(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 21737, 599] NotebookOptionsPosition[ 20836, 567] NotebookOutlinePosition[ 21228, 584] CellTagsIndexPosition[ 21185, 581] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["Consider a charged line segment with constant charge per unit \ length \[Lambda] and length 2 \[ScriptL], located on the \[ScriptZ] axis from \ \[ScriptZ]= -\[ScriptL] to \[ScriptZ]=+\[ScriptL]. The electrostatic \ potential throughout the space around the line segment is the function\n\n\t", FontSize->14], StyleBox["V(\[ScriptX],\[ScriptY],\[ScriptZ]) = ", "DisplayFormula", FontSize->14], StyleBox[Cell[BoxData[ FormBox[ RowBox[{ FractionBox["\[Lambda]", RowBox[{"4", SubscriptBox["\[Pi]\[Epsilon]", "0"]}]], "ln", RowBox[{"{", FractionBox[ RowBox[{"\[ScriptZ]", "+", "\[ScriptL]", "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{"z", "+", "\[ScriptL]"}], ")"}], "2"]}]]}], RowBox[{"\[ScriptZ]", "-", "\[ScriptL]", "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["y", "2"], "+", SuperscriptBox[ RowBox[{"(", RowBox[{"z", "-", "\[ScriptL]"}], ")"}], "2"]}]]}]], "}"}]}], TraditionalForm]], "DisplayFormula", FormatType->"TraditionalForm", FontSize->14], "DisplayFormula"], StyleBox["\n\t\nThis function looks pretty complicated, so we use a computer \ to study it.\n\na) Let ", "DisplayFormula", FontSize->14], StyleBox["\[ScriptL]", FontSize->14], StyleBox[" be the unit of length. Plot V(", "DisplayFormula", FontSize->14], StyleBox["\[ScriptX]", FontSize->14], StyleBox[",0,0) in units of ", "DisplayFormula", FontSize->14], Cell[BoxData[ FormBox[ RowBox[{"\[CapitalLambda]", "\[Congruent]", RowBox[{"\[Lambda]", "/", RowBox[{"(", RowBox[{"4", SubscriptBox["\[Pi]\[Epsilon]", "0"]}], ")"}]}]}], TraditionalForm]], FormatType->"TraditionalForm", FontSize->14], StyleBox[" for \[ScriptX] in the domain (0,5).\n\nb) The elecric field is \ E(x)=-\[Del]V. Plot ", FontSize->14], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["E", "x"], "(", RowBox[{"x", ",", "0", ",", "0"}], ")"}], " "}], TraditionalForm]], FormatType->"TraditionalForm", FontSize->14], StyleBox["in units of \[CapitalLambda]/\[ScriptL] for \[ScriptX] in the \ domain (0,5). [Using ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[", the derivative can be calculated analytically by the program. \ The result may be reduced to a simple form.]\n\nc) Make a log-log plot of ", FontSize->14], Cell[BoxData[ FormBox[ RowBox[{ RowBox[{ SubscriptBox["E", "x"], "(", RowBox[{"x", ",", "0", ",", "0"}], ")"}], " "}], TraditionalForm]], FontSize->14], StyleBox[" vs \[ScriptX], over a sufficiently large range of \[ScriptX], and \ show that the functional dependence is ", FontSize->14], Cell[BoxData[ FormBox[ SuperscriptBox["\[ScriptX]", RowBox[{"-", "1"}]], TraditionalForm]], FormatType->"TraditionalForm", FontSize->14], StyleBox["for \[ScriptX]\[LessLess]\[ScriptL] and ", FontSize->14], Cell[BoxData[ FormBox[ SuperscriptBox["\[ScriptX]", RowBox[{"-", "2"}]], TraditionalForm]], FormatType->"TraditionalForm", FontSize->14], StyleBox["for \[ScriptX]\[GreaterGreater]\[ScriptL]. We are often \ interested in such asymptotic expansions in field theory.