Magnetism

I'm having some problems finding an expression to the magnetic moment of a rotating sphere of m mass with a uniformly charged surface and an angular speed w, the rotation axis is z through the center. It's supposed to be (5Q/6m)*L, where L is the angular momentum (mwr^2).
The integrals just won't lead me to it, I must be missing something crucial. So I would like some guidance on how to solve it, since this is pretty much freaking me out.

Well, made the same problem but in the case of sphere fully charged (Q=p*(4/3)pi*(R^3)), the Jacobian being (R^2)*Sin[@] and not integrating dI but du=dI*a renders the correct result for this case, which is (Q/5m)L, But changing the charge to a surface one won't, don't know what's going on.