  We consider the electrodynamics of electric charges and currents in vacuum
and then generalise our results to the description of a dielectric and magnetic
material medium : first in spatial algebra (SA) and then in space-time algebra
(STA). Introducing a polarisation multivector $\tilde{P} =
\boldsymbol{\tilde{p}} -\,\frac{1}{c}\,\boldsymbol{\tilde{M}}$ and an auxiliary
electromagnetic field multivector $G = \varepsilon_0\,F + \tilde{P}$, we
express the Maxwell equation in the material medium in SA. Introducing a bound
current vector $\tilde{J} = J -\,c\,\nabla\cdot\tilde{P}$ in space-time, the
Maxwell equation is then expressed in STA. The wave equation in the material
medium is obtained by taking the gradient of the Maxwell equation. For a
uniform electromagnetic medium consisting of induced electric and magnetic
dipoles, the stress-energy momentum vector is written as
$\dot{T}\left(\dot{\nabla}\right) = \frac{1}{c}\,J \cdot F = f$ where $f$ is
the electromagnetic force density vector in space-time. Finally, the Maxwell
equation in the material medium can be written in STA as a wave equation for
the potential vector $A$.
