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 38c3a757 e6e1 4b51 bbc8 f0050dbd0f16 in regions (a) and (b).

(b) With the permittivities equal, sketch 38c3a757 e6e1 4b51 bbc8 f0050dbd0f16 and 703beb49 9d06 4eec 8832 5a23cf42f4f6. (Use physical reasoning rather than the mathematical result.)

(c) Assuming that the permittivities are nearly equal, use the result of (b) to deduce 8fae7d41 3f4c 47c1 bf23 7a17b8a77ba8 on the interface between dielectrics in the case where f3b4b6dd 93e2 4633 8803 e8df484cb01da/f3b4b6dd 93e2 4633 8803 e8df484cb01db is somewhat greater than and then somewhat less than 1. Sketch 703beb49 9d06 4eec 8832 5a23cf42f4f6 deduced as the sum of the fields induced by these surface charges and the imposed field.

(d) With f3b4b6dd 93e2 4633 8803 e8df484cb01da much greater that f3b4b6dd 93e2 4633 8803 e8df484cb01db, draw a sketch of 38c3a757 e6e1 4b51 bbc8 f0050dbd0f16 and 703beb49 9d06 4eec 8832 5a23cf42f4f6 in region (b).

 

(e) With f3b4b6dd 93e2 4633 8803 e8df484cb01da much less than f3b4b6dd 93e2 4633 8803 e8df484cb01db, sketch 38c3a757 e6e1 4b51 bbc8 f0050dbd0f16 and 703beb49 9d06 4eec 8832 5a23cf42f4f6 in both regions.

Fig. P6.6.9

5077ec9a 8754 4bc5 a01b f5ecbe59dc18

Fig. 6.6.8

9d043309 e92f 4d13 a467 5b861ed5d497

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