Show that the vector potential given in cylindrical coordinates by a- bor θ describes a uniform magnetic field b =-boz. b): find the lagrangian for a particle with mass m and charge q moving through this field and find the equations of motion. find the two conserved quantities po and p, associated with the fact that the lagrangian is independent of θ and z c): show that if we choose the origin to be on the path of the particle, then 0 at all times. solve the equations of motion for this case and show that the particle moves in a helix.