  Gauss' law and the equation of continuity must be satisfied in all materials
be they solids, liquids or gases. Most materials are classified as simple
materials; i.e., their electrical properties are linear, isotropic and
homogeneous. Charge transport in these simple materials should be described by
a constitutive equation known as Ohm's law. When Ohm's law is combined with
Gauss' law and the equation of continuity, a differential equation for volume
charge density relaxation results. The usual solution to this equation shows
that charge decays exponentially with a relaxation time given by the material's
permittivity divided by its electrical conductivity. Experiments show that good
conductors follow this exponential decay but that poor conductors (insulators)
tend to follow a decay that initially is more hyperbolic than exponential. This
suggests that either Ohm's law is not valid for insulator materials or that a
deeper understanding of Ohm's law is needed to explain charge decay in these
less than good conductors. This paper examines the latter approach and shows
that, when all the free charges within a simple material are taken into
account, a new unipolar charge decay equation is derived which is valid for any
simple material: conductor, insulator or anywhere in between. For good
conductors the equation reduces to the standard exponential law of decay. For
very poor conductors it reduces to the Vellenga-Klinkenberg modified hyperbolic
law with the initial decay producing the characteristic Bustin hyperbolic law
of decay. Explicit definitions for a good conductor and a good insulator are
obtained and are used to define the range where explicit deviations from both
of these hyperbolic laws occur.
