Finding magnetic flux density from magnetization vector

[moeidur]

Homework Statement

A long cylinder of radius a with magnetization vector M=M_0*(r/a)^2*a_φ. Find the magnetic flux density inside and outside the cylinder.

Homework Equations

J_m=∇×M
J_ms=M×a_n[/B]
A=(μ_0/4*π)*(∫(J_m/R)dv+∫(J_ms/R)ds)
B=∇×A

The Attempt at a Solution

basically what I thought I'd do is find J_m and J_ms and insert that into A equation and then insert A into B equation. My main problem is I'm not sure how to compute the integrals and also not sure how to divide the problem between inside and outside the cylinder.

 

[TSny]

Welcome to PF!

Can you get explicit expressions for ∇ x M and M x a_n? That might help you see how to proceed.