In reference to Figure 1.7 of $\textit{Quantum Computing for Everyone}$ by Chris Bernhardt (attached below), the book states:
..., both situations depicted in Figure 1.7 represent an electron having spin N in the $0^\circ$ direction, or equivalently, spin S in the $180^\circ$ direction.
I find outcome (a) reasonable, as the $\textbf{N}$ pole of the electron's spin is attracted to the magnet's $\textbf{South}$ pole. However, how is outcome (b) possible?
The force experienced by the particle is not due to the direction of the field. It is given by the gradient (how the field changes) along the $z$ direction:
$$ F_z =\mu_z \frac{\partial B_z}{\partial z} .$$
Here, $\mu_z$ is the dipole moment of the object, and $B_z$ the magnetic field along $z.$
In the first image, the field $B_z$ is positive along $z$, and it's strength also increases along $z$ because it is more concentrated in the pointy part of the $S$ magnet. Therefore the total gradient is positive along $z$.
In the second image, the field $B_z$ is negative along $z$, but it's strength also decreases along $z$ because it is more concentrated in the pointy part of the $S$ magnet which is now below $N$. Therefore the total gradient is positive because both the field and the way it changes are both negative.
Note: This description is for a classical magnet, but it works for the case of spin $1/2$ because we’re only discussing spin up and spin down. When considering superpositions, the explanation is a bit more involved.
