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

**Follow-Ups**:**Re: Magnetic field for a straight conductor with finite***From:*"Curtis F. Osterhoudt" <cfo@lanl.gov>