Is it possible to find the magnetic field on the axis above a current loop using Ampere's law? I was thinking you could treat an infinitesimal piece of the loop as a straight wire and draw a circle around it with radius sqrt(a^2 + z^2), with a=radius of current loop and z=position of point of interest, and take the integral of B around the big circle, then multiply by 2*pi*a*cos(theta) to get the full contribution in the right direction. I tried doing this but it doesn't work. Is there a reason I can't use Ampere's law for a circular current loop? In general, do we have to use Biot-Savart for this configuration, or is there some way to use Ampere?