# 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  has the potential V . A second electrode has the shape of an “L.” One of its sides is in the plane , while the other is in the plane , extending from  almost to . This electrode is at zero potential.

Fig. P5.5.4

(a) The electrodes extend to infinity in the  direction. Show that, far to the left, the potential between the electrodes tends to

(b) Using this result as a part of the solution, , the potential between the plates is written as  . Show that the boundary conditions that must be satisfied by  are

(c) Show that the potential between the electrodes is

(d) Show that a plot of  and E appears as shown in Fig. 6.6.9c, turned upside down.

Fig. 6.6.9c

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