# Magnetic field through ferromagnetic cylinder when length is much bigger than the radius?

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.