The cross-section of a system that extends to “infinity” out of the paper is shown in Fig….

The cross-section of a system that extends to “infinity” out of the paper is shown in Fig. P5.5.4. An electrode in the plane 1e50282e ec6d 4939 9328 dcf0e9e2fcb4 has the potential V . A second electrode has the shape of an “L.” One of its sides is in the plane 07c1d3a2 36a7 4d83 b5c9 766e77bb18af, while the other is in the plane b56119a7 080b 4a12 b6b8 b1c878c6c5b9, extending from 07c1d3a2 36a7 4d83 b5c9 766e77bb18af almost to 1e50282e ec6d 4939 9328 dcf0e9e2fcb4. This electrode is at zero potential.

Fig. P5.5.4

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(a) The electrodes extend to infinity in the a44013b4 1ca9 4563 b116 37132ab14384 direction. Show that, far to the left, the potential between the electrodes tends to

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(b) Using this result as a part of the solution, 3af8405a 55c1 4c65 a19d 78f5813a5dbb, the potential between the plates is written as ae96d1b2 6a63 44d0 bfd1 2a08bd698775 9648a5ba 5143 4130 b155 f4a014df21c9. Show that the boundary conditions that must be satisfied by 4fcef695 0e5a 4d13 9b8b 07bdcdd63b98 are

c86a7741 468e 468f a7db 780186f3d4f3

(c) Show that the potential between the electrodes is

68c8164f ec1c 4882 80c1 e76e6a078131

(d) Show that a plot of f697f184 7128 4403 8e3f 1bfd1ab579c1 and E appears as shown in Fig. 6.6.9c, turned upside down.

Fig. 6.6.9c

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