Biot-Savarts law: Off-axis radial field

[Niles]

Homework Statement

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

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

 

[rude man]

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.