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.