Example-2: In the earlier example, we considered a situation where the potential function was a function of only one coordinate. In the figure 2.32 we consider a problem where the potential is a function of two coordinate variables. We consider two number of grounded semi-infinite parallel plate electrodes separated by a distance d. A third electrode maintained at potential V₀ and insulated from the grounded conductors is placed as shown in the figure 2.32. The potential function is to be determined in the region enclosed by the electrodes.

Fig 2.32: Potential Function Enclosed by the Electrodes

As discussed above, we can write V(x,y,z) = X(x) Y(y) Z(z). We now construct the solution for V such that it satisfies the stated conditions at the boundary.