Electromagnetic boundary conditions and uniqueness revisited

The formulation of the boundary conditions for electromagnetic problems is reexamined. It is shown that specifying a pair of two collinear field components on the boundary surface, one electric and one magnetic, ensures uniqueness, regardless of whether the pair is tangential or normal to the surface. Such boundary conditions, although not commonly used, are a possibility that the author may want to add to the well-known boundary conditions in terms of the tangential E field or the tangential H field. The treatment herein also provides an insight into the relation between the field-based analysis using Maxwell's equations and the potential-based analysis using the Helmholtz equation.