Conservation of Angular Momentum in a Varying Magnetic Field

Charged particles traveling through a varying magnetic field are focused as by a magnetic lens. When this lens has axial symmetry, there is conservation of a generalized form of angular momentum that leads to pretty results with practical advantages. Attention is directed to such properties, which may serve as a source of problems and results in dynamics as well as an illustration of classical Hamiltonian mechanics and the significance of canonical momentum. A new treatment of the development in vector form is given together with a careful interpretation of what should be understood as an enclosing trajectory. The resulting constants of motion can usefully be employed to decrease the order of the system equations to be solved. A mathematical model suitable for class work is given to demonstrate these properties.