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On your own time, you learned about solid \ mechanics. This week we will learn the joys of Electrostatics, that is, \ stationary charges. Next week we will let our charges run free, but for now \ let us ponder them while they sleep.\ \>", "Text", PageWidth->PaperWidth], Cell[TextData[{ "Charge comes in Minimum Packets (of size ", StyleBox["e", FontSlant->"Italic"], ")" }], "Subsubsection"], Cell[CellGroupData[{ Cell["Coulomb's Law (Force between two particles)", "Subsubsection"], Cell[TextData[{ "For all electrostatics problems on the MCAT,\n\t", Cell[BoxData[ FormBox[ RowBox[{"k", "=", RowBox[{\(9\ \[CenterDot]\ 10\^9\), " ", FractionBox[ RowBox[{ StyleBox["N", FontSlant->"Plain"], "\[CenterDot]", SuperscriptBox[ StyleBox["m", FontSlant->"Plain"], "2"]}], SuperscriptBox[ StyleBox["C", FontSlant->"Plain"], "2"]]}]}], TraditionalForm]]], "\n\t", Cell[BoxData[ FormBox[ RowBox[{"e", "=", RowBox[{\(1.6\[CenterDot]10\^\(-19\)\), StyleBox["C", FontSlant->"Plain"]}]}], TraditionalForm]]] }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Electric Field (Map of the Force in a region)", "Subsubsection"], Cell[TextData[{ StyleBox["Electric Field", FontSlant->"Italic"], ": ", StyleBox["Map of the ", FontWeight->"Bold"], StyleBox["Force", FontWeight->"Bold", FontSlant->"Italic"], " for an arbitrary charge. Units: ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["N", FontSlant->"Plain"], "/", StyleBox["C", FontSlant->"Plain"]}], TraditionalForm]]], " (Newtons per Coulomb)" }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Electric Potential (Map of the PE in a region)", "Subsubsection"], Cell[TextData[{ StyleBox["Electric Potential", FontSlant->"Italic"], ": ", StyleBox["Map of the ", FontWeight->"Bold"], StyleBox["Potential Energy", FontWeight->"Bold", FontSlant->"Italic"], " for an arbitrary charge. Units: ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["V", FontSlant->"Plain"], "=", RowBox[{ StyleBox["J", FontSlant->"Plain"], "/", StyleBox["C", FontSlant->"Plain"]}]}], TraditionalForm]]], " (a Volt is a Joule per Coulomb).\n", StyleBox["Voltage", FontSlant->"Italic"], ": ", StyleBox["Difference in ", FontWeight->"Bold"], StyleBox["Electric Potential ", FontWeight->"Bold", FontSlant->"Italic"], "between two different locations. Units: also Volts.\n\nA + is happy at Low \ Potential\t\t\t\t\tA - is happy at High Potential." }], "Text"] }, Open ]], Cell[CellGroupData[{ Cell["Electrostatic problems come in Two Flavors", "Subsubsection", PageWidth->PaperWidth], Cell[TextData[{ "There are two flavors of electrostatic problems: ", StyleBox["field-particle", FontSlant->"Italic"], " problems and ", StyleBox["particles-particle", FontSlant->"Italic"], " problems", "\n\t- In ", StyleBox["field-particle", FontSlant->"Italic"], " problems,", "you are told ", StyleBox["what is going on in a region of space", FontWeight->"Bold"], ", and asked about the physics \n\t at a certain point (or equivalently, \ about the behavior of a particle at some point in that region).\n\t- In ", StyleBox["particles-particle", FontSlant->"Italic"], " problems, you are ", StyleBox["given one or more particles", FontWeight->"Bold"], ", and ", "asked about the physics \n\t at a certain point (or equivalently, about \ the behavior of a particle at some point in that region).