1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Magnetic field from a coil (on Mathematica)

  1. Sep 20, 2013 #1
    Hello guys,

    I'm trying to find the configuration of two circular coils in a configuration similar to Helmholtz coils that would homogenize the magnetic field best at a volume between them.

    So the first thing step I took in that is use the Biot-Savart law to calculate the magnetic field produced at each point through that coil. The coordinate system is Cylinderical coordinates, and the coil is placed on the xy-plane, its center matches the origin (0,0,0).

    The function is

    dl = \sqrt {d{x^2} + d{y^2}} = Rd\theta \\
    B\left( {\overrightarrow r } \right) = \frac{{{\mu _0}I}}{{4\pi {R^3}}}\int\limits_0^{2\pi } {\left( {\overrightarrow {dl} \times \left( {\overrightarrow r - \overrightarrow R } \right)} \right)d\theta } \\
    B\left( {x,y,z} \right) = \frac{{{\mu _0}I}}{{4\pi {R^3}}}\int\limits_0^{2\pi } {\left( {\left( { - R\sin \theta ,R\cos \theta ,0} \right) \times \left( {x - R\cos \theta ,y - R\sin \theta ,z} \right)} \right)d\theta }

    where r(x,y,z) is the position vector from origin to the point, at which the magnetic field is to be calculated; R is the radius of the coil.

    I wrote a Mathematica script to do this integral, but it always gives a single number (representing a 2 pi R^2 constant result from the cross product and the integral), no matter how I change x,y and z. This is the function I'm using.

    FieldAtPoint[x_, y_, z_] :=
    (u0 i)/(4 Pi r^2)
    Cross[r{-Sin[t], Cos[t], 0}, ({x - r Cos[t], y - r Sin[t], z})], {t,
    0, 2 Pi}]
    Do you find anything wrong within my calculations? Please advise. How do I do this correctly?

    Thank you for any efforts.
    Last edited: Sep 20, 2013
  2. jcsd
  3. Sep 21, 2013 #2
    You need this term in the denominator: |x(obs) - x(coil)|3

    The R3 term is an error -- it's |x(coil)|3
  4. Sep 21, 2013 #3
    @lpetrich Thanks a lot! what a stupid mistake!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook