File:Anti-Helmholtz-coil-field-3D.png

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Description
English: 3D plot of the absolute value of the magnetic field B of two thin circular coils in anti-Helmholtz configuration. The coil radius is set to 1, the distance to , which yields a constant gradient near the center. The B-field is given in units of .
Date
Source Own work
 
This diagram was created with Mathematica.
Author Geek3


Mathematica Source Code[edit]

Bx[x_, z_, R_] = 
  If[Abs[x/R] < 10^-5, 0, z/(2 Pi x) (\[Beta] = (x + R)^2 + z^2;
     m = 4 x*R/\[Beta];
     1/Sqrt[\[Beta]] ((R^2 + x^2 + z^2)/((R - x)^2 + z^2) EllipticE[
          m] - EllipticK[m]))];
Bz[x_, z_, R_] = 1/(2 Pi) (\[Beta] = (x + R)^2 + z^2;
    m = 4 x*R/\[Beta];
    1/Sqrt[\[Beta]] ((R^2 - x^2 - z^2)/((R - x)^2 + z^2) EllipticE[
         m] + EllipticK[m]));
B[x_, z_, R_] = {Bx[x, z, R], Bz[x, z, R]};
ColorFunc[x_] = 
  Blend[{{0, Hue[0.65, 0.6, 1]}, {1/4, Hue[1/3, 0.7, 0.8]}, {1/2, 
     Hue[1/6, 0.9, 0.8]}, {1, RGBColor[0.95, 0.2, 0.2]}}, x];
R = 1;
plot = Plot3D[
  R Norm[B[x, z + R Sqrt[3]/2, R] - B[x, z - R Sqrt[3]/2, R]],
  {x, -2, 2}, {z, -2.5, 2.5}, PlotRange -> {0, 1},
  BoxRatios -> {4, 5, 2.5}, AxesLabel -> {"\[Rho]", "z", "B"}, 
  AxesEdge -> {{-1, -1}, {1, -1}, {1, 1}}, PlotPoints -> 21, 
  MaxRecursion -> 5, Method -> {Refinement -> {ControlValue -> 0.05}},
   ImageSize -> 800, ClippingStyle -> None, 
  Mesh -> {7, 9, Range[0, 3/4, 1/4]}, 
  MeshFunctions -> {#1 &, #2 &, #3 &}, 
  MeshStyle -> {Black, Black,{LightGray,Thickness[0.002]}}, 
  ColorFunction -> (Directive[SurfaceColor@Darker[ColorFunc[#3], 0.2],
       Glow@Darker[ColorFunc[#3], 0.8], Specularity[0.3, 40]] &),
  Lighting -> {{"Ambient", GrayLevel[0.35]}, {"Directional", 
     GrayLevel[0.37], ImageScaled[{-2, 0, 3}]}, {"Directional", 
     GrayLevel[0.37], ImageScaled[{-2, 1, 3}]}, {"Directional", 
     GrayLevel[0.37], ImageScaled[{0, 1, 3}]}},
  BaseStyle -> {FontSize -> 20}, ViewPoint -> {7, -2, 7}]
SetDirectory[NotebookDirectory[]];
Export["Anti-Helmholtz-coil-field-3D.png", plot, ImageResolution -> 300];


Licensing[edit]

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current23:02, 19 February 2018Thumbnail for version as of 23:02, 19 February 20182,808 × 2,320 (907 KB)Geek3 (talk | contribs)User created page with UploadWizard

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