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(adsbygoogle = window.adsbygoogle || []).push({}); Hfield is radial through the torus and 0 on the inside and outside of the torus. Then from Ampere's lawHis 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 forHexcept 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.

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# Magnetic Circuits

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