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Effect of material size on magnetization

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I'm a bit confused about the effect of the size of ferromagnetic material on the magnetic field it generates so I was hoping someone could explain it to me.

The saturation magnetization is given by
M = [itex]\frac{N}{V}[/itex]*μ
but this suggests that the magnetization is independant of the size of the material, but since
B = μ0(H + M)
and since B fields add up vectorially this would suggest cutting a piece of ferromagnetic material in two would double the magnetic field, which doesn't make sense, so I was wondering what I was missing?

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