Ampere's law with current loop

[Sturk200]

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?

 

[Hesch]

In general, do we have to use Biot-Savart for this configuration, or is there some way to use Ampere?

Yes, in general you have to use B-S to find the B-field at some specific location, because the circulation integral in Amperes law only speaks about the mean value of the H-field, following some circulation path.

However there are exceptions. For example you can calculate the H-field in the middle of an infinit long solenoid, by choosing a "smart" circulation path:

http://physics.stackexchange.com/questions/112155/using-amperes-law-for-a-solenoid

And of course you can also find the H-field in a toroid due to the symmetry.