  A simple model of eddy currents in which current is computed solely from
magnetic forces acting on electrons proves accessible to introductory students
and gives a good qualitative account of eddy current forces. However, this
model cannot be complete; it ignores the electric fields that drive current
outside regions of significant magnetic field. In this paper we show how to
extend the model to obtain a boundary value problem for current density.
Solution of this problem in polar coordinates shows that the electric field
significantly affects the quantitative results and presents an exercise
suitable for upper division students. We apply elliptic cylindrical coordinates
to generalize the result and offer an exercise useful for teaching graduate
students how to use non-standard coordinate systems.
