Biot-Savarts law: Off-axis radial field

  • #1

Homework Statement


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

B \propto \int_{0}^{2\pi}{\frac{Rz_0}{(z_0^2 + (x_0-R\sin\phi))^{3/2}}d\phi}
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.
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  • #2
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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