756}}]},
{Arrowheads[{{0.02495454130854903, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.663265306122449}, \
{-0.30612244897959207`, -0.7653061224489797}}]},
{Arrowheads[{{0.020723618574984323`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.5306122448979593}, \
{-0.30612244897959207`, -0.6122448979591839}}]},
{Arrowheads[{{0.0167079154428951, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.39795918367346955`}, \
{-0.30612244897959207`, -0.45918367346938793`}}]},
{Arrowheads[{{0.013106767211504678`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.2653061224489798}, \
{-0.30612244897959207`, -0.30612244897959207`}}]},
{Arrowheads[{{0.010361809287492162`, 1.}}],
ArrowBox[{{-0.2653061224489798, -0.13265306122449}, \
{-0.30612244897959207`, -0.15306122448979614`}}]},
{Arrowheads[{{0.009267883974688454, 1.}}],
ArrowBox[{{-0.2653061224489798, -2.061842760018148*^-16}, \
{-0.30612244897959207`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.010361809287492156`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.13265306122448958`}, {-0.30612244897959207`, 0.15306122448979567`}}]},
{Arrowheads[{{0.01310676721150466, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.2653061224489794}, {-0.30612244897959207`, 0.30612244897959157`}}]},
{Arrowheads[{{0.016707915442895092`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.39795918367346916`}, {-0.30612244897959207`, 0.4591836734693875}}]},
{Arrowheads[{{0.0207236185749843, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.530612244897959}, {-0.30612244897959207`, 0.6122448979591835}}]},
{Arrowheads[{{0.024954541308549006`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.6632653061224487}, {-0.30612244897959207`, 0.7653061224489792}}]},
{Arrowheads[{{0.029307622450189773`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.7959183673469384}, {-0.30612244897959207`, 0.9183673469387751}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{-0.2653061224489798,
0.9285714285714282}, {-0.30612244897959207`, 1.071428571428571}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.13265306122449, -0.9285714285714286}, \
{-0.15306122448979614`, -1.0714285714285714`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.7959183673469389}, \
{-0.15306122448979614`, -0.9183673469387756}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.6632653061224492}, \
{-0.15306122448979614`, -0.7653061224489797}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.13265306122449, -0.5306122448979593}, \
{-0.15306122448979614`, -0.6122448979591838}}]},
{Arrowheads[{{0.014653811225094899`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.39795918367346955`}, \
{-0.15306122448979614`, -0.45918367346938793`}}]},
{Arrowheads[{{0.010361809287492162`, 1.}}],
ArrowBox[{{-0.13265306122449, -0.2653061224489798}, \
{-0.15306122448979614`, -0.30612244897959207`}}]},
{Arrowheads[{{0.006553383605752339, 1.}}],
ArrowBox[{{-0.13265306122449, -0.13265306122449}, \
{-0.15306122448979614`, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344227, 1.}}],
ArrowBox[{{-0.13265306122449, -2.061842760018148*^-16}, \
{-0.15306122448979614`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.00655338360575233, 1.}}],
ArrowBox[{{-0.13265306122449,
0.13265306122448958`}, {-0.15306122448979614`, 0.15306122448979567`}}]},
{Arrowheads[{{0.010361809287492139`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.2653061224489794}, {-0.15306122448979614`, 0.30612244897959157`}}]},
{Arrowheads[{{0.014653811225094886`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.39795918367346916`}, {-0.15306122448979614`, 0.4591836734693875}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{-0.13265306122449, 0.530612244897959}, {-0.15306122448979614`,
0.6122448979591835}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{-0.13265306122449,