\nThe equations you \ will learn apply to one or the other flavor. Please be aware of the \ difference." }], "Text", PageWidth->PaperWidth], Cell[TextData[{ StyleBox["Particles-Particle Equations\t\t\t\tField-Particle Equations", FontFamily->"Andale Mono", FontWeight->"Bold"], "\n ", Cell[BoxData[ \(TraditionalForm\`F\&\[RightVector] = k\ \(\(q\_1\) q\_2\)\/r\^2\)]], "\t\t\tForce between two particles\t\t", Cell[BoxData[ \(TraditionalForm\`F\&\[RightVector]\ = \ E\&\[RightVector]\ \[CenterDot]\ q\)]], "\tForce on a particle, due to Electric Field\n ", Cell[BoxData[ \(TraditionalForm\`E\&\[RightVector] = k\ q\_1\/r\^2\)]], "\t\t\t\tElectric Field ", StyleBox["due", FontSlant->"Italic"], " to a particle\t--\t\t--", StyleBox["\n ", FontSlant->"Italic"], Cell[BoxData[ \(TraditionalForm\`\[CapitalPhi] = k\ q\_1\/r\)]], "\t\t\t\tElectric Potential ", StyleBox["due", FontSlant->"Italic"], " to a particle\t", Cell[BoxData[ \(TraditionalForm\`\[CapitalPhi]\ = \ E\ \[CenterDot]\ d\)]], "\tPotential (uniform Electric Field ", StyleBox["ONLY!)", FontSlant->"Italic"], "\n ", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]PE = k\ \(q\_1\) \(\(q\_2\)(1\/r\_f - 1\/r\_o)\)\)]], "\t\[CapitalDelta]PE as 2 particles are moved\t\t", Cell[BoxData[ \(TraditionalForm\`\[CapitalDelta]PE\ = \ q\ \[CapitalDelta]\[CapitalPhi]\)]], "\tPotential Energy change\n\t\n", StyleBox["Electric Field", FontSlant->"Italic"], ": ", StyleBox["Map of the ", FontWeight->"Bold"], StyleBox["Force", FontWeight->"Bold", FontSlant->"Italic"], " for an arbitrary charge. Units: ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["N", FontSlant->"Plain"], "/", StyleBox["C", FontSlant->"Plain"]}], TraditionalForm]]], " (Newtons per Coulomb)\n", StyleBox["Electric Potential", FontSlant->"Italic"], ": ", StyleBox["Map of the ", FontWeight->"Bold"], StyleBox["Potential Energy", FontWeight->"Bold", FontSlant->"Italic"], " for an arbitrary charge. Units: ", Cell[BoxData[ FormBox[ RowBox[{ StyleBox["V", FontSlant->"Plain"], "=", RowBox[{ StyleBox["J", FontSlant->"Plain"], "/", StyleBox["C", FontSlant->"Plain"]}]}], TraditionalForm]]], " (a Volt is a Joule per Coulomb).\n", StyleBox["Voltage", FontSlant->"Italic"], ": ", StyleBox["Difference in ", FontWeight->"Bold"], StyleBox["Electric Potential ", FontWeight->"Bold", FontSlant->"Italic"], "between two different locations. Units: also Volts.\n\nWant to know about \ a vector (", Cell[BoxData[ \(TraditionalForm\`a\&\[RightVector], \ v\&\[RightVector], \ d\&\[RightVector], \ ... \)]], ")? Use the Electric Field.\nWant to know about a scalar (", Cell[BoxData[ \(TraditionalForm\`PE, \ KE, \ Work, \ Speed, \ ... \)]], ")? Use the Electric Field." }], "Text", PageWidth->PaperWidth] }, Open ]], Cell["Electric Stuff and Gravity Stuff are Similar", "Subsubsection"] }, Open ]] }, FrontEndVersion->"4.1 for Microsoft Windows", ScreenRectangle->{{0, 1600}, {0, 1091}}, ShowPageBreaks->True, WindowSize->{1155, 815}, WindowMargins->{{2, Automatic}, {Automatic, 17}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PrintingMargins"->{{36, 36}, {36, 36}}, "PrintCellBrackets"->False, "PrintRegistrationMarks"->False, "PrintMultipleHorizontalPages"->False}, Magnification->1.5 ] (******************************************************************* Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. *******************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[1727, 52, 81, 1, 98, "Section"], Cell[1811, 55, 556, 9, 104, "Text"], Cell[2370, 66, 131, 5, 35, "Subsubsection"], Cell[CellGroupData[{ Cell[2526, 75, 68, 0, 35, "Subsubsection"], Cell[2597, 77, 772, 23, 82, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[3406, 105, 70, 0, 35, "Subsubsection"], Cell[3479, 107, 467, 18, 39, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[3983, 130, 71, 0, 35, "Subsubsection"], Cell[4057, 132, 914, 31, 104, "Text"] }, Open ]], Cell[CellGroupData[{ Cell[5008, 168, 92, 1, 35, "Subsubsection"], Cell[5103, 171, 998, 28, 147, "Text"], Cell[6104, 201, 2999, 95, 279, "Text"] }, Open ]], Cell[9118, 299, 69, 0, 35, "Subsubsection"] }, Open ]] } ] *) (******************************************************************* End of Mathematica Notebook file. *******************************************************************)