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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 68098, 1661]*) (*NotebookOutlinePosition[ 68763, 1684]*) (* CellTagsIndexPosition[ 68719, 1680]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(Clear["\<`*\>"]\)], "Input"], Cell[TextData[{ "An AC field I = ", Cell[BoxData[ \(TraditionalForm\`I\_0\)]], " ", Cell[BoxData[ \(TraditionalForm\`e\^\(-i\[Omega]t\)\)]], " is applied to the plates of a capacutor with circular plates (radius a, \ separation d). 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" }], "Text"], Cell[BoxData[ \(eqn\ := \ Q\_0\ \[Equal] \ 2\ \[Pi]\ \[Epsilon]\_0\ A\ Integrate[\[Rho]\ BesselJ[0, k\ \[Rho]], {\[Rho], 0, a}, Assumptions\ \[Rule] \ k\ a > 0]\)], "Input"], Cell[BoxData[ \(sol\ := \ Solve[eqn, A] // First\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(A\ = \ A /. \ sol\)], "Input"], Cell[BoxData[ \(\(k\ Q\_0\)\/\(2\ a\ \[Pi]\ BesselJ[1, a\ k]\ \[Epsilon]\_0\)\)], \ "Output"] }, Open ]], Cell["Lets look at E and B to second order", "Text"], Cell[BoxData[ \(Esec\ := \ Normal[Series[\ A\ BesselJ[0, k\ \[Rho]], {k, 0, 2}]]\)], "Input"], Cell[BoxData[ \(E2\ := \ Expand[Esec/Esec[\([2]\)]]\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(E2\ = \ Esec[\([2]\)] \((1 + \ Coefficient[E2, k^2]\ k^2)\)\)], "Input"], Cell[BoxData[ \(\(\((1 + k\^2\ \((a\^2\/8 - \[Rho]\^2\/4)\))\)\ Q\_0\)\/\(a\^2\ \[Pi]\ \ \[Epsilon]\_0\)\)], "Output"] }, Open ]], Cell[BoxData[ \(Bsec\ := \ \ \ Normal[ Series[\(-\((I/c)\)\)\ A\ BesselJ[1, k\ \[Rho]], {k, 0, 4}]]\)], "Input"], 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