0.6632653061224487}, {-0.15306122448979614`, 0.7653061224489792}}]},
{Arrowheads[{{0.02818716868819308, 1.}}],
ArrowBox[{{-0.13265306122449,
0.7959183673469384}, {-0.15306122448979614`, 0.9183673469387751}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{-0.13265306122449,
0.9285714285714282}, {-0.15306122448979614`, 1.071428571428571}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.9285714285714286}, \
{-2.379049338482478*^-16, -1.0714285714285714`}}]},
{Arrowheads[{{0.027803651924065337`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.7959183673469389}, \
{-2.379049338482478*^-16, -0.9183673469387756}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.6632653061224492}, \
{-2.379049338482478*^-16, -0.7653061224489797}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.5306122448979593}, \
{-2.379049338482478*^-16, -0.6122448979591838}}]},
{Arrowheads[{{0.013901825962032668`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.39795918367346955`}, \
{-2.379049338482478*^-16, -0.45918367346938793`}}]},
{Arrowheads[{{0.009267883974688454, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.2653061224489798}, \
{-2.379049338482478*^-16, -0.30612244897959207`}}]},
{Arrowheads[{{0.004633941987344227, 1.}}],
ArrowBox[{{-2.061842760018148*^-16, -0.13265306122449}, \
{-2.379049338482478*^-16, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344214, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.13265306122448958`}, {-2.379049338482478*^-16,
0.15306122448979567`}}]},
{Arrowheads[{{0.009267883974688428, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.2653061224489794}, {-2.379049338482478*^-16, 0.30612244897959157`}}]},
{Arrowheads[{{0.013901825962032655`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.39795918367346916`}, {-2.379049338482478*^-16, 0.4591836734693875}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.530612244897959}, {-2.379049338482478*^-16, 0.6122448979591835}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.6632653061224487}, {-2.379049338482478*^-16, 0.7653061224489792}}]},
{Arrowheads[{{0.02780365192406531, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.7959183673469384}, {-2.379049338482478*^-16, 0.9183673469387751}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{-2.061842760018148*^-16,
0.9285714285714282}, {-2.379049338482478*^-16, 1.071428571428571}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.9285714285714286}, {
0.15306122448979567`, -1.0714285714285714`}}]},
{Arrowheads[{{0.028187168688193105`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.7959183673469389}, {
0.15306122448979567`, -0.9183673469387756}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.6632653061224492}, {
0.15306122448979567`, -0.7653061224489797}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.5306122448979593}, {
0.15306122448979567`, -0.6122448979591838}}]},
{Arrowheads[{{0.014653811225094897`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.39795918367346955`}, {
0.15306122448979567`, -0.45918367346938793`}}]},
{Arrowheads[{{0.010361809287492156`, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.2653061224489798}, {
0.15306122448979567`, -0.30612244897959207`}}]},
{Arrowheads[{{0.00655338360575233, 1.}}],
ArrowBox[{{0.13265306122448958`, -0.13265306122449}, {
0.15306122448979567`, -0.15306122448979614`}}]},
{Arrowheads[{{0.004633941987344214, 1.}}],
ArrowBox[{{0.13265306122448958`, -2.061842760018148*^-16}, {
0.15306122448979567`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.006553383605752321, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.13265306122448958`}, {
0.15306122448979567`, 0.15306122448979567`}}]},
{Arrowheads[{{0.010361809287492144`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.2653061224489794}, {
