I am looking for a first-order correction on the intensity of the field generated by a (neodymium) magnet in the presence of an external magnetic field $B$ (possibly generated by another magnet). For simplicity, we may assume that $B$ and the magnet magnetization $B_r$ are collinear (but not necessarily with the same orientation). We may also assume here that the external magnetic field is uniform in the volume around the magnet.
I understand that the fact that the magnet is placed in a magnetic field will change its magnetization and therefore the strength of the magnetic field that it produces. The question is: How can I calculate the change in the "effective" $B_r$ value of the magnet from $B$ and from the $\mu_r$ value of the magnet? Do I need more than just $B$ and $\mu_r$ for that?
