A general technique is outlined for investigating supersymmetry properties of
a charged spin-\half quantum particle in time-varying electromagnetic fields.
The case of a time-varying uniform magnetic induction is examined and shown to
provide a physical realization of a supersymmetric quantum-mechanical system.
Group-theoretic methods are used to factorize the relevant Schr\"odinger
equations and obtain eigensolutions. The supercoherent states for this system
are constructed.Comment: 47 pages, submitted to Phys. Rev. A, LaTeX, IUHET 243 and
LA-UR-93-20