\n", FontSize->14] }], "Text", CellChangeTimes->{{3.460365715591769*^9, 3.460365757737679*^9}, { 3.460365809780972*^9, 3.460365888621296*^9}, {3.460365990903892*^9, 3.460366191886549*^9}, {3.460366231540436*^9, 3.460366308763316*^9}, { 3.4603663543174267`*^9, 3.460366638568851*^9}, {3.4603666686545143`*^9, 3.460366757801012*^9}, 3.4609004617959833`*^9, {3.460902041591301*^9, 3.460902047507085*^9}, {3.460911230787414*^9, 3.460911232723556*^9}}], Cell[TextData[{ "\n", StyleBox[" a) On the x axis the potential function is\n V(\[ScriptX],0,0) \ = ", "Text", FontSize->14, FontWeight->"Plain"], StyleBox[Cell[BoxData[ FormBox[ RowBox[{ FractionBox["\[Lambda]", RowBox[{"4", SubscriptBox["\[Pi]\[Epsilon]", "0"]}]], "ln", RowBox[{"{", FractionBox[ RowBox[{"\[ScriptL]", "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}], RowBox[{ RowBox[{"-", "\[ScriptL]"}], "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}]], "}"}]}], TraditionalForm]], "Text", FormatType->"TraditionalForm", FontWeight->"Plain"], "Text"], StyleBox[" \n Mathematica uses Log[x] to mean the natural log of ", "Text", FontSize->14, FontWeight->"Plain"], StyleBox["x", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox[", and Log[", "Text", FontSize->14, FontWeight->"Plain"], StyleBox["b", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox[",", "Text", FontSize->14, FontWeight->"Plain"], StyleBox["x", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox["] to give the log of ", "Text", FontSize->14, FontWeight->"Plain"], StyleBox["x", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox[" to the base", "Text", FontSize->14, FontWeight->"Plain"], StyleBox[" b", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox[". As an example, below is the plot from 0 to 3 in ", "Text", FontSize->14, FontWeight->"Plain"], StyleBox["x", "Text", FontSize->14, FontWeight->"Plain", FontSlant->"Italic"], StyleBox[", in units of 10\[ScriptL].", "Text", FontSize->14, FontWeight->"Plain"] }], "Input", CellChangeTimes->{{3.460903234995607*^9, 3.460903345516037*^9}, { 3.4609035512242928`*^9, 3.4609035730192347`*^9}, {3.460903619295723*^9, 3.460903627372797*^9}, {3.460904442471895*^9, 3.460904487182563*^9}}, FormatType->"TextForm"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"\[CapitalLambda]", "=", "1"}], "\[IndentingNewLine]", RowBox[{"\[ScriptL]", "=", "10"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"line", "=", FormBox[ RowBox[{"\[CapitalLambda]", "*", RowBox[{"Log", "[", FractionBox[ RowBox[{"\[ScriptL]", "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}], RowBox[{ RowBox[{"-", "\[ScriptL]"}], "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}]], "]"}]}], TraditionalForm]}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", "line", "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "3"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", "Blue", "}"}]}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", "10"}], ",", " ", RowBox[{ "PlotLabel", "\[Rule]", " ", "\"\\""}]}], " ", "]"}]}], "Input", CellChangeTimes->{{3.460900208937854*^9, 