Magnetic Field near a Ferromagnetic Object

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Considering a bar of ferromagnetic (FM) material (eg, Nickel) placed in a uniform magnetic field (eg, B = 1kG along x). I know the H field produced by a given magnetization M of the ferromagnet (ie, I have [itex]\vec{H}=M \cdot \vec{\alpha}[/itex] for a calculated alpha). How do I determine the total magnetic field near the ferromagnet? I'm having difficulty determining how M relates to the input B (I know of the hysteresis, but I don't quite understand even what saturation magnetization relates to), and reconciling H and B in and outside of the ferromagnet.
 

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