OK, so that was quite the title. I haven't done one of these in a while, but classes are about to start again and i figured I may as well get started deriving things again. Plus, I had to do it for the can crusher magnet simulation code [1] for the experiment [3]. Here's what's really going on. I have a Sage function that will give me the magnetic field in the z direction produced by a coil of wire that sits at z = 0 and a has a radius of 'rcoil'. I'd like to know the magnetic field produced by the loop of wire along a circular path that is perpendicular to the plane of the current carrying coil. A circular path perpendicular to the plane of a coil kind of begs for spherical coordinates, but the routine I have takes a z coordinate and a radius coordinate in the cylindrical coordinate system. In the picture above, the circular path is shown, and the coil of wire is at the diameter of the circle and perpendicular to the page. Note: ...