3.460900226757229*^9}, 3.4609006703400784`*^9, {3.460900700458189*^9, 3.460900715433003*^9}, { 3.460900749877636*^9, 3.4609007973942747`*^9}, 3.460900853789598*^9, { 3.460900884586632*^9, 3.460900928897027*^9}, {3.460900964740982*^9, 3.4609009885729427`*^9}, {3.46090108470815*^9, 3.4609011012706013`*^9}, { 3.460901168076275*^9, 3.4609012007887363`*^9}, {3.4609012690206127`*^9, 3.4609012695642223`*^9}, 3.460901357576586*^9, {3.4609013990109797`*^9, 3.4609014269372797`*^9}, {3.4609014686978083`*^9, 3.460901495908188*^9}, { 3.4609015302641706`*^9, 3.460901543673357*^9}, {3.460901584211939*^9, 3.460901595974024*^9}, {3.460901665510953*^9, 3.460901827719553*^9}, { 3.4609019451722107`*^9, 3.460902085966649*^9}, {3.460902129439283*^9, 3.460902190894017*^9}, {3.4609022286278133`*^9, 3.460902257412978*^9}, { 3.460902393674165*^9, 3.460902471720422*^9}, {3.4609025514439497`*^9, 3.460902561671307*^9}, {3.460902595887313*^9, 3.460902600526621*^9}, { 3.460902633808573*^9, 3.460902662943122*^9}, {3.460902709663484*^9, 3.460902786347445*^9}, {3.460902818604273*^9, 3.460902892671858*^9}, { 3.4609030238206882`*^9, 3.460903027696979*^9}, {3.460903116352264*^9, 3.460903134078292*^9}, {3.460903165190028*^9, 3.460903229387192*^9}, { 3.460903393042918*^9, 3.460903544163175*^9}, {3.460903585256166*^9, 3.4609035939623213`*^9}, {3.460903645264946*^9, 3.4609036456605577`*^9}, 3.460904490543531*^9}], Cell[BoxData["1"], "Output", CellChangeTimes->{{3.460903197786146*^9, 3.460903216104602*^9}, 3.460903430794362*^9, {3.460903472881295*^9, 3.460903532297818*^9}, { 3.460903588138036*^9, 3.4609035950849237`*^9}, {3.460903647439727*^9, 3.460903657901988*^9}, 3.460904492202261*^9}], Cell[BoxData["10"], "Output", CellChangeTimes->{{3.460903197786146*^9, 3.460903216104602*^9}, 3.460903430794362*^9, {3.460903472881295*^9, 3.460903532297818*^9}, { 3.460903588138036*^9, 3.4609035950849237`*^9}, {3.460903647439727*^9, 3.460903657901988*^9}, 3.460904492204257*^9}], Cell[BoxData[ RowBox[{"Log", "[", FractionBox[ RowBox[{"10", "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], RowBox[{ RowBox[{"-", "10"}], "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}]], "]"}]], "Output", CellChangeTimes->{{3.460903197786146*^9, 3.460903216104602*^9}, 3.460903430794362*^9, {3.460903472881295*^9, 3.460903532297818*^9}, { 3.460903588138036*^9, 3.4609035950849237`*^9}, {3.460903647439727*^9, 3.460903657901988*^9}, 3.4609044922057457`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0, 0, 1], LineBox[CompressedData[" 1:eJwdkHs403scx9e29pPym8usCG37IVkeXVA61fdDpUen0MUlzXVuaXXUGTLp iDglq7F0c8sRpShRSkqEbeIsHTqdQnIpmUhU0sLpnPfzvJ7Xv6/nzQ78ZVsw mUQi8X/wn3dEh9IyHGoR6f+ZAoND1Ndn16JMOz1erIoAcwcxVT+5Dk2nVGas OELA3F6pxoVLdSg6kTeoFhGgkXRhzoK6OlRycMtAo5AAleIyYxGpHr3ilYYm hBFww+2R6RpRPQofanAJdCNgpf/4+uB9DQipk31lbAKcfwtIuu0hR2SPlzzR Yw4sO1XrlCeUo3e5HLpPAweMctka4nQ5ck7XWO9Uw4GR6u6UIKUcOZz/Psat 4MCZqQCJnpMCeZO1rjv+wYG+uMDM/baNyKX06HZJLAfiD/FvWjGa0MGCtwu3 LONAeGrdAYNlTWjbJqFvnxUHdmQRNjPdmpC7UCmIX8SBhfd7KzpONKGi3rK3 MhYHlGr+/ROUZhSXZmudSv/RExskHxhtRvwv+Yc+DLHhTkxwZ8FTJbI3bHd5 