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Magnetic field for a straight conductor with finite length - Biot-Savart Integral

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91660] Magnetic field for a straight conductor with finite length - Biot-Savart Integral
  • From: robert prince-wright <robertprincewright at yahoo.com>
  • Date: Tue, 2 Sep 2008 07:18:24 -0400 (EDT)

I am trying to create a plot which shows the magnetic field around a straight line of finite length. I started by looking online at Michael Trott's Mathematica Guidebook for Numerics which gives an example of how Mathematica can solve the Biot-Savart equation for the case of an infinite line running along the Z-axis:  

infiniteWire[t_] = {0, 0, t};
sol1 = Integrate[
 Cross[D[infiniteWire[t], t], {x, y, z} - infiniteWire[t]]/
  Norm[{x, y, z} - infiniteWire[t]]^3, {t, -Infinity, Infinity}, 
 GenerateConditions -> False]


However, if you evaluate the expression above using Mathematica 6 the output is different to the book in that it includes Im[] terms. Can someone explain why, and how do I get rid of them? I tried Re[] but result is left unevaluated if expr is not a numeric quantity. Note I have used the built in Norm[] function, not a user defined function like Michael. 

Ultimately, what I need is the solution for the Integral below:


sol2 = Integrate[
  Cross[D[infiniteWire[t], t], {x, y, z} - infiniteWire[t]]/
   Norm[{x, y, z} - infiniteWire[t]]^3,
  {t, 0, L},
  GenerateConditions -> False]


This corresponds to the case where current flows in a straight line from the origin in x-y-z space to a point at a distance L along the Z axis.


Robert 


      


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