The configuration of perfectly conducting electrodes and perfectly insulating dielectrics shown…
The configuration of perfectly conducting electrodes and perfectly insulating dielectrics shown in Fig. P6.6.9 is similar to that shown in Fig. 6.6.8 except that at the left and right, the electrodes are “shorted” together and the top electrode is also divided at the middle. Thus, the ⊃ shaped electrode is grounded while the ⊂ shaped one is at potential V .
(a) Determine 
in regions (a) and (b).
(b) With the permittivities equal, sketch and 
. (Use physical reasoning rather than the mathematical result.)
(c) Assuming that the permittivities are nearly equal, use the result of (b) to deduce 
on the interface between dielectrics in the case where 
a/b is somewhat greater than and then somewhat less than 1. Sketch deduced as the sum of the fields induced by these surface charges and the imposed field.
(d) With a much greater that b, draw a sketch of and in region (b).
(e) With a much less than b, sketch and in both regions.
Fig. P6.6.9
Fig. 6.6.8