WcKGwrV7nhuOKlEhTRpWWMSGM5T9T0/pPkFqKnMgqoANUeJDDTHbn6CW8v4J 02w22OVJS7Y8e4I+ZjT630plw66+19UiQQuK9rnedE7Ahpez6ac4EU9Ru2TD VgdrNrzw3mN9ILoVeZe+9squZkFKz0bB2eRW1GS7d1VCFQtWhZsW3c9oRaqb vKO777IgK6aTg91qRYVupxxRGQv8z7kys0ZaUViUMxkrZEH/s+WTDbvb0GEC F1FPsuCz2/fHBrxnqL//7NKLfizQ2SgOqYXnqJQsLL6jwQLttuCyFbvaUb5r ubKj3gQIlqAoKbALRf3a3qm8ZgwrO/c2OaR3I8qgnUVivRHUfovf3JbZizZp XvSx65sPYQ8ViuqEN2gdY3ElaeF8OM+/bKjv348K8t/JuXGGYOXV/WUqeABd etbEv9pqAK/GXJXgPIhUs6gydwcDGO0yWMJ0H0J8lw1pLSXzQHJNFOrp+QEx hDaGj8zngTldY8vBzBG0fEOVWWTpXKiIiL92MvcjSv0rpTJlxVxoM5NiW9NH UeKIn6SnmQmmia0WPufHkA9t9X4/PybYu3XZ5GZ+QgS//XrAhD50RiStFad+ RsdWeQfdztGHMvudWg1pX9CV7RYZ/4A+MD3kL64kjSMis2b5rCEGoB5S2iPh V1QzO+UhN4cB55lhWuYHJ9BuE4U7bTMDEnJ2/24b/g29CScx3ckMyFaek52M UKNa1yhK1G09iNsnHTE+8B19S+IvbRHowWCAxbydgZOotbn3YQhXD05Mqqiv QqZQxM8Sy463unDv/cYPuPc0IqKYFd+v6MLfZit7VpmSwCNytdbSfboQtohv LS0gwd0saY73El2o9dgV62AyAyaW5guDv+rAci9VESNvBoiOLWAkP9ABQaLT 8zXzybA3qPg9cUwHjoVofJshJYOYYZiwwl0HHhgHTKsYFHBeY54Wu0AHKqeS KZYnKaA4PRxTPKwNyvJ1KrEOFWxsN6i4VdrQwAqRpaZTYcJoxtnR49pw9I57 XrfmTMjUHLvB9dEGHqfDd5d4JlTRbMVKK21QV1jP52I0YDe6Vl8ma8MhykBz xmEaXPA8l51TRgemqX2AGQmDecKW8c/edIje5/FJMwYDX/9IG+psOhjZBSnM YzFwGLZakj+LDjWT+7Mc4zAoCTRycdSgg6ZYvF50BIM5rMSR+Jl0yLlWf3rg OAbDi58qp6dxkL1bZqu4gEHCo7XvKZ9xYPDpUUn3MVCPcY+YdeFQaWm8Ka8a g3YD67uKThx8Ry1NHtRgwLQq1hZ04HDliJPsUz0GbtRJs/IXOPx0MY4Z9CcG exZ6dTu24RDYOVjh+AoDScNwRlgjDljBRIrvawwIi65uLQUOxQLMT9SDgf3j IZdyGQ5f1Bys7C0GhkzX1Kk6HFIMvT3ZHzDQZSVKz1TjYN0Tyl3zEYMauax/ 9QMc2ooip73GMOgMVfN6q3AwsU+7LBnHwFKTfXVJJQ51pNzY4gkM3JtpCc/v 4BCmKHZVqDEYoclFhytwmCO5R/RN/vjLmHfa7DYONz0V49PTGNyIrFE2l+Pw L86kt+Y= "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotLabel->FormBox["\"Potential from a line charge\"", TraditionalForm], PlotRange->{{0, 3}, {-10, 10}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Automatic}]], "Output", CellChangeTimes->{{3.460903197786146*^9, 3.460903216104602*^9}, 3.460903430794362*^9, {3.460903472881295*^9, 3.460903532297818*^9}, { 3.460903588138036*^9, 3.4609035950849237`*^9}, {3.460903647439727*^9, 3.460903657901988*^9}, 3.460904492207685*^9}] }, Open ]], Cell[TextData[{ "\n", StyleBox[" b) On the ", FontSize->14], StyleBox["x", FontSize->14, FontSlant->"Italic"], StyleBox[" axis the electric field is ", FontSize->14], Cell[BoxData[{ FormBox[ RowBox[{ RowBox[{ RowBox[{ SubscriptBox["E", "x"], "(", RowBox[{"x", ",", "0", ",", "0"}], ")"}], " ", "=", " ", FractionBox[ RowBox[{"-", RowBox[{"\[PartialD]", "V"}]}], RowBox[{"\[PartialD]", "x"}]]}], " "}], TraditionalForm], "\[IndentingNewLine]", FormBox[ RowBox[{"\t ", RowBox[{ RowBox[{"=", " ", RowBox[{"2", FractionBox["\[ScriptL]\[CapitalLambda]", RowBox[{"x", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}]]}]}], "=", " ", RowBox[{ FractionBox["\[CapitalLambda]", "\[ScriptL]"], FractionBox[ RowBox[{"2", SuperscriptBox["\[ScriptL]", "2"]}], RowBox[{"x", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}]]}]}]}], TraditionalForm]}], FormatType->"TraditionalForm", FontSize->14], StyleBox["\n We could simply plot this, as we did for the first part. Of \ course ", FontSize->14], StyleBox["Mathematica", FontSize->14, FontSlant->"Italic"], StyleBox[" has