Derivation of Green’s Function for the Interior Region of a Closed Cylinder

The importance of constructing the appropriate Green function to solve a wide range of problems inelectromagnetics and partial differential equations is well-recognized by those dealing with classical electrodynamics and related fields. Although the subject of obtaining the Green function for certain geometries has been extensively studied and addressed in numerous sources, in this paper a systematic method using the Method of Separation of Variables has been employed to scrutinize the Green function with Dirichlet boundary condition for the interior region of a closed cylinder. With further rigorous elaboration, we have demonstrated clearly the path through which the Green function can be accomplished. Additional verifications both in analytical and computer-simulating problems have also been performed to demonstrate the validity of our analysis.