Understanding Magnetic Dipole Fields in a Linear Magnetic Sphere

[StatusX]

I need to find the field of a magnetic dipole embedded in the center of a linear magnetic sphere of radius R. My idea was that the field would be identical to that of a superposition of a dipole in a linear magnetic material throughout space and a surface current on the sphere equal to the bound surface current from this field. The answer I get for the field insid the sphere has the reduced dipole moment term right, and I also got that the extra term would be constant, and a multiple of the dipole moment. But where as I got this for the extra term:

-\frac{\mu}{4\pi}\frac{2(\mu_0 - \mu) \vec m}{(3\mu) R^3}

the book gave:

-\frac{\mu}{4\pi}\frac{2(\mu_0 - \mu) \vec m}{(2\mu_0 + \mu) R^3}

Do you know what I did wrong? I'm close, and I can't find a step where a simple change will result in this small difference in the final answer. Am I way off, and its just a coincidence its so close?

EDIT: Never mind, I got it.

 

[kuruman]

EDIT: Never mind, I got it.

I'm glad you got it even though it was 15 years ago. I responded just to have your post removed from the unanswered list.