derivatives built in as you can also see here:", FontSize->14] }], "Text", CellChangeTimes->{{3.46090451082668*^9, 3.4609045353870792`*^9}, { 3.46090462305173*^9, 3.460904643668071*^9}, {3.460904679625828*^9, 3.4609048612321987`*^9}, {3.460907568597542*^9, 3.460907586237492*^9}, { 3.460911279985388*^9, 3.460911298567753*^9}}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"\[IndentingNewLine]", RowBox[{ RowBox[{"\[CapitalLambda]", "=", "2.5"}], "\[IndentingNewLine]", RowBox[{"\[ScriptL]", "=", "10"}], "\[IndentingNewLine]", RowBox[{"line", "=", FormBox[ RowBox[{"\[CapitalLambda]", "*", RowBox[{"Log", "[", FractionBox[ RowBox[{"\[ScriptL]", "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}], RowBox[{ RowBox[{"-", "\[ScriptL]"}], "+", SqrtBox[ RowBox[{ SuperscriptBox["x", "2"], "+", SuperscriptBox["\[ScriptL]", "2"]}]]}]], "]"}]}], TraditionalForm]}], "\[IndentingNewLine]", RowBox[{"dline", "=", RowBox[{"D", "[", RowBox[{"line", ",", "x"}], "]"}]}], "\[IndentingNewLine]", "\[IndentingNewLine]", RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{"-", "dline"}], "}"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "3"}], "}"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", " ", RowBox[{"{", "Blue", "}"}]}], ",", " ", RowBox[{"PlotRange", " ", "\[Rule]", "10"}], ",", " ", RowBox[{ "PlotLabel", "\[Rule]", " ", "\"\\""}]}], " ", "]"}]}]}]], "Input", CellChangeTimes->{{3.460907260338788*^9, 3.460907557551474*^9}, { 3.460907590708551*^9, 3.460907613072137*^9}}], Cell[BoxData["2.5`"], "Output", CellChangeTimes->{{3.460907433593102*^9, 3.46090746058517*^9}, { 3.4609075196252337`*^9, 3.460907559006872*^9}, 3.46090761671343*^9}], Cell[BoxData["10"], "Output", CellChangeTimes->{{3.460907433593102*^9, 3.46090746058517*^9}, { 3.4609075196252337`*^9, 3.460907559006872*^9}, 3.4609076167154617`*^9}], Cell[BoxData[ RowBox[{"2.5`", " ", RowBox[{"Log", "[", FractionBox[ RowBox[{"10", "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], RowBox[{ RowBox[{"-", "10"}], "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}]], "]"}]}]], "Output", CellChangeTimes->{{3.460907433593102*^9, 3.46090746058517*^9}, { 3.4609075196252337`*^9, 3.460907559006872*^9}, 3.460907616716977*^9}], Cell[BoxData[ FractionBox[ RowBox[{"2.5`", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "10"}], "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], ")"}], " ", RowBox[{"(", RowBox[{ FractionBox["x", RowBox[{ SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "10"}], "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], ")"}]}]], "-", FractionBox[ RowBox[{"x", " ", RowBox[{"(", RowBox[{"10", "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], ")"}]}], RowBox[{ SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "10"}], "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}], ")"}], "2"]}]]}], ")"}]}], RowBox[{"10", "+", SqrtBox[ RowBox[{"100", "+", SuperscriptBox["x", "2"]}]]}]]], "Output", CellChangeTimes->{{3.460907433593102*^9, 3.46090746058517*^9}, { 3.4609075196252337`*^9, 3.460907559006872*^9}, 3.4609076167190113`*^9}], Cell[BoxData[ GraphicsBox[{{}, {}, {RGBColor[0, 0, 1], LineBox[CompressedData[" 1:eJwdkHk41Akch2cMfhMjtTPINYxjNiTtLh4qfb9l46EkPWVERo5QJLU6KB1K uxQxOgyF6aKHsqOnerKrHNF0sB2S2hzjqDVTqBF+Y45t9/M87/P+/X44MTvW bdGhUChB3/jPF7/eu2U12QeU/+eAEbQ4QZZTP4j5j9wXttnjlcm5a5tF/TB/ lZjS7WmPXj3bnywXSKHCMy+L42aHN5x2mSSWSGHc1WCglmuHDnv2ROVflAL7 YCrDj22Hc4wPKd7WSYEZIjubY2SHI1hgmfZSCppV6RuTP3Kw5HJd0lXWAFxY rck9V81BVdKUoeG5AZj+O0Mf3TjYpDy8urN0EJjTrw1kAbbYab5rcselQTi+ 8ETuaV9bfO8VW2FYPQiJ4XGjvj62yNi7cmJF/SDoDQ+vEi+yxVDFrPPi7kFQ WQqbWs1sUSYXyPNNhgC3BJWJ2m2Q1XM5N+DUENS/enX9zBwbTLwvkdzLGoaa 2gDqsVprFMZWWphs/gC/d11rSF9jia5h0knNlhEweyhBAdscexXBHRggh4p+ dWA73wy/9JkvMt3wCQ7YaSpD6k2woDojgccbA7aVf+sf61jINaYH7Ssdh/Hl EYZbnZl4O/VwdX75Z7iw7FBLGuM77HQsIkIEX4BeMpwhsp6LDkdfzo8UKiC/ VRj00H0Oeq/tcy8vnYDA3pYWz/bZ2JOavSzv5FewSfeeNtthhHXeG41aCydB fiL2Fy8WA01DH76pyp6C+8VPfALlBggDlMLmtGlwFXksSe2dhULTRCPuPhLC osXFb57RMats668e25Qwy5FuWP+BwAsdxW35qTMwrOC2aFX6mJlSNG69SwVR a0aednD1UR49f97GGDU868lGZrIenlDLdHvjNXBuAZdMuqGL9R/9x2aHa6E4 hzG6nq6LXY5eA4sdKOhoodPxNoWGiU6xbkVXKJhi5bGz77kONoVG7F/OpmLh A55xub8O/hQmu8YSUXFNjsuE4i4Vk4/6vfax1MFD8uxHjUup+Fs8XUkt0sEy e0oLR0LBButorYxFQ6XLB/VUMAXvao7TnPNp6OrX6Fv1WAsdN31leXN1sfug il45qoFW2/i2kwJdDDfLGZzH0cCxOxtEUgM95DL5Cbrb1LDJ7h0/Ik8Pz1xf eiO4RgUzt90sXQh9TNoudh/VUcEB2sjTMwf10cnyjqgqdgZMHbyjHSkEJvSs XEI2KGFvSuiEQTqBl5+/b77kpAQrzzgJdz+BNDOx0OJ7JTSqd55fkUlgJKNN WuigBIO8vJ8zjhB4UpfXesRGCWXVD06P5BBYkiHpijdRQts/P3pISgh8HFVJ 96MqgRVrvCf7TwLvrE/r5r0h4a6zdaDoHoHTts1l77pI4H9xZjc0Etg2dPVF dCcJVUf82iYeEMgvacra/hcJSyoyTePaCUz6xKTmtpIQ0yO/vaKXQLazceRr MQnEFTKX30+gmyxkLKaWhJpkIipjgMDFm6I/jdaQMDljR9S9J3ADd/cCehUJ uRbhPM4YgY4/hN+EMhLcBhJcfD4TWG/+saKjlITOa7u1YQoCmbytZKSQBLZ3 YWXB1Le/em/JMk+T0EIp319DEvjOP+jobAEJiZKaYMkMgc4rNx8vP0UCo6De fkj9rVfzQrEojwQxTzKl1RJ49mrOk+ZcEv4Fcf85hQ== "]]}}, AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948], Axes->True, AxesOrigin->{0, 0}, PlotLabel->FormBox["\"Electric field from a line charge\"", TraditionalForm], PlotRange->{{0, 3}, {-10, 10}}, PlotRangeClipping->True, PlotRangePadding->{ Scaled[0.02], Automatic}]], "Output", CellChangeTimes->{{3.460907433593102*^9, 3.46090746058517*^9}, { 3.4609075196252337`*^9, 3.460907559006872*^9}, 3.4609076167214317`*^9}] }, Open ]] }, WindowSize->{640, 652}, WindowMargins->{{4, Automatic}, {Automatic, 4}}, PrintingCopies->1, PrintingPageRange->{1, Automatic}, FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (November 10, 2008)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 3906, 109, 353, "Text"], Cell[4454, 131, 2168, 78, 122, "Input"], Cell[CellGroupData[{ Cell[6647, 213, 2628, 52, 151, "Input"], Cell[9278, 267, 290, 4, 27, "Output"], Cell[9571, 273, 291, 4, 27, "Output"], Cell[9865, 279, 552, 15, 65, "Output"], Cell[10420, 296, 2801, 51, 253, "Output"] }, Open ]], Cell[13236, 350, 1732, 56, 126, "Text"], Cell[CellGroupData[{ Cell[14993, 410, 1467, 40, 181, "Input"], Cell[16463, 452, 169, 2, 27, "Output"], Cell[16635, 456, 170, 2, 27, "Output"], Cell[16808, 460, 463, 14, 65, "Output"], Cell[17274, 476, 1310, 45, 92, "Output"], Cell[18587, 523, 2233, 41, 253, "Output"] }, Open ]] } ] *) (* End of internal cache information *)