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Biot-Savarts law: Off-axis radial field

  1. Sep 24, 2013 #1
    1. The problem statement, all variables and given/known data
    Hi

    I am trying to find the off-axis x-component of the magnetic field produced by a current-carrying coil. The on-axis case is done here, where the axial (z-) field is found and the x-component is of course 0 due to symmetry.

    I am pretty sure I know how to do it: I end up getting

    [tex]
    B \propto \int_{0}^{2\pi}{\frac{Rz_0}{(z_0^2 + (x_0-R\sin\phi))^{3/2}}d\phi}
    [/tex]
    where R is the coil-radius, z0 is the (axial) distance from the coil-axis and x0 the radial distance away from the symmetry axis. However, this is the magnitude of the field - I am trying to find only the radial component along x, which is what I am stuck with.

    I'd be very happy to get a hint or two.

    Thanks in advance.
     
    Last edited: Sep 24, 2013
  2. jcsd
  3. Sep 26, 2013 #2

    rude man

    User Avatar
    Homework Helper
    Gold Member

    Not sure what you are calling x and "(axial) distance from the coil-axis" but in general any computation of off-axis mag field of a single coil like this requires advanced math including elliptic integrals. Not for the timid.
     
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