0.15306122448979567`, 0.3061224489795916}}]},
{Arrowheads[{{0.014653811225094883`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.39795918367346916`}, {
0.15306122448979567`, 0.4591836734693875}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.530612244897959}, {
0.15306122448979567`, 0.6122448979591835}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.6632653061224487}, {
0.15306122448979567`, 0.7653061224489792}}]},
{Arrowheads[{{0.028187168688193077`, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.7959183673469384}, {
0.15306122448979567`, 0.9183673469387751}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.13265306122448958`, 0.9285714285714282}, {
0.15306122448979567`, 1.071428571428571}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.2653061224489794, -0.9285714285714286}, {
0.30612244897959157`, -1.0714285714285714`}}]},
{Arrowheads[{{0.029307622450189797`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.7959183673469389}, {
0.3061224489795916, -0.9183673469387756}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.2653061224489794, -0.6632653061224492}, {
0.30612244897959157`, -0.7653061224489797}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.2653061224489794, -0.5306122448979593}, {
0.30612244897959157`, -0.6122448979591838}}]},
{Arrowheads[{{0.016707915442895085`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.39795918367346955`}, {
0.30612244897959157`, -0.45918367346938793`}}]},
{Arrowheads[{{0.01310676721150466, 1.}}],
ArrowBox[{{0.2653061224489794, -0.2653061224489798}, {
0.30612244897959157`, -0.30612244897959207`}}]},
{Arrowheads[{{0.010361809287492139`, 1.}}],
ArrowBox[{{0.2653061224489794, -0.13265306122449}, {
0.30612244897959157`, -0.15306122448979614`}}]},
{Arrowheads[{{0.009267883974688428, 1.}}],
ArrowBox[{{0.2653061224489794, -2.061842760018148*^-16}, {
0.30612244897959157`, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.010361809287492144`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.13265306122448958`}, {
0.3061224489795916, 0.15306122448979567`}}]},
{Arrowheads[{{0.013106767211504642`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.2653061224489794}, {
0.30612244897959157`, 0.30612244897959157`}}]},
{Arrowheads[{{0.016707915442895075`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.39795918367346916`}, {
0.30612244897959157`, 0.4591836734693875}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.2653061224489794, 0.530612244897959}, {0.30612244897959157`,
0.6122448979591835}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.2653061224489794, 0.6632653061224487}, {
0.30612244897959157`, 0.7653061224489792}}]},
{Arrowheads[{{0.029307622450189766`, 1.}}],
ArrowBox[{{0.2653061224489794, 0.7959183673469384}, {
0.30612244897959157`, 0.9183673469387751}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.2653061224489794, 0.9285714285714282}, {
0.30612244897959157`, 1.071428571428571}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.9285714285714286}, {
0.4591836734693875, -1.0714285714285714`}}]},
{Arrowheads[{{0.03108542786247645, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.7959183673469389}, {
0.4591836734693875, -0.9183673469387756}}]},
{Arrowheads[{{0.027020292811707983`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.663265306122449}, {
0.4591836734693875, -0.7653061224489797}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.5306122448979593}, {
0.4591836734693875, -0.6122448979591838}}]},
{Arrowheads[{{0.01966015081725699, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.39795918367346955`}, {
0.4591836734693875, -0.45918367346938793`}}]},
{Arrowheads[{{0.016707915442895092`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.2653061224489798}, {
