TABLE OF CONTENTS The equations below are useful for one-dimensional analysis. (That is, it is assumed that all quantities involved vary only with the horizontal dimension x; they are constant over a plane perpendicular to the x dimension for any given x.) The following symbols will be used:
?( x) = charge density per unit volume at point x.
electric field intensity at point x (in V/cm), with the field defined in the positive x direction.
?( x) = electric potential at point x with respect to an arbitrary reference.
? = permittivity of material; it is equal to k ? 0 where k is the dielectric constant of the material and ? 0 the permittivity of free space (8.854 10 ?14 F/cm). The material is assumed to be characterized by a single value of ? everywhere, unless noted otherwise.
The above quantities are related as follows [1] (Fig. B.1):
or, in integral form:
Combining (B.1) with (B.2) we obtain Poisson's equation:
[1]J. D. Kraus, Electromagnetics, McGraw-Hill, New York, 1992.
Consider a parallelepiped as shown in Fig. B.2. The charge in a vanishingly thin, vertical slice of length ? x around point x will be ?( x) A ? x. [As stated in the beginning of this...
