Plane parallel electrodes having zero potential extend to infinity in the planes at and (a) In a…

Plane parallel electrodes having zero potential extend to infinity in the 248bfcdb d66a 4eb0 a970 f20af2dd3b08 planes at ea5fbbce 2e6a 4e45 90bb 7dcb26e929be and eb82b557 1436 4462 8b97 278ccc6aca65

(a) In a first configuration, the region between the electrodes is free space, except for a segmented electrode in the plane 5099cd0d d468 47c7 a9c0 54caa44a040c which constrains the potential there to be d80994af 9ad0 4059 8c62 622e46bac2a9. Given d80994af 9ad0 4059 8c62 622e46bac2a9, what is the potential distribution in the regions f2fcb7c0 28f6 4d4b ac30 11b2ebf31216 and 7ae78da4 7e10 4f63 a26a 4c09d3cde735, regions (a) and (b), respectively?

(b) Now the segmented electrode is removed and the region x 6af6b311 2b93 406d 8f50 36c2748a6c6d, where 61e90b1a 3ead 4860 9b1d 223998ad201f is a given constant. What continuity conditions must the potential satisfy in the x = 0 plane?

(c) Show that the potential is given by

2c99aa7b 2e4b 4235 b933 00a85e8ea467

(The method used here to represent d41c685c 95ab 459b 8e42 a869a2f00dee is used in Example 6.6.3.)

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