0.4591836734693875, -0.30612244897959207`}}]},
{Arrowheads[{{0.014653811225094886`, 1.}}],
ArrowBox[{{0.39795918367346916`, -0.13265306122449}, {
0.4591836734693875, -0.15306122448979614`}}]},
{Arrowheads[{{0.013901825962032655`, 1.}}],
ArrowBox[{{0.39795918367346916`, -2.061842760018148*^-16}, {
0.4591836734693875, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.014653811225094883`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.13265306122448958`}, {
0.4591836734693875, 0.15306122448979567`}}]},
{Arrowheads[{{0.016707915442895075`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.2653061224489794}, {
0.4591836734693875, 0.30612244897959157`}}]},
{Arrowheads[{{0.01966015081725698, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.39795918367346916`}, {
0.4591836734693875, 0.4591836734693875}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.530612244897959}, {0.4591836734693875,
0.6122448979591835}}]},
{Arrowheads[{{0.02702029281170796, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.6632653061224487}, {
0.4591836734693875, 0.7653061224489792}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.7959183673469384}, {
0.4591836734693875, 0.9183673469387751}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.39795918367346916`, 0.9285714285714282}, {
0.4591836734693875, 1.071428571428571}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.530612244897959, -0.9285714285714286}, {
0.6122448979591835, -1.0714285714285714`}}]},
{Arrowheads[{{0.03341583088579019, 1.}}],
ArrowBox[{{0.530612244897959, -0.7959183673469389}, {
0.6122448979591835, -0.9183673469387756}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.530612244897959, -0.6632653061224492}, {
0.6122448979591835, -0.7653061224489797}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{0.530612244897959, -0.5306122448979593}, {
0.6122448979591835, -0.6122448979591838}}]},
{Arrowheads[{{0.023169709936721107`, 1.}}],
ArrowBox[{{0.530612244897959, -0.39795918367346955`}, {
0.6122448979591835, -0.45918367346938793`}}]},
{Arrowheads[{{0.0207236185749843, 1.}}],
ArrowBox[{{0.530612244897959, -0.2653061224489798}, {
0.6122448979591835, -0.30612244897959207`}}]},
{Arrowheads[{{0.01910623227680484, 1.}}],
ArrowBox[{{0.530612244897959, -0.13265306122449}, {
0.6122448979591835, -0.15306122448979614`}}]},
{Arrowheads[{{0.01853576794937688, 1.}}],
ArrowBox[{{0.530612244897959, -2.061842760018148*^-16}, {
0.6122448979591835, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.019106232276804837`, 1.}}],
ArrowBox[{{0.530612244897959, 0.13265306122448958`}, {0.6122448979591835,
0.15306122448979567`}}]},
{Arrowheads[{{0.02072361857498429, 1.}}],
ArrowBox[{{0.530612244897959, 0.2653061224489794}, {0.6122448979591835,
0.30612244897959157`}}]},
{Arrowheads[{{0.0231697099367211, 1.}}],
ArrowBox[{{0.530612244897959, 0.39795918367346916`}, {0.6122448979591835,
0.4591836734693875}}]},
{Arrowheads[{{0.02621353442300932, 1.}}],
ArrowBox[{{0.530612244897959, 0.530612244897959}, {0.6122448979591835,
0.6122448979591835}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.530612244897959, 0.6632653061224487}, {0.6122448979591835,
0.7653061224489792}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.530612244897959, 0.7959183673469384}, {0.6122448979591835,
0.9183673469387751}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.530612244897959, 0.9285714285714282}, {0.6122448979591835,
1.071428571428571}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.9285714285714286}, {
0.7653061224489792, -1.0714285714285714`}}]},
{Arrowheads[{{0.036192243904825436`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.7959183673469389}, {
0.7653061224489792, -0.9183673469387756}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.6632653061224492}, {
