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.

>>3
Actually, I just realized they make no sense. I began finding an expression for a differential amount of current I in the sphere's surface. Where dI=(dQ*v)/(2pi*R*Sin[@]), where @ is the angle between the z axis and the radius R. Now v/R*Sin[@]=w since it's rotating in the z axis. so dI=dQ*w/2pi, Now dQ=p*dA, where p is the charge density, it's constant. But now dA=2pi*R^2*Sin[@]*d@ (?), and p=Q/(4pi*R^2), so now dI=(Q*w*Sin[@]*d@)/4pi, Now, an infinitesimal amount of magnetic moment should be the current times an infinitesimal amount of vector area da, which in this case would be all a areas of radius R*Sin[@]. So, du=Ida. And well, first I integrated dI, then found da, and integrated the product. I gives a similar result, but it's off by the scalar accompanying (Q/m)*L, which should be 5/6.