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Off-axis Magnetic Field of Current loop (MATLAB?)

  1. Nov 2, 2006 #1
    I have checked the forums for similar problems and have only seen that one would use 'MATLAB' to perform this integration.

    All I want to do is find the 3 components of the magnetic field at a point (x, y, z) off of the axis of a current loop (given current, radius and that the loop lies on the xy plane centered at the origin).

    Can someone point me in the right direction to even get started on this problem? I have been told that this is achievable in Excel!

    Any help would be awesome!
  2. jcsd
  3. Nov 2, 2006 #2


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    If I'm not mistaken, this would involve a so-called "elliptic integral".
    You may have to resort to numerical approximations.
  4. Nov 2, 2006 #3
    I was hoping that would be the case, but I haven't had any luck finding a numerical approximation for a circle.

    Centered on origin
    Lying on x-y plane

    Can anyone help?
  5. Nov 2, 2006 #4


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    I don't think you're understanding this correctly. When robphy said that you have to do numerical approximations, what he meant was that the solution to that problem cannot be solved analytically. Furthermore, you won't have a simple, closed form solution. What you will have is an infinite series.

    So you have to solve the differential equation numerically and obtain an approximate answer based on where you truncate the series. It doesn't mean that you find a "numerical approximation for a circle".

    Please refer to Jackson's classic text on this where this example is illustrated using Green's function technique.

  6. Nov 18, 2008 #5
    i use simple code written in fortran for calculating magnetic fields in the space due to any shaped current carrying loop,,,,,just give the input file with geometry of the loop as a summation of straight and arcs and ask the magnetic field in the space in RZT or XYZ system,,,that's it........i use to calculate the fields due to PF and TF coil system in a tokamak
  7. Nov 29, 2010 #6
    This was posted years ago, but incase someone else is searching through this (as I was), you can use Matlab quite easily to calculate this.

    You can use the equations found here:


    They are simple equations which you just plug in the values for the variables. The only confusing thing is the complete elliptic integrals which Matlab can also calculate for you.

    Use the Matlab function [K,E] = ellipke(k^2) to calculate the complete elliptic integrals of the first and second kind, E(k) and K(k).

    Remember to give k^2 as the argument in Matlab function. If you're confused type "help ellipke" in the Matlab command line.
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