0.7653061224489792, -0.7653061224489797}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.5306122448979593}, {
0.7653061224489792, -0.6122448979591838}}]},
{Arrowheads[{{0.02702029281170797, 1.}}],
ArrowBox[{{0.6632653061224487, -0.39795918367346955`}, {
0.7653061224489792, -0.45918367346938793`}}]},
{Arrowheads[{{0.024954541308549006`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.2653061224489798}, {
0.7653061224489792, -0.30612244897959207`}}]},
{Arrowheads[{{0.023628560618325092`, 1.}}],
ArrowBox[{{0.6632653061224487, -0.13265306122449}, {
0.7653061224489792, -0.15306122448979614`}}]},
{Arrowheads[{{0.023169709936721083`, 1.}}],
ArrowBox[{{0.6632653061224487, -2.061842760018148*^-16}, {
0.7653061224489792, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.02362856061832509, 1.}}],
ArrowBox[{{0.6632653061224487, 0.13265306122448958`}, {
0.7653061224489792, 0.15306122448979567`}}]},
{Arrowheads[{{0.024954541308549, 1.}}],
ArrowBox[{{0.6632653061224487, 0.2653061224489794}, {0.7653061224489792,
0.30612244897959157`}}]},
{Arrowheads[{{0.02702029281170796, 1.}}],
ArrowBox[{{0.6632653061224487, 0.39795918367346916`}, {
0.7653061224489792, 0.4591836734693875}}]},
{Arrowheads[{{0.029671706254021504`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.530612244897959}, {0.7653061224489792,
0.6122448979591835}}]},
{Arrowheads[{{0.032766918028761624`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.6632653061224487}, {0.7653061224489792,
0.7653061224489792}}]},
{Arrowheads[{{0.03619224390482543, 1.}}],
ArrowBox[{{0.6632653061224487, 0.7959183673469384}, {0.7653061224489793,
0.9183673469387751}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.6632653061224487, 0.9285714285714282}, {0.7653061224489792,
1.071428571428571}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.7959183673469384, -0.9285714285714286}, {
0.9183673469387751, -1.0714285714285714`}}]},
{Arrowheads[{{0.03932030163451398, 1.}}],
ArrowBox[{{0.7959183673469384, -0.7959183673469389}, {
0.9183673469387751, -0.9183673469387756}}]},
{Arrowheads[{{0.03619224390482541, 1.}}],
ArrowBox[{{0.7959183673469384, -0.6632653061224492}, {
0.9183673469387751, -0.7653061224489797}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.7959183673469384, -0.5306122448979593}, {
0.9183673469387751, -0.6122448979591838}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.7959183673469384, -0.39795918367346955`}, {
0.9183673469387751, -0.45918367346938793`}}]},
{Arrowheads[{{0.029307622450189773`, 1.}}],
ArrowBox[{{0.7959183673469384, -0.2653061224489798}, {
0.9183673469387751, -0.30612244897959207`}}]},
{Arrowheads[{{0.02818716868819308, 1.}}],
ArrowBox[{{0.7959183673469384, -0.13265306122449}, {
0.9183673469387751, -0.15306122448979614`}}]},
{Arrowheads[{{0.02780365192406531, 1.}}],
ArrowBox[{{0.7959183673469384, -2.061842760018148*^-16}, {
0.9183673469387751, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.028187168688193077`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.13265306122448958`}, {
0.9183673469387751, 0.15306122448979567`}}]},
{Arrowheads[{{0.029307622450189766`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.2653061224489794}, {0.9183673469387751,
0.30612244897959157`}}]},
{Arrowheads[{{0.03108542786247643, 1.}}],
ArrowBox[{{0.7959183673469384, 0.39795918367346916`}, {
0.9183673469387751, 0.4591836734693875}}]},
{Arrowheads[{{0.033415830885790164`, 1.}}],
ArrowBox[{{0.7959183673469384, 0.530612244897959}, {0.9183673469387751,
0.6122448979591835}}]},
{Arrowheads[{{0.03619224390482543, 1.}}],
ArrowBox[{{0.7959183673469384, 0.6632653061224487}, {0.9183673469387751,
0.7653061224489793}}]},
{Arrowheads[{{0.03932030163451396, 1.}}],
ArrowBox[{{0.7959183673469384, 0.7959183673469384}, {0.9183673469387751,
