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First, permanent magnets as I understand them: Permanent magnets have a 'Br' rating, which is the amount of flux that would flow if this magnet were part of a magnetic circuit with 0 Reluctance. They also have an Hc rating, which defines the opposing magnetic field intensity that would result in 0 flux in that same magnetic circuit. If Br is plotted as a point on the vertical axis, and Hc as a point on the negative horizontal axis, then the curve between them is the B-H curve.

The B-H curve (most of it) is drawn by reducing the net flux in the circuit by A) Adding an air gap that will store potential energy as a magnetic field, or B) Using an electromagnet to create an H-field that opposes the one from the magnet. It is my understanding that a magnetic circuit is roughly analogous to an electric circuit, in that Kirchoff's loop law can be applied to both.

****If I add an air gap that has a reluctance of 10 Ampturn/Tesla, and there is 1 Tesla flowing through the circuit from the permanent magnet, then is that air gap the equivalent to using a coil to supply 10 amp turns opposing the permanent magnet flux? If the air gap and coil were swapped, would the total flux in the circuit remain the same: 1 Tesla?****

By choosing my air gap and core material, I can know the reluctance of my magnetic circuit. I will take that reluctance, multiply it with the chosen flux density (flux needed to produce rated [email protected]) to get H opposing. Br is constant, no matter how thick or thin the magnet is, and since Hc is rated per unit length, I should be able to scale the H axis of the B-H curve to find the correct magnet thickness. It should be similar to how I would do per-unit calculations or normalized filter design in other EE calculations.