Just a simple question. If I have a homogeneous magnetic field and I put an iron ball into this field, it would be attracted to the source of the magnetic field. But how do I calculate the force that is acting on the ball? I have this formula $$F=\mu_0 M B V$$ where $M$ is the magnetization, $B$ is the magnetic field and $V$ is the volume. But is this actually right?
I have found this formula in other forms as well like this: $$F=\mu_0 M V \nabla (H)$$ Here $ \nabla (H) $ is the field gradient which can be arranged as $B=\mu H$.
But I don't know if this is the right way to calculate this force in an easy way. By the way, $M$ is defined as $M = χ_m B/\mu_0$.
