What is the magnetic field inside a cylinder?

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Jefferson Yun
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The axis of the cylinder is perpendicular(not parallel) to M, magnetization. It's not hard to find bound surface current density, but it depends on the angle while the answer says the magnetic field is uniform inside the cylinder.
Anyone can silve this problem??
 
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It can't depend on angle, due to symmetry. Smyrhe solves this problem exactly in his classic text.