k_x, k_y and k_z are seperation constant satisfying

All the second order differential equations above has the same form, therefore we discuss the possible form of solution for the first one only.

Depending upon the value of k_x , we can have different possible solutions.

.........................(2.119)

A,B,C and D are constants.

Similarly we have the possible solutions for other two differential equations. The particular solutions for X(x), Y(y) and Z(z) to be used will be chosen based on the nature of the problems and the constants A,B etc are evaluated from the boundary conditions. We illustrate the method discussed above with some examples.

Example 1: As shown in the figure 2.31, let us consider two electrodes, one grounded and the other maintained at a potential V. The region between the plates is filled up with two dielectric layers. Further, we assume that there is no variation of the field along x or y and there is no free charge at the interface.