Show that the vector potential given in cylindrical coördinates by ar 0 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 e0 at all times. solve the equations of motion for this case and show that the particle moves in a helix.