# Question about the magnetic dipole moment of the electron

Let's say that an electron is moving with constant velocity through a magnetic field. If the magnitude of the field is the same everywhere in space and if it is perpendicular to the velocity of the particle everywhere, the electron will follow a circular path. We all know that. What I need to know is, in what way does the direction of the magnetic dipole moment of the electron change as it moves along this circular path?

$$a e^{i\mu_B B/\hbar }\left| \uparrow\right>+ b e^{-i\mu_B B/\hbar}\left| \downarrow\right>$$