The general solution for the potential function can therefore be written as
.........................(2.131)
n the region y > 0 and 0< z< d .

Boundary Value Problem in Cylindrical and Spherical Polar Coordinates

As in the case of Cartesian coordinates, method of separation of variables can be used to obtain the general solution for boundary value problems in the cylindrical and spherical polar coordinates also. Here we illustrate the case of solution in cylindrical coordinates with a simple example where the potential is a function of one coordinate variable only.

Example 3: Potential distribution in a coaxial conductor

Let us consider a very long coaxial conductor as shown in the figure 2.33, the inner conductor of which is maintained at potential V₀ and outer conductor is grounded.