Chapter 6: Dielectrics & Capacitance

Illustration 1

At the interface between two different dielectric regions, region 1 and region 2, the normal component of the flux density  and the tangential components of the field intensity  are continuous:

                                                               , .

On the other hand, the tangential components of the flux density  and the normal component of the electric intensity  are discontinuous (they change with a jump):

                                                                , .

As a result, the orientation of the streamlines (the E-field) and the equipotential surfaces changes abruptly. This orientation is usually represented by the angles  and  between the E vector and the unit normal to the interface in regions 1 and 2, respectively (see Figure 1). We can show that

.

Thus, by looking at the field map at the dielectric interface, we can tell what the ratio of the dielectric permittivities is.

Figure 2 shows the cross-section of a transmission line often used in microwave engineering: the microstrip line. It consists of a dielectric (alumina) slab () backed by a grounded metallic plate. A metallic strip is printed on top of the slab. The region above the slab is air (). The direction of the equipotential lines changes abruptly at the dielectric-to-air interface.

The continuity of the tangential  field component and the discontinuity of the normal  component are best seen in Figure 3 where their values are plotted versus a vertical line originating at the ground plate. The jump in  corresponds to a change by a factor of 9.8.

 
Figures (click to enlarge)
Figure 1

Figure 2

Figure 3

Figure 1

Figure 2

Figure 3