Background: In the text books I’ve read the simple magnetic circuit is developed by first looking at a ferrous torus symmetrically wrapped with a condutor. Symmetry arguments indicate that the H field is radial through the torus and 0 on the inside and outside of the torus. Then from Ampere's law H is obtained. H = NI/L, N = number of turns, I = current, L = length around the torus (Pi R). I'm okay with this but next the shape of the torus changes to a square and the turns are bunched together on 1 leg of the square, say l1. And two assumptions are discussed: (1) flux is constand around the square core and (2) no leakage field. With these assumptions Ampere's law is used again to obtains the same equation for H except the Lenght "L" changes to match the square core. With a square core: L = l1 + l2 + l3 + l4. (l's are lengths of the square edges) My Problem: If I use Ampere's law for other paths I get "VERY" different answers. I can say integrate through l1 (that contains all the conductors) and would obtain: H = NI/l1. Or I could integrate say the half of the square that does not have a conductor and obtain: H = NI/(l2 +l3+l4), but here I is zero. So H=0 under the assumptions. So does the assumptions of no leakage field and constant flux for this geometry immediately cause a violation of Ampere's law? Thanks for any comments.