File:Wire Array B-field Strength.png

DescriptionWire Array B-field Strength.png	A diagram of 12 staggered, parallel wires that carry current through a plane, in the direction indicated. Plotted is the magnetic field strength resulting from this arrangement.
Date	09/11/2007
Source	self-made,   This diagram was created with Mathematica.
Author	Inductiveload
Permission (Reusing this file)	Public domainPublic domainfalsefalse I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Mathematica Code[edit]

wireno = 12; (*The number of wires*)

wires = Table[
   {(i + 0.5)/1.5, (-1)^i},
   {i, -wireno/2, 
    wireno/2 - 
     1}]; (*This table contains the locations of the wires*)

symbcircle[{xi_, yi_}, rad_] = Graphics[{
    White,
    EdgeForm[Thick],
    Disk[{xi, yi}, rad]}];

cdot[{xi_, yi_}, rad_] = Graphics[Disk[{xi, yi}, rad/3]];

ccross[{xi_, yi_}, rad_] = Graphics[{
    Thick,
    {Line[{{xi - rad, yi}, {xi + rad, yi}}],
     Line[{{xi, yi - rad}, {xi, yi + rad}}]}}];

iinsymbol[{xi_, yi_}, rad_] = 
 Show[symbcircle[{xi, yi}, rad], 
  ccross[{xi, yi}, rad]]; (*Symbol for current going into the page*)
ioutsymbol[{xi_, yi_}, rad_] = 
 Show[symbcircle[{xi, yi}, rad], 
  cdot[{xi, yi}, rad]]; (*Symbol for current comng out of the page*)

wiresin[rad_] = Graphics[Show[
   Table[
    iinsymbol[{wires[[n, 1]], wires[[n, 2]]}, rad],
    {n, 1, wireno, 
     2}]]];(*Table containing positions of all "in" current symbols*)
\


wiresout[rad_] = Graphics[Show[
   Table[
    ioutsymbol[{wires[[n, 1]], wires[[n, 2]]}, rad],
    {n, 2, wireno, 
     2}]]];(*Table containing positions of all "out" current symbols*)
\


wiresymbols[rad_] = 
  Show[wiresout[rad], wiresin[rad]]; (*All current symbols*)

r[{xi_, yi_}] = 
  Sqrt[(x - xi)^2 + (y - yi)^2]; (*Distance from {x,y} to {xi, yi}*)

f[{xi_, yi_}] =
  {(y - yi)/r[{xi, yi}]^2,
   -(x - xi)/r[{xi, yi}]^2}; (*Circular vector field*)

ftot = Sum[
   wires[[k, 2]]*f[wires[[k]]],
   {k, 1, 
    wireno}]; (*Sum of effects of all wores (including direction \
governed by y-positon*)

cplot = ContourPlot[
   Sqrt[ftot[[1]]^2 + 
     ftot[[2]]^2], (*Magnitude of resultant vecotr*)
   {x, -6, 6},
   {y, -4, 4},
   PlotPoints -> 50,
   PlotRange -> {0, 6.01},(*We want a line at the top edge, 
   and this ensures it*)
   Contours -> Table[i/3, {i, 0, 18}],
   Frame -> False,
   AspectRatio -> 4/6,
   ImageSize -> 1200,
   ColorFunction -> "Rainbow"];

Show[cplot, wiresymbols[0.07]]