0.9183673469387751}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.7959183673469384, 0.9285714285714282}, {0.9183673469387751,
1.071428571428571}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, -0.9285714285714286}, {
1.071428571428571, -1.0714285714285714`}}]},
{Arrowheads[{{0.0427228341648362, 1.}}],
ArrowBox[{{0.9285714285714282, -0.7959183673469389}, {
1.071428571428571, -0.9183673469387756}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.6632653061224492}, {
1.071428571428571, -0.7653061224489797}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.9285714285714282, -0.5306122448979593}, {
1.071428571428571, -0.6122448979591838}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.3979591836734696}, {
1.071428571428571, -0.45918367346938793`}}]},
{Arrowheads[{{0.033735606888416876`, 1.}}],
ArrowBox[{{0.9285714285714282, -0.2653061224489798}, {
1.071428571428571, -0.30612244897959207`}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.9285714285714282, -0.13265306122449}, {
1.071428571428571, -0.15306122448979614`}}]},
{Arrowheads[{{0.03243759391140954, 1.}}],
ArrowBox[{{0.9285714285714282, -2.061842760018148*^-16}, {
1.071428571428571, -2.379049338482478*^-16}}]},
{Arrowheads[{{0.03276691802876164, 1.}}],
ArrowBox[{{0.9285714285714282, 0.13265306122448958`}, {1.071428571428571,
0.15306122448979567`}}]},
{Arrowheads[{{0.03373560688841687, 1.}}],
ArrowBox[{{0.9285714285714282, 0.2653061224489794}, {1.071428571428571,
0.30612244897959157`}}]},
{Arrowheads[{{0.035291050761349654`, 1.}}],
ArrowBox[{{0.9285714285714282, 0.39795918367346916`}, {1.071428571428571,
0.4591836734693875}}]},
{Arrowheads[{{0.03736003469263192, 1.}}],
ArrowBox[{{0.9285714285714282, 0.530612244897959}, {1.071428571428571,
0.6122448979591835}}]},
{Arrowheads[{{0.039862676243740895`, 1.}}],
ArrowBox[{{0.9285714285714282, 0.6632653061224487}, {1.071428571428571,
0.7653061224489792}}]},
{Arrowheads[{{0.04272283416483618, 1.}}],
ArrowBox[{{0.9285714285714282, 0.7959183673469384}, {1.071428571428571,
0.9183673469387751}}]},
{Arrowheads[{{0.0458736852402663, 1.}}],
ArrowBox[{{0.9285714285714282, 0.9285714285714282}, {1.071428571428571,
1.071428571428571}}]}}},
AspectRatio->1,
BaseStyle->{FontFamily -> "Helvetica"},
DisplayFunction->Identity,
Frame->True,
FrameTicks->{{Automatic, Automatic}, {Automatic, Automatic}},
GridLinesStyle->Directive[
GrayLevel[0.5, 0.4]],
LabelStyle->{FontFamily -> "Helvetica"},
Method->{
"DefaultBoundaryStyle" -> Automatic, "TransparentPolygonMesh" -> True},
PlotLabel->FormBox["\"2D Position Vector\"", TraditionalForm],
PlotRange->{{-1.101015254455221, 1.101015254455221}, {-1.101015254455221,
1.101015254455221}},
PlotRangeClipping->True,
PlotRangePadding->{{
Scaled[0.02],
Scaled[0.02]}, {
Scaled[0.02],
Scaled[0.02]}},
Ticks->{Automatic, Automatic}]], "Output",
CellChangeTimes->{3.6908123620757537`*^9, 3.690812450966962*^9,
3.690812501277421*^9}]
}, Open ]],
Cell["(b)", "Text",
CellChangeTimes->{{3.6908123765356874`*^9, 3.6908123780677032`*^9}}],
Cell["", "Text",
CellChangeTimes->{{3.6908123765356874`*^9, 3.6908123910689707`*^9}}],
Cell[CellGroupData[{
Cell[BoxData[{
RowBox[{
RowBox[{
RowBox[{
RowBox[{"Fb", "[",
RowBox[{"x_", ",", " ", "y_"}], "]"}], " ", ":=", " ",
RowBox[{
RowBox[{"(",
RowBox[{
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "1"}], "]"}], "+", " ", "\n", " ",
RowBox[{"UnitVector", "[",
RowBox[{"2", ",", " ", "2"}], "]"}]}], ")"}], "/",
SqrtBox["2"]}]}], ";"}], " "}], "\[IndentingNewLine]",
RowBox[{"VectorPlot", "[",
RowBox[{
RowBox[{"Fb", "[",
RowBox[{"i", ",", " ", "j"}], "]"}], ",", " ",
RowBox[{"{",
RowBox[{"i", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ", "\n", " ",
RowBox[{"{",
RowBox[{"j", ",", " ",
RowBox[{"-", "1"}], ",", " ", "1"}], "}"}], ",", " ",
RowBox[{
"PlotLabel", " ", "->", " ", "\n", " ", "\"\<2D Position Vector\>\""}]}],