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To preface, this is indeed a homework problem. I am a mathematician taking an electromagnetism module and have trouble wrapping my head around the problem at hand, and am struggling to start a solution.

The problem is as follows.

A sample of ferromagnetic material, relative permeability $\mu$, has a shape of a right cylinder of radius $R$ and length $L$. The sample is placed in air, with an external magnetic field $\mathbf{B}$ applied perpendicular to its base surface. Find the magnitude and direction of the magnetic field inside the sample when $L>>R$. Explain why the result depends on the shape of the cylinder.

I have the understanding that one must apply boundary conditions to the sample. However, it is not clear to me how I do this. In fact, I am not sure how the magnetic field inside the sample will look at all.

If anybody has a pointer that clearly explains how to approach this style of problem I would be eternally thankful.

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