# Calculating Flux from a Permanent Magnet

I am hoping someone here has experience with permanent magnets. I have a theory on how to size a permanent magnet for an alternator I am designing, and I want someone to confirm that my technique will yield a result that is useful enough to go through the expense of building a prototype. My goal is to find the minimum thickness of Neodymium magnet that will produce the needed voltage at the RPM I plan to run.

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.

In magnetic circuits, the conserved quantity corresponding to electric current is magnetic flux. Where B is measured in Tesla, or Webers per square meter, then the flux, Phi is in units of Webers. $\Phi = \int B \cdot dA_e$ The flux passing through any cross section of the magnetic circuit is the same when leakage flux is taken into consideration.

Another useful quantity, akin to Kirchhoff's voltage law is the integral of H around the loop. Magnetomotive force, NI = $NI = \oint H \cdot dl_e$. dl_e is an element of the magnetic path. NI is current times number of turns of wire. It is the equivalent of a voltage source. Unfortunately, I'm unclear how permanent magnets or magnetic reluctance might modify this equation.

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