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The above image shows the flux flow through a rectangular core. We know the purpose of the core is to concentrate as much of the flux through it as possible, so we'll assume no or minimal stray field lines exist. Let's assume the primary coil is the same as the secondary and each are energized equally with opposite current direction. Let also assume I slice this core vertically in the middle forming two equally magnetized core with a miniscule air gap between them. What is the closest approximation to calculating the force between the two half cores with a simple equation relating force to a magnetic field property (like magnetic flux) that's accurate enough to use in a practical application not requiring the upmost precision. A simple equation showing the approximated relationship of force to area and flux should do.

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