The system shown in cross-section by Fig. P7.5.6a extends to infinity in the and directions. The…
The system shown in cross-section by Fig. P7.5.6a extends to infinity in the 
and 
directions. The material of uniform conductivity 
to the right is bounded at 
and 
by electrodes at zero potential. The material of uniform conductivity 
to the left is bounded in these planes by electrodes each at the potential 
. The approach to finding the fields is similar to that used in Example 6.6.3.
(a) What is 
as 
and 
as 
?
(b) Add to each of these solutions an infinite set such that the boundary conditions are satisfied in the planes 
and and as 
.
(c) What two boundary conditions relate to in the plane 
?
(d) Use these conditions to determine the coefficients in the infinite series, and hence find 
throughout the region between the electrodes.
Fig. P7.5.6a
(e) In the limits 
(A numerical evaluation of the expressions for is not required.)
(f) Shown in Fig. P7.5.6b is a similar system but with the conductors bounded from above by free space. Repeat the steps (a) through (e) for the fields in the conducting layer.
Fig. P7.5.6b
