  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.
