is called the charge relaxation time. For a good conductor like copper, τ is of the order of
10−19 s, whereas for a good insulator like silica glass, it is of the order of
103 s. For a pure insulator, it becomes infinite.
When modeling real-world devices, there is not only the intrinsic time scale of the charge relaxation time but also an
external time scale t at which a device is energized or the observation time. It is the relation between the external time scale and the charge relaxation time that determines what physics interface and study type to use. The results are summarized in
Table 10-1 below,
By combining the definition of the potential with Gauss’ law, you can derive the classical Poisson’s equation. Under static conditions, the electric potential V is defined by the equivalence
E = −∇V. Using this together with the constitutive relation
D = ε0E + P between
D and
E, you can rewrite Gauss’ law as a variant of Poisson’s equation
where Je is an externally generated current density. The static form of the equation of continuity then reads