Magnetostatics boundary conditions.

[0ddbio]

I am sometimes just not sure how to go about solving magnetics problems and applying the right boundary conditions. I was hoping for a little advice.

For example in an infinitely long cylinder (along z-axis) with radius a, and a permanent magnetization given by:
$$\vec{M} = M_{0}r^{2}\hat{\phi}$$

If I first find the bound current distributions I get that the surface bound current is 0, and the volume bound current is:
$$\frac{3M_{0}r}{a^{2}}\hat{k}$$

So I was doing it with legendre polynomials matching boundary conditions.. I thought it would be best to solve first for the magnetic field on the z-axis, so that could be another boundary condition.
However when I try to find it I end up with a magnetic field along the z-axis with a $\hat{\phi}$ dependence only...
This doesn't make sense to me, how could it have a tangential component when it is at the center?

Am I going about this all wrong?
Thanks

 

[cragar]

Ok so the curl of M is the J(bound), the bound current per area.
So the integral of J*DA would be your current , and then can't you use amperes law to find the B field. Or am I crazy.