  This paper presents an exterior-algebra generalization of electromagnetic
fields and source currents as multivectors of grades $r$ and $r-1$ respectively
in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the
Maxwell equations and the Lorentz force for arbitrary values of $r$, $n$, and
$k$ are postulated in terms of interior and exterior derivatives, in a form
that closely resembles their vector-calculus analogues. These formulas lead to
solutions in terms of potentials of grade $r-1$, and to conservation laws in
terms of a stress-energy-momentum tensor of rank 2 for any values of $r$, $n$,
and $k$, for which a simple explicit formula is given. As an application, an
expression for the flux of the stress-energy-momentum tensor across an
$(n+k-1)$-dimensional slice of space-time is given in terms of the Fourier
transform of the potentials. The abstraction of Maxwell equations with exterior
calculus combines the simplicity and intuitiveness of vector calculus, as the
formulas admit explicit expressions, with the power of tensors and differential
forms, as the formulas can be given for any values of $r$, $n$, and $k$.
