Precession in B field

There is a problem about precession in general that I am trying to understand, and it can be exampled by electron orbiting around nucleus in external [itex]\vec{B}[/itex] field.

We could consider electron motion as loop current which is characterized by the magnetic moment [itex]\vec{μ}[/itex], [itex]\vec{μ}[/itex]=-[itex]\frac{e}{2m}[/itex][itex]\vec{L}[/itex]. Suppose that external [itex]\vec{B}[/itex] field is orthogonal to [itex]\vec{μ}[/itex].

The torque due to [itex]\vec{B}[/itex] is: [itex]\vec{τ}[/itex]=[itex]\vec{μ}[/itex]×[itex]\vec{B}[/itex].

Assume that [itex]\vec{B}[/itex] was suddenly turned on. What happens after that? I am not sure.

If you write [itex]\vec{τ}[/itex]=[itex]\frac{d\vec{L}}{dt}[/itex], you get [itex]d\vec{L}[/itex]=[itex]\vec{τ}dt[/itex]. Therefore, since [itex]\vec{τ}[/itex] is orthogonal to both [itex]\vec{μ}[/itex] and [itex]\vec{B}[/itex] increment of [itex]\vec{L}[/itex] is orthogonal to itself. From this reasoning I conclude that [itex]\vec{L}[/itex] would rotate in a plane that is orthogonal on vector [itex]\vec{B}[/itex].

But, when I sketch all the forces in this example, I think this "current loop's" vector [itex]\vec{L}[/itex] would change, and become antiparalel to vector [itex]\vec{B}[/itex] in the end.