For the previous problem, find the angular speed by which the particle spins about the magnetic field in terms of the radius of the circular orbit \(ho\) and other constants in the problem.

Data from the previous problem

Consider a charged relativistic particle of charge \(q\) and mass \(m\) moving in a cylindrically symmetric magnetic field with \(\mathrm{B}^{\varphi}=0\).

(a) Show that this general setup can be described with a vector potential that has one non-zero component \(\mathrm{A}^{\varphi}(ho, z)\).

(b) Write the equations of motion in cylindrical coordinates.

(c) Consider circular orbits only and show that this implies that we need \(\mathrm{B}^{ho}=0\). Then find the form of \(\mathrm{B}^{z}\) needed to achieve circular orbits.