Deriving Larmor frequency problem

[fisher garry]

I don't get how they get Eq. 5. Why is the direction of $\mu$ going outwards from the direction of B? And why does the fact that $\frac{d\mu}{dt}$ is perpendicular to both $\mu$ and $B$ mean that $\mu$ goes in circle?

 

[Sturk200]

All that they are assuming is that $\vec{\mu}$ and $\vec{B}$ are not aligned. If they are aligned, then the equation does not apply, since then the cross product is zero, so that there is no change in $\vec{\mu}$. But they are assuming that they are not aligned, and that the equation does apply.

As for why it goes in a circle... Start with two vectors. Call them $\vec{\mu}$ and $\vec{B}$. Now draw a third, infinitesimal, vector perpendicular to both $\vec{\mu}$ and $\vec{B}$, call this third vector $\vec{\delta}$. Form the sum $\vec{\mu} + \vec{\delta} = \vec{\mu '}$. Now draw another infinitesimal vector perpendicular to $\vec{\mu '}$ and $\vec{B}$. Add that one to $\vec{\mu '}$ to form $\vec{\mu ''}$. Keep doing that forever. You'll find that you've drawn a circle.