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## Homework Statement

Consider a cylinder of thickness a=1 mm and radius R = 1 cm that is uniformly magnetized across z axis being its magnetization M= 10^5 A./m. Calculate the bound currents on the cylinder and, doing convenient approximations, the B field on the axis of the cylinder for z=0.

## Homework Equations

## The Attempt at a Solution

So I had no problems with the first question. The bound current is only at the surface since the magnetization is constant. It's also only in the lateral of the cylinder because M is parallel to the exterior normal on the top and on the bottom. We conclude that $$\vec{J}=10^5 \vec{e}_{\theta} A/m$$

Now the second part is what is giving me trouble. The magnetization is across the z axis, so the vectors B and H will also be in that direction. That means the problem doesn't have symmetry right? So that don't let me apply any of the versions of Ampere's law listed above.

Should I apply Biot-Savart law? But I'm not in vacuum. Doesn't that make it invalid? Wouldn't that be like applying Coulomb's law in a dielectric? They talk about making approximations, what should I do? Also the fact that they don't give us any information about the permeability or the susceptibility is making me confused too? Can someone please help me to clarify this problem?

Thanks!