(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 4.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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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[ 98678, 2424]*) (*NotebookOutlinePosition[ 99350, 2448]*) (* CellTagsIndexPosition[ 99306, 2444]*) (*WindowFrame->Normal*) Notebook[{ Cell["Coils.nb - magnetic fields from coaxial coils", "Title"], Cell["\<\ Authors: Mike Gehm , Michael Stenner \ Version: 1.3 Date: 2004-05-18\ \>", "Text", FontSize->14], Cell["\<\ This Mathematica notebook calculates the magnetic field from sets of coils. \ You must evaluate the \"Definitions\" section first. See the \"Description\" \ section for help and examples.\ \>", "Text", FontSize->13], Cell["\<\ This notebook was originally written by Mike Gehm and was modified \ by Michael Stenner.\ \>", "Text", FontSize->13], Cell[CellGroupData[{ Cell["Definitions", "Subsection", FontSize->13], Cell[CellGroupData[{ Cell["Constants", "Subsubsection", FontSize->13], Cell[BoxData[ \(\(\(\[Mu]0 = 4\ Pi*\ 10^\(-3\);\)\( (*\ Gives\ answers\ in\ Gauss\ *) \)\)\)], "Input", FontSize->13] }, Closed]], Cell[CellGroupData[{ Cell["Calculation Functions", "Subsubsection", FontSize->13], Cell["\<\ These functions calculate the radial and axial field for a single coil.\ \>", "Text", FontSize->13], Cell[BoxData[ \(Bz[r_, z_, coil_] := coil[\([3]\)]\ *\ coil[\([4]\)]\ *\(\[Mu]0\ /\((2\ Pi)\)\)\/\@\(\((coil[\([1]\)]\ + \ \ r)\)\^2 + \ \((z - coil[\([2]\)])\)\^2\)\ *\ \((EllipticK[\(4\ coil[\([1]\)]\ \ r\)\/\(\((coil[\([1]\)] + r)\)\^2 + \((z - coil[\([2]\)])\)\^2\)]\ + \ \ \((\(coil[\([1]\)]\^2\ - \ r\^2\ - \ \((z - \ coil[\([2]\)])\)\^2\)\/\(\((coil[\([1]\)] - r)\)\^2 + \((z - coil[\([2]\)])\)\ \^2\))\)*EllipticE[\(4\ coil[\([1]\)]\ r\)\/\(\((coil[\([1]\)] + r)\)\^2 + \ \((z - coil[\([2]\)])\)\^2\)])\)\)], "Input", FontSize->13], Cell[BoxData[ \(Br[r_, z_, coil_] := coil[\([3]\)]* coil[\([4]\)]*\ \((z - coil[\([2]\)])\)*\(\(\[Mu]0\ /\((2\ Pi\ r)\)\)\(\ \ \)\)\/\@\(\((coil[\([1]\)]\ + \ r)\)\^2 + \ \((z - coil[\([2]\)])\)\^2\)*\ \ \((\(-EllipticK[\(4\ coil[\([1]\)]\ r\)\/\(\((coil[\([1]\)] + r)\)\^2 + \((z \ - coil[\([2]\)])\)\^2\)]\)\ + \ \((\(coil[\([1]\)]\^2\ + \ r\^2\ + \ \((z \ - coil[\([2]\)])\)\^2\)\/\(\((coil[\([1]\)] - r)\)\^2 + \((z - coil[\([2]\)])\ \)\^2\))\)* EllipticE[\(4\ coil[\([1]\)]\ r\)\/\(\((coil[\([1]\)] + r)\)\^2 \ + \((z - coil[\([2]\)])\)\^2\)])\)\)], "Input", FontSize->13], Cell["\<\ These functions calculate the field for all of the coils listed in \"coils\".\ \ \>", "Text", FontSize->13], Cell[BoxData[ \(AxialField[r_, z_, coils_] := Module[{}, TempFunc[coil_] := Bz[r, z, coil]; \[IndentingNewLine]Plus @@ Map[TempFunc, coils, {1}]]\)], "Input", FontSize->13], Cell[BoxData[ \(RadialField[r_, z_, coils_] := Module[{}, TempFunc[coil_] := Br[r, z, coil]; \[IndentingNewLine]Plus @@ Map[TempFunc, coils, {1}]]\)], "Input", FontSize->13], Cell["\<\ This function calculates the field magnitude at any point using the previous \ functions.\ \>", "Text", FontSize->13], Cell[BoxData[ \(FieldMag[r_, z_, coils_] := If[r \[Equal] 0, AxialField[r, z, coils], \@\(AxialField[r, z, coils]\^2 + RadialField[r, z, \ coils]\^2\)]\)], "Input", FontSize->13] }, Open ]], Cell[CellGroupData[{ Cell["Tools for generating \"coils\" list", "Subsubsection", FontSize->13], Cell[BoxData[ \(WithTurns[precoil_, turns_] := Module[{}, TempFunc[coil_] := Append[coil, turns]; \[IndentingNewLine]Map[ TempFunc, precoil, {1}]]\)], "Input", FontSize->13], Cell[BoxData[ \(WithCurrent[precoil_, current_] := Module[{}, TempFunc[coil_] := Append[coil, current]; \[IndentingNewLine]Map[ TempFunc, precoil, {1}]]\)], "Input", FontSize->13], Cell[BoxData[ \(WithTurnsAndCurrent[precoil_, turns_, current_] := WithCurrent[WithTurns[precoil, turns], current]\)], "Input", FontSize->13], Cell[BoxData[{ \(Helmholtz[r_, z_, turns_, current_] := {{r, \(-z\), turns, current}, {r, z, turns, current}}\), "\[IndentingNewLine]", \(AntiHelmholtz[r_, z_, turns_, current_] := {{r, \(-z\), turns, \(-current\)}, {r, z, turns, current}}\), "\[IndentingNewLine]", \(TrueHelmholtz[z_, turns_, current_] := Helmholtz[2\ z, z, turns, current]\), "\[IndentingNewLine]", \(TrueAntiHelmholtz[z_, turns_, current_] := AntiHelmholtz[2\ z, z, turns, current]\)}], "Input", FontSize->13] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Description", "Subsection", FontSize->13], Cell[CellGroupData[{ Cell["What this notebook does", "Subsubsection", FontSize->13], Cell["\<\ This notebook calculates the magnetic field at any point in space for an \ arbitrary number of coils. Each coil can have a different position, size, \ number of turns, and current. The one restriction is that all coils must \ share the same axis. \ \>", "Text", FontSize->13] }, Closed]], Cell[CellGroupData[{ Cell["How to use this notebook", "Subsubsection", FontSize->13], Cell["\<\ First, you must make your \"coils\" list. This is a list of lists. You have \ one internal list for each coil. Each of these internal coil (singular) \ lists contains the radius of the coil (in meters), the position of the coil \ (in meters), the number of turns, and the current (in Amperes). The \ following coils list defines one coil with a radius of 10 cm, position of z = \ 5 cm, 100 turns, and a 1 mA current.\ \>", "Text", FontSize->13], Cell[BoxData[ \(\(ExampleCoils\ = \ {{ .1, \ .05, \ 100, \ .001}};\)\)], "Input", FontSize->13], Cell["\<\ Once this is defined, you can determine the axial field (parallel to z), \ radial field (perpendicular to z), and field magnitude at any point (r, z) \ with the functions: AxialField, RadialField, and FieldMag. each of these \ functions takes r, z, and your coils list. All of these functions return the \ magnetic field in Gauss. 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To use these functions, create a \ \"precoils\" list without the current or without both current and turns.\ \>", "Text", FontSize->13], Cell[CellGroupData[{ Cell[BoxData[ \(ExamplePreCoils = {{ .1, \(- .1\)}, \ { .1, \ .1}}\)], "Input", FontSize->13], Cell[BoxData[ \({{0.1`, \(-0.1`\)}, {0.1`, 0.1`}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(NewExamplePreCoils = WithTurns[ExamplePreCoils, \ 30]\)], "Input", FontSize->13], Cell[BoxData[ \({{0.1`, \(-0.1`\), 30}, {0.1`, 0.1`, 30}}\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(ExampleCoils = WithCurrent[NewExamplePreCoils, \ .4]\)], "Input", FontSize->13], Cell[BoxData[ \({{0.1`, \(-0.1`\), 30, 0.4`}, {0.1`, 0.1`, 30, 0.4`}}\)], "Output"] }, Open ]], Cell["Or simply", "Text", FontSize->13], Cell[CellGroupData[{ Cell[BoxData[ \(ExampleCoils = WithTurnsAndCurrent[ExamplePreCoils, \ 30, \ .4]\)], "Input", FontSize->13], Cell[BoxData[ \({{0.1`, \(-0.1`\), 0.4`, 30}, {0.1`, 0.1`, 0.4`, 30}}\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Function Summary", "Subsubsection", FontSize->13], Cell[TextData[{ "coils = ", Cell[BoxData[ \(TraditionalForm\`{{rad\_1, z\_1, turns\_1, I\_1}, \ {rad\_2, z\_2, turns\_2, I\_2}, \ ... }\)]], "\ncoils = Helmholtz[rad, z, turns, I]\ncoils = TrueHelmholtz[z, turns, I]\n\ coils = AntiHelmholtz[rad, z, turns, I]\ncoils = TrueAntiHelmholtz[z, turns, \ I]\ncoils = WithCurrent[precoils, I] (where precoils is a coils list \ with the current missing)\nprecoils = WithTurns[preprecoils, turns] \ (where preprecoils is a coils list with both currents and turns missing)\n\n\ AxialField[r, z, coils]\nRadialField[r, z, coils]\nFieldMag[r, z, coils]" }], "Text", FontSize->13] }, Closed]], Cell[CellGroupData[{ Cell["Example", "Subsubsection", FontSize->13], Cell["\<\ List of coils. 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