Bookmark 5,7,8,9 &10. Motion of the electron in different uniform magnetic fields along the OZ axis of varying intensities. The CM cyclotron radius changes (and the computed time needed for each turn changes linearly with it), approximately doubling the radius for each halving of the intensity or for each doubling of the speed , but the spin always precesses backwards with Larmor angular velocity: in one complete turn of the CM in the cyclotron motion, the spin has only precessed half a turn and in the opposite direction to the cyclotron motion.
B
z
B
z
v
The cyclotronic angular velocity is :
ω=andthenv=ωR
v
R
The cyclotronic frequency, derived from the centripetal force, is :
F=m=evB
2
v
R
ω==
eB
m
v
R
so there is a linear relationship between the CM velocity and the radius of the cyclotron and an inverse relationship between the radius of the cyclotron and the magnetic field intensity B, as seen in the previous